MATHS NOTES, CLASS - 5 Chapter No: 1. Large Numbers

Key points Recall Exercise 1. Number Names 2. Smallest One-Digit Number is 1. 3. Largest One-Digit Number is 9. 4. Smallest Two-Digit Number is 10. 5. Largest Two-Digit Number is 99. Recall Exercise: CW: Page.no. 2 A: 1-4 B: 1-6 C: 1-3 Exercise 1.1 1. Place Value Chart: The place value chart of the Indian System is given below:

Reading of number according to Indian System of Numeration In Indian System of Numeration periods such as ones, thousands, lakhs, crores, etc. are used so that number can be easily read. Different periods like ones, thousands, lakhs and crores are separated by comma (,) starting from the right to differentiate the periods. We start with the first period, named as ones period, consist the first three digits of the given number. The second period (i.e. thousands period) is consist of the next two digits of the given number. The third period (i.e. lakhs period), consist of the next two digits of the given number. The fourth period (i.e. crore period), consist of the next two digits of the given number. Exercise 1.1; TB: Page.no. 2 A: 1-4; Page.no. 3 C: 1-5; / CW: Page.no. 2 B: 1-6; Page.no. 3 D : 1-5; Exercise 1.2; CW: Page.no. 3 A: 1-5; C: 1-6 Exercise 1.3; TB: Page. No. 4 A: 1 - 6; / CW: Page. No. 4 B: 1, 2, 5; C: 1, 2, 5; Page. No. 5 D: 1 – 4; E: 1 – 4; F: 1 – 4 ; / HW: Page. No. 4 B: 3, 4; C: 3, 4; Exercise 1.4 International Place Value System: In place value chart, the digits are grouped in the threes in a big number. The number is read from left to right as ………. billion ………. million ……….. Thousands ……….. Ones. The place value chart of the International System is given below:

Reading of number according to International System of Numeration In International System of Numeration places such as ones, thousands, millions, billions etc. are used so that number can be easily read. Different period like ones, thousands, millions and billions are separated by comma (,) starting from the right to differentiate the period. We start with the first period, named as ones place, consist the first three digits of the given number. The second period (i.e. thousands place) is consist of the next three digits of the given number. The third period (i.e. millions place), consist of the next three digits of the given number. The fourth period (i.e. billions place), consist of the next three digits of the given number. Exercise 1.4; CW: Page. No. 6 A: 1 – 4; B: 1, 2, 5; / HW: Page. No. 6 B: 3, 4;

MATHS NOTES, CLASS - 5 Exercise 1.5 Rounding Numbers 1. Rounding to the nearest 10’s Place: Look at the ones digit. If it is less than 5 then round the number down by changing the ones digit to zero; If it is 5 or more then round the number up by adding one on to the tens digit and changing the ones digit to zero. 2. Rounding to the nearest 100’s Place: Look at the tens digit. If it is less than 5 then round the number down by changing the tens digit and ones digit to zero; If it is 5 or more then round the number up by adding one on to the hundreds digit and changing the tens and ones digit to zero. 3. Rounding to the nearest 1000’s Place: Look at the hundreds digit.

If it is less than 5 then round the number down by changing the hundreds, tens and ones digits to zero;

If it is 5 or more then round the number up by adding one on to the thousands digit and changing the hundreds, tens and ones digits to zero. 4. Rounding to the nearest 10000’s Place: Look at the Thousands digit.

If it is less than 5 then round the number down by changing the thousands, hundreds, tens and ones digits to zero;

If it is 5 or more then round the number up by adding one on to the ten thousands digit and changing the thousands, hundreds, tens and ones digits to zero. 5. Rounding to the nearest 100000’s Place: Look at the Ten Thousands digit.

If it is less than 5 then round the number down by changing the ten thousands, thousands, hundreds, tens and ones digits to zero;

If it is 5 or more then round the number up by adding one on to the Lakhs digit and changing the ten thousands, thousands, hundreds, tens and ones digits to zero. Exercise 1.5; CW: Page. No. 7 A: 1, 2; B: 1, 2; C: 1, 2, 3; D: 1, 2, 5; E: 1, 3, 5; F: 1, 3, 5; G: 1, 2; / HW: Page. No. 7 A: 3, 4; B: 3, 4; C: 4, 5; D: 3, 4; E: 2, 4; F: 2, 4; Exercise 1.6 Roman Numbers

There is No Zero in the Roman Number System The Only difference between Hindu Arabic System and Roman Number System is in Roman Number system doesn’t support Place value. The certain rules that we need to follow for Roman-number system Rule 1: The roman digits I, X and C are repeated up to three times. Repetition of these numbers called addition of these numbers. Rule 2: I, X and C cannot be repeated more than 3 times. Rule 3: The digits V, L and D are not repeated. The repetition of V, L and D is invalid. Rule 4: When a digit of lower value is written to the right or after a digit of higher value, the values of all the digits are added. Rule 5: When a digit of lower value is written to the left or before a digit of higher value, then the value of the lower digit is subtracted from the value of the digit of higher value. Exercise 1.6; CW: Page. No. 8 A: 1, 3, 6, 10, 11, 12; B: 1, 2, 7, 11, 12 / HW: Page. No. 8 A: 2, 4, 5, 7, 8, 9; B: 3, 4, 5, 6, 8, 9, 10 ---------------------------------------------------------------------------------------------------------------------------------------------------------

Chapter No: 2. Operations with Large Numbers Key Points

MATHS NOTES, CLASS - 5 1. 5-digit and 6-digit Addition and Subtraction. 2. Simplification 3. 3-digit by 3-digit multiplication 4. 4-digit by 2-digit and 3-digit division 5. Simplification by Using BDMAS/ BODMAS Rule 6. Finding Averages 7. Unitary Method Recall Exercise TB: Page. No. 11 A: 1 - 4; B: 1, 2; Page. No. 12 D: 1 - 4; / CW: Page. No. 11 C: A, B; Page. No. 12 E: 1, 3; F: Story Sums; G: Story Sums; HW: Page. No. 12 E: 2, 4; C: 3, 4; Exercise 2.1; Text book Page. No. 12 A: 1 - 8; Page. No. 13 B: 1 - 8; Exercise 2.2; CW: Page. No. 14 / Story Sums 1,3,4,6,7,8,9 / HW: Page. No. 14 / Story Sums 2,5,10 Exercise 2.3; CW: Page. No. 14 / Multiply 1, 2,7,8,13,14 / HW: Page. No. 14 / Multiply 3,4,5,6,9,10,11,12,15 Exercise 2.4; CW: Page. No. 15 / Story sums 1-4, 8,9,10 / HW: Page. No. 15 / Story sums 5, 6, 7 Exercise 2.5: CW: Page. No. 16 / Division 1, 5 / HW: Page. No. 16 / Division 2, 3, 4, 6, 7, 8 Exercise 2.6: CW: Page. No. 17 / Division 1, 9, 16 / HW: Page. No. 17 / Division 2-8, 10 -15 Exercise 2.7: CW: Page. No. 18 / Story sums 1 – 5 / HW: Page. No. 18 / Story sums 7, 8 Exercise 2.8 Key Points BODMAS rule gives us an order in which to perform the mathematical operations in a given problem or equation. B: Brackets O: Of D: Division M: Multiplication A: Addition S: Subtraction This is the order in which you perform the operations to arrive at the correct answer.

First solve the operations within the bracket. This is called “opening the bracket’.

Then you move on to division, after which you perform multiplication if the equation requires it from left to right.

Finally, you add the numbers and lastly perform the subtraction. The best way to understand the BODMAS rule is through examples. So let us see a problems and solve those using BODMAS. Example 1. {[42 ÷ 2 +( 3 × 3)] – 22} Sol: = {[42 ÷ 2 + (3 × 3)] − 22 Let us open the brackets first according to BODMAS i.e., opening inner brackets ( ) = {[42 ÷ 2 + 9] – 22} (Move to next inner bracket, i.e., [ ], in this according to BODMAS division comes first) = {[21 + 9] – 22} = {30 – 22} = 8. Exercise 2.8: CW: Page. No. 21 A: 1, 2, 4; B: 1, 3, 5, 9; C: 1 - 4; D: 1-6; HW: Page. No. 21 A: 3, 5, 6; B: 2,4,6,7,8,10 Exercise 2.9 Key Points

Averages: A calculated "Middle Value” of a set of numbers. To calculate average adds up all the numbers, then divide by how many numbers there are. 1. Example: What is the average of 2, 7 and 9? Add the numbers: 2 + 7 + 9 = 18 divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 = 6 So the average is 6 2. Example: Average weight of a group of chimpanzee Chimp 1 weighs 48 kg

MATHS NOTES, CLASS - 5

Chimp 2 weighs 54 kg Sol: Sum of three Chimpanze weight = Chimp 1 weight + Chimp 2 weight No. Of Chimpanzees = 2

Average = Sum of three Chimpanze weight

No.of Chimpanzees

Sum = 48 kg + 54 kg = 102 No. Of Chimpanzees = 2 Average = 102 ÷ 2 = 51 Exercise 2.9: CW: Page. No. 24, 25 A: 1-10; Exercise 2.10 Key Points

Unitary Method: Unitary method is a method in which you find the value of a unit and then the value of a required number of units. Example: Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this, the apples are the units and the cost of the apples is the value. While solving a problem using unitary method, it is important that you recognize the units and values. Always write the things to be found on the right hand side and things known on the left hand side.\ in this, we know the amount of number of apples and the value of the apples is unknown. 10 apples = Rs. 100 1 apple = Rs. 100 ÷ 10 = Rs. 10 => 6 apples = 6 X 10 = Rs. 60 Exercise 2.10: CW: Page. No. 27 / Story sums 1, 2, 4,7,10 / HW: Page. No. 27 / Story sums 3, 5,6,8,9 ---------------------------------------------------------------------------------------------------------------------------------------------------------

Chapter No: 3. Factors and Multiples Key Points 1. Factors and multiples 2. Prime Numbers and Composite Numbers 3. Prime Factors and Prime Factorization 4. Co-Prime or Non-Co-Prime Numbers. 5. Factor Tree 6. Lowest Common Multiple ( LCM) 7. Highest Common Factor (HCF) 8. Tests of divisibility OR Divisibility Tests. Recall Exercise 1. Factor: A factor is a Number that we multiply with other numbers to get required number. Example: 2 and 3 are factors of 6, because 2 × 3 = 6. A number can have MANY factors. Example: What are the factors of 12? • 3 × 4 = 12, so 3 and 4 are factors of 12 • 2 × 6 = 12, so 2 and 6 are also factors of 12 and 1 × 12 = 12, So 1 and 12 are factors of 12 as well. So 1, 2, 3, 4, 6 and 12 are all factors of 12 2. Multiple: Factors are what we can multiply to get the number Multiples are what we get after multiplying the two numbers. Factors: 1 × 6 = 6, so 1 and 6 are factors of 6 2 × 3 = 6, so 2 and 3 are factors of 6 Multiples:

0 × 6 = 0, so 0 is a multiple of 6

1 × 6 = 6, so 6 is a multiple of 6

MATHS NOTES, CLASS - 5

2 × 6 = 12, so 12 is a multiple of 6 Important points: Factors and multiples are different things. But they both involve multiplication. . 1 is a Factor of Every Number Every Whole Number is a Multiple of itself. Every whole number is a multiple of 1. All Even Numbers are multiples of 2. 3. Prime Numbers and Composite Numbers: A whole number that cannot be made by multiplying other whole numbers is called Prime Number. If we can make it by multiplying other whole numbers it is a Composite Number.

2 is Prime, 3 is Prime, 4 is Composite (=2×2), 5 is Prime, and so on... Example: Is 7 a Prime Number or Composite Number?

We cannot divide 7 exactly by 2 (we get 2 lots of 3, with one left over)

We cannot divide 7 exactly by 3 (we get 3 lots of 2, with one left over)

We cannot divide 7 exactly by 4, or 5, or 6. We can only divide 7 by 7 or 7 by 1. So 7 is a prime Number. Example: Is 6 a Prime Number or Composite Number? 6 can be divided exactly by 2, or by 3, as well as by 1 or 6: 6 = 1 × 6 6 = 2 × 3 So 6 is a Composite Number. Any whole number greater than 1 is either Prime or Composite 1 is not prime and also not Composite. Each Prime Number has exactly two factors 1 and the number itself. e.g., 7 X 1 = 7 so 1, 7 are only Factors of 7. So 7 is a prime number. All even numbers are divisible by 2. So 1, 2 are the factors of all the even numbers. This means all even numbers are Composite Numbers. Recall Exercise: CW: Page. No. 30 1: i - V; 2: i- vii; Page. No. 31 4: i - v; 5: i-iv; TB: Page. No. 31 3: i-ii; Recall Exercise: CW: Page. No. 30 1: i - V; 2: i- vii; Page. No. 31 4: i - v; 5: i-iv; TB: Page. No. 31 3: i-ii; Exercise 3.1 4. Prime Factors: Factors of a number which are prime are called its prime factors. Example: The prime factors of 15 are 3 and 5, because 3×5=15, and 3 and 5 are prime numbers. Every factor is a prime number. This is called Prime Factorization. 5. Prime factorization: A factorization in which every factor is a prime number. Example: 24 = 2 x 2 x 2 x 3. Here 2, 3 are prime numbers. 6. Co-prime numbers: When two numbers are co-prime that should have only one common factor that is 1. Example: 21 and 22 Factors of 21 are 1, 3, 7 and 21. Factors of 22 are 1,2,11 and 22. 21 and 22 are having only one common factor that is 1. This means 21, 22 are co-prime numbers. 7. Factor Tree : A special diagram where we find the factors of a number, then the factors of those numbers, etc., until we can't factor any more.

MATHS NOTES, CLASS - 5 The ends are all the prime factors of the original number. Here we see the factor tree of 48 which reveals that 48 = 2 × 2 × 2 × 2 × 3

48

8 6

4 2 2 3

2 2 48 = 2 × 2 × 2 × 2 × 3

Exercise 3.1: CW: Page. No. 32 A: 1, 2; B: 1, 3, 6; C: 1, 4; / HW: Page. No. 32 B: 2, 4, 5; C: 2, 3; Exercise 3.2 8. Highest Common Factor (HCF) or Greatest Common Factor (GCD): The HCF or GCD is a greatest number which divides two or more numbers without a remainder. Here is a Question that what is a Common Factor? Ans: Common factors are those that are found in both the number factors list. Example: Common Factors of 12 and 30 Factors of 12 are 1, 2, 3, 4, 6 and 12 Factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30 Here, the common Numbers that are presented in the both the factors list are 1, 2, 3 and 6. Therefore Common Factors of 12 and 30 are 1, 2, 3 and 6.

Let us see in the above example, the Greatest or Highest Common Factors (HCF) of 12 and 30. Sol: Firstly, The Common Factors of 12 and 30 are 1, 2, 3 and 6. Next, finding the highest factor (number) in common factors list. i.e., 6. Therefore HCF of 12 and 30 is 6. Note: In HCF, LCM we follow two methods 1. Prime Factorization; 2. Division Method Exercise 3.2: CW: Page. No. 33 A: 1, 3, 5; B: 1, 3, 7, 8; C: 1, 3, 4, 5; / HW: Page. No. 33 A: 2, 4, 6; B: 2, 4, 5, 6; C: 2, 6; Exercise 3.3 & 3.4

9. Lowest Common Multiple (LCM): It is simply the smallest of the common multiples.

Here is a Question that what is a Common Multiple?

The common multiples are those that are found in both the numbers Multiples lists: Example: Common Multiples of 4 and 5. The Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…… The Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40 …. We have listed the first few multiples of 4 and 5: The common multiples are those that are found in both lists: Therefore, Common Multiples of 4 and 5 are 20 and 40…. Now, we find the least multiple (number) in the common multiples list of 4 and 5 i.e., 20 Therefore we say that LCM of 4 and 5 are 20.

Exercise 3.3: CW: Page. No. 35 A: 1, 3; B: 1, 5, 11, 15; TB: Page. No. 35 C: 1-4; / HW: Page. No. 35 A: 2, 4; B: 2-4, 6-10, 12-16; Exercise 3.4: CW: Page. No. 36, 37 / Story Sums: 1-8 Exercise 3.5

10. Divisibility tests: Divisibility means One number divides into another number and there is nor a remainder.

The following table gives the Divisibility Rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

MATHS NOTES, CLASS - 5

Exercise 3.5: TB: Page. No. 39 A: 1-5 B: 1-5 C: 1-4; D: 1-5 --------------------------------------------------------------------------------------------------------------------------------------------------------- Chapter No: 4. Fractions Key points

Fractions

Types of Fractions

Equivalent Fractions and Conversion Fractions

Comparing of Fractions.

Addition and subtraction of Fractions

Multiplication and Division of Fractions

Converting Mixed Fractions into improper fractions/improper to mixed fraction

Properties of multiplication of fractional numbers

Reciprocal of a fraction Recall Exercise 1. Fraction: A fraction represents a part of a whole or any number of equal parts. The denominator shows how many equal parts make up a whole, and the numerator shows how many of these parts we have. How many parts of a whole:

• The top number (the numerator) says how many parts we have. • The bottom number (the denominator) says how many equal parts the whole is divided into So we can define the three types of fractions like this: Proper Fractions: The numerator is less than the denominator

Examples: 1

3 ,

3

4 ,

6

9

Improper Fractions: The numerator is greater than (or equal to) the denominator

Examples: 5

3 ,

8

3 ,

6

3

MATHS NOTES, CLASS - 5 Mixed Fractions: A whole number and proper fraction together

Examples: 21

3 , 4

3

3 , 5

6

3

Like Fractions: Fractions with same denominator are called like fractions.

Examples: 1

3 ,

3

3 ,

6

3

Unlike Fractions: Fractions with different denominator are called like fractions.

Examples: 1

5,

1

6 ,

1

8

2. Converting Improper Fractions to Mixed Fractions: To convert an improper fraction to a mixed fraction, follow these steps:

Divide the numerator by the denominator.

Write down the whole number answer

Then write down any remainder above the denominator.

Example: Convert 11

4to a mixed fraction.

Divide: 11 ÷ 4 = 2 with a remainder of 3

Write down the 2 and then write down the remainder (3) above the denominator (4), like this 2 3

4.

3. Converting Mixed Fractions to Improper Fractions: To convert a mixed fraction to an improper fraction, follow these steps:

Multiply the whole number part by the fraction's denominator.

Add that to the numerator

Then write the result on top of the denominator.

Example: Convert 3 2

5 to an improper fraction.

Multiply the whole number by the denominator: 3 × 5 = 15 Add the numerator to that: 15 + 2 = 17

Then write that down above the denominator, like this:17

5 .

Exercise: 4.1 Addition/ Subtraction of fractions: To Add Fractions there are Three Simple Steps: Step 1: Make sure the bottom numbers (the denominators) are the same Step 2: Add the top numbers (the numerators), put that answer over the denominator Step 3: Simplify the fraction (if needed)

Example: 1. Add fractions 2

6 ,

1

6(denominators are same)

= 2

6+

1

6 =

2+1

6 Add fractions

1

3 ,

1

4(denominators are different)

We need to add 1/3 and ¼

Recall Exercise: Text book Page.no. 43 F.B: i - v

1 +

1

=

?

3 4 ?

First make the bottom numbers (the denominators) the same. I. Multiply top and bottom of 1/3 by 4:

1 × 4 +

1 =

?

3 × 4 4 ?

II. And multiply top and bottom of 1/4 by 3:

1 × 4 +

1 × 3 =

?

3 × 4 4 × 3 ?

III. Now do the calculations:

4 +

3 =

4+3 =

7

12 12 12 12

MATHS NOTES, CLASS - 5 Exercise: 4.2 2. Multiplication of fractions: There are 3 simple steps to multiply fractions 1. Multiply the top numbers (the numerators). 2. Multiply the bottom numbers (the denominators). 3. Simplify the fraction if needed.

Example: 1. multiply fractions 2

6 ,

6

2

Step 1, 2: Multiply the top and bottom numbers: 2

6X

6

2 =

2 𝑋 6

6 𝑋 2=

12

12

Step 3: simplify the fraction 12

12 = 1.

3. Fractions and Whole Numbers: multiplying fractions and whole numbers make the whole number a fraction, by putting it over 1.

Example: Multiply6

2 X 5 make 5 into

5

1now just go a head

6

2X

5

1 =:

6 𝑋 5

2 𝑋 1=

30

2= 15. Or just think whole number as being

a topper. Exercise 4.2: CW: Page.no. 47 A: 1-20 Exercise 4.3: CW: Page.no. 49 A: 1-5, B: 1-4; C: 1-4; Exercise 4.3: HW: Page.no. 49 A: 6-12, B: 5-8; Exercise 4.4: CW: Page.no. 50 A: 1-8, B: 1-8; Exercise 4.5: Text Book Page.no. 51 A: 1-6; B: 1-6; Exercise 4.6: CW: Page.no. 51 A: 1, 4, 10; / HW: Page.no. 51 A: 2, 3, 5-9; Exercise: 4.7 4. Reciprocal of a number: To get the reciprocal of a fraction, just turn it upside down. In other words swap over the Numerator and Denominator.

Example: Reciprocal of 6

2 =

2

6

Multiplication of the number and the reciprocal we get 1. This means 6

2 X

2

6 = 1.

Exercise 4.1: CW: No. 46 A:1-8, B:1,3,5,6,11; C:1,4,6,9,12; D:1,4,5 / HW: Page.no. 46 B:2,4,7,8,9,10; :2,3,5,7,8,10,11; D:2,3,4,6 Exercise 4.7: CW: Page.no. 52, 53 Story Sums1- 7; Exercise 4.8: CW: Page.no. 54 A: 1- 10; Exercise 4.9: CW: Page.no. 55 A: 1- 12; Exercise 4.10: CW: Page.no. 56 A: 1- 12; Exercise: 4.11

5. Dividing Fractions by Fractions: To Divide Fractions: Invert (i.e. turnover) the denominator fraction and multiply the fractions Multiply the numerators of the fractions Multiply the denominators of the fractions Place the product of the numerators over the product of the denominators Simplify the Fraction

Example: Divide 6

2 and

8

6

Invert the denominator fraction and multiply 6

2 ÷

8

6 =

6

2X

6

8

Multiply the numerators (6 x 6 =36) Multiply the denominators (2 x 8=16 )

Place the product of the numerators over the product of the denominators (36

16)

Simplify the Fraction (36

16=

9

4)

The Easy Way. After inverting, it is often simplest to "cancel" before doing the multiplication. Canceling is dividing one factor of the numerator and one factor of the denominator by the same number. Exercise 4.13: CW: Page.no. 58 A: 1- 8; Exercise 4.11: CW: Page.no. 57 A: 1- 12; Exercise 4.12: CW: Page.no. 57, 58 A: 1- 8;

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MATHS NOTES, CLASS - 5 Chapter No: 5.Decimals and their applications Key points

Decimals

Mixed numbers as decimals

Place Value Chart of Decimals

Reading / writing of Decimal numbers.

Converting decimals into Fractions

Comparing decimal numbers

Ascending and descending form of Decimal numbers

Add/ Subtract/multiplication and division of decimal numbers

Like decimals and unlike decimals

Rounding the decimal numbers

Division Properties of decimal numbers Warm Up Exercise 1. Decimal: A decimal is any number in our base-ten number system. The decimal point is used to separate the ones place from the tenths place in decimals. As we move to the right of the decimal point, each number place is divided by 10. Why do we use decimals? Decimals are used in situations which require more accuracy than whole numbers can provide 2. Expanded form: Expanded form is a way to write numbers by showing the value of each digit. Ex: whole number 159 in expanded form as follows: 159 = (1 x 100) + (5 x 10) + (9 x 1). Decimals can also be written in expanded form. Example: Write each decimal in expanded form.

9.7350= (9 x 1) + (7 x ) + (3 x ) + (5 x ) 3. Decimal Digits: In a decimal number, the digits to the right of the decimal point that name the fractional part of that number are called decimal digits. Example: In the decimal number 1.0827. The digits 0, 8, 2 and 7 are called decimal digits. Warm up Exercise: TB: Page. No. 61 Fill in the blanks 1-10, TB: Page. No. 62 Fill in the blanks 1-12, TB: Page. No. 63 Fill in the blanks 1-12, TB: Page. No. 64 Place value Chart Exercise: 5.1 4. Reading and writing decimal numbers: When reading decimal numbers, read the whole number part as normal, use "and" to represent the decimal point, and continue reading the number as normal, but end with the last place value. If there are no whole numbers in front of the decimal value, you do not use the word "and". You read the number as normal and end with the last place value of the number. Examples: Read the following decimal 124.23 = One hundred twenty four and twenty three hundredths. (Or) = One hundred and twenty four point two three Exercise: 5.1 CW: Page. No. 64 A: 1-9 B: 1-8; C: 1-8; Exercise: 5.2 5. Decimal Place Value Chart:

The first digit after the decimal represents the tenths place.

The next digit after the decimal represents the hundredths place.

The remaining digits continue to fill in the place values until there are no digits left. Example: The number 87.654 can be placed on a place value chart as follows:

Tens Ones . Tenths Hundredths Thousandths

8 7 . 6 5 4

MATHS NOTES, CLASS - 5 6. Mixed Numbers as Decimals: Convert the mixed numbers in the form of improper fractions and then divide the numerator by denominator then will get a quotient as a decimal number with a remainder Zero. Example: Exercise: 5.2 CW: Page. No. 65 A: 1-6 B: 1-9; Exercise: 5.3 7. Converting Fraction to Decimal Numbers / Decimals: by dividing improper fraction, which means divide the numerator with denominator until you get remainder as zero then the quotient becomes a decimal number?

Example: 8. Converting the decimals into fractions:

Step 1: Write down the decimal divided by 1, like this: 𝑑𝑒𝑐𝑖𝑚𝑎𝑙

1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) Step 3: Simplify (or reduce) the fraction. Example: Convert 0.75 as Fraction

Step 1: Write down the decimal divided by 1, like this: 0.75

1

Step 2: Multiply both top and bottom by 100 (because there are 2 digits after the decimal point so that is 10 X 10 = 100) Step 3: Simplify (or reduce) the fraction.

75

100 =

15

20 =

3

4

Note: 75/100 is called a decimal fraction and ¾ is called a common fraction Exercise: 5.3 CW: Page. No. 66 A: 1-10 Exercise: 5.4 9. Equivalent Decimals: Equivalent decimals have the same value, even though they may look different. These fractions are really the same:

1

2 =

2

4 =

4

8

Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps its value. The rule to remember “Change the bottom using multiply or divide, And the same to the top must be applied". 10. Like and Unlike Decimals:

Like decimals: Decimals having same number of decimal places are called like decimals. Ex: 2.67, 5.94, 3.24, 7.80 are like decimals, each having 2 decimal places.

Unlike decimals: Some given decimals, all not having same number of decimal places are called unlike decimals. Ex: 16.78, 9.876, 0.4 are unlike decimals.

Steps to Convert Unlike to Like Decimals: 1. First determine the number of decimal places in each decimal number. 2. We take the number with the greatest number of decimal places. 3. We make the other decimal numbers with the same number of decimal places by adding extra zero’s to the last number till we get to the greatest number of decimal places. Examples: Convert 16.78, 9.876 and 0.4 to like decimals. Solution: 1.The number of decimal places in each of these is 16.78 have 2 decimal places

Mixed Number Fractional Part Decimal

6.9000

9.7200

MATHS NOTES, CLASS - 5 9.876 has 3 decimal places 0.4 has 1 decimal place 2. The highest number of decimals is 3 3. We have to make 16.78 and 0.4 to have 3 places of decimals. => 16.78 has 2 places, we add one 0 after 8. => 16.78 will become 16.780. 0.4 has 1 decimal place, =>we add two 0’s after 4. => 0.4 will become 0.400 16.780, 9.876 and 0.400 are like decimals. Exercise: 5.4 CW: Page. No. 67 A: 1-5; B: 1-5; / CW: Page. No. 68 C: 1-5; D: 1-5; Exercise: 5.5 11. Comparing the decimal numbers: While comparing natural numbers we first compare total number of digits in both the numbers. If they are equal then we compare the digit at the extreme left. If they also equal then we compare the next digit and so on. We follow the same pattern while comparing the decimals. Example: Compare 0.6 and 0.8. 0.6 = 6 tenths 0.8 = 8 tenths Because 8 tenths > 6 tenths; Thus, 0.8 > 0.6 Exercise: 5.5 TB; Page. No. 68, 69 A: 1-12 / CW: Page. No. 69 B: 1-6; C: 1-6; Exercise: 5.6 12. Addition of Decimals: The rules of adding decimal numbers are: (i) Write the digits of the given numbers one below the other such that all the decimal points are in the same vertical line. (ii) Add as we add whole numbers. (iii) Put the decimal point of the sum vertically below the other decimal points. Example: Add 91.4; 31.83; 101 Sol: 91.40 + 31.83 + 101.00

Exercise: 5.6 CW: Page. No. 69, 70 A: 1, 4, 7 B: 1,3,6,8 / HW; Page. No. 69, 70 A: 2,3,5,6,8,9; B: 2,4,5,7,9,10; Exercise: 5.7 13. Subtraction of decimals: To subtract decimal follow the below steps: ● Write down the two decimal numbers, one number under the other number and line up the decimal points. ● Convert the given decimals to like decimals. ● Write the smaller decimal number under the larger decimal number in the column. ● Arrange the decimal numbers in the column in such a way that the digits of the same place are in the same column. ● Subtract the numbers in the column from the right. ● Remember to place the decimal point down in the answer in the same place as the numbers above it. Example: Subtract the decimals we have 27.59 from 31.4, converting both the decimal numbers into like decimals, 31.40 - 27.59. Now arrange them in columns and subtract we get

MATHS NOTES, CLASS - 5 Exercise: 5.7 CW: Page. No.71 A: 1, 2, 11, 12 B: 1, 4, 9 / HW: Page. No. 71 A: 3-10; B: 2, 3, 5-8, 10-12; Exercise: 5.8 TB: Page. No.72 A: 1-12 / TB: Page. No.73 B: 1-6 Exercise: 5.9 14. Multiplication of decimals: The rules of multiplying decimals are: (i) Take the two numbers as whole numbers (remove the decimal) and multiply. (ii) In the product, place the decimal point after leaving digits equal to the total number of decimal places in both numbers. (iii) Counting decimal point must always be done from the unit’s place of the product. Example: Find 91.32 × 83. First we will perform the multiplication ignoring decimal point.

Here the multiplicand contains two decimal places, so the product must contain two decimal places. Thus, 91.32 × 83 = 7579.56 Exercise: 5.9 CW: Page. No.75 A: 1,2,13,14,23,24 / HW; Page. No. 75 A: 3-12, 15-22; Exercise: 5.10 - Exercise: 5.17 15. Division of decimal numbers: The rules to divide a decimal by a whole number are: (i) Divide as in division of numbers ignoring the decimal point. (ii) When you reach the tenths digit, place the decimal in the quotient. Note: When the number of digits in the dividend is less and the division is not complete, keep adding zeroes at every step till the division is complete Example: Solve: 100.4 ÷ 25 100.4 ÷ 25

Therefore, 100.4 ÷ 25 = 4.016 16 . Properties of Multiplication of Decimal Numbers: 1. The product of a decimal and a whole number multiplied in any order remains the same. For Example: (i) 0.9 × 12 = 12 × 0.9 = 10.8; (ii) 1.1 × 30 = 30 × 1.1 = 33.0 2. The product of two decimal numbers remains the same, even if the order is changed. For Example: (i) 2.5 × 3.5 = 3.5 × 2.5 = 8.75; (ii) 1.4 × 0.8 = 0.8 × 1.4 = 1.12 3. The product of a decimal fraction and 1 is the decimal fraction itself. For Example: (i) 1.092 × 1 = 1.092; (ii) 1.002 × 1 = 1.002 4. The product of a decimal fraction and zero is zero. For Example: (i) 891.56 × 0 = 0 (ii) 1.009 × 0 = 0 5. While performing multiplication in decimals, the numbers can be taken in any order and the product remains the same. For Example:

(i) 1.02 × (11.2 × 2.3) = 1.02 × 25.76 = 26.2752

(1.02 × 2.3) × 11.2 = 2.346 × 11.2 = 26.2752

MATHS NOTES, CLASS - 5 So the product of more than two decimals does not change if their grouping order is changed. Therefore, 1.02 × (11.2 × 2.3) = (1.02 × 2.3) × 11.2 17 . Properties of Multiplication of Decimal Numbers: 1. When a decimal number is divided by 1, the quotient is the decimal number itself. For example: (i) 5.6 ÷ 1 = 5.6 (ii) 3.19 ÷ 1 = 3.19 2. When the decimal number is divided by itself the quotient is 1. For example: (i) 3.1 ÷ 3.1 = 1 (ii) 11.19 ÷ 11.19 = 1 3. When 0 is divided by any decimal number, the quotient is 0. For example: (i) 0 ÷ 2.0 = 0 (ii) 0 ÷ 3.12 = 0 4. The reciprocal of 0 does not exist, so we cannot divide any decimal number by 0. 18 .Rounding Decimals: Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate values and to limit the amount of decimal place. We round off the numbers or approximate the value of decimal to a specified decimal place to make it easy to understand, instead of having a long string of decimal places. In, rounding decimals we will learn how to round a decimal in different conditions. ● Rounding off to the nearest whole number means, rounding off a decimal to the nearest whole number. ● Rounding off to the nearest tenths means, rounding off a decimal number correct to 1 decimal place. ● Rounding off to the nearest hundredths means, rounding off a decimal number correct to 2 decimal places. ● Rounding off to the nearest thousandths means, rounding off a decimal number correct to 3 decimal places. Exercise: 5.10 TB; Page. No.76 A: 1-20; Page. No. 77 B: 1-4; Exercise: 5.11 CW: Page. No.78 A: 1, 3,9,12 B: 1-6 / HW; Page. No. 79 A: 2,4-8,10,11; Exercise: 5.12 TB; Page. No.79 Fill in the blanks / TB; Page. No. 80 1-12; Exercise: 5.13 CW: Page. No.81 A: 1-4; B: 1-4; C: 1, 3, 5, 11, 12 /HW: Page. No. 81 A: 5-12; B: 5-12; C: 2,4,6-10; Exercise: 5.14 CW: Page. No. 82 A: 1, 2, 6, 12 / HW: Page. No. 82 A: 3-5,7-11; Exercise: 5.15 CW: Page. No.83 A: 1-12 / HW: Page. No. 83 A: 1-12; Exercise: 5.16 CW: Page. No.85 A: 1-5, 14, 15, 17; B: 1-10 / HW: Page. No. 85 A: 6-13,16,18-20; Exercise: 5.17 CW: Page. No.86 A: 1,2,14, 16, 18 / HW: Page. No. 86 A: 3-13,15,17,19,20; Exercise: 5.18 CW: Page. No.88 A: 1, 2, 6; B: 1, 4, 6; C: 1, 4, 7; D: 1, 2, 4; / HW: Page. No. 88 A: 3-5; B: 2,3,5; C: 2,3,5,6,8; D: 3,4,6; ---------------------------------------------------------------------------------------------------------------------------------------------------------

Chapter No: 6. Metric measures and Temperature Key Points

Measures of length

Measures of Weight

Measures of Capacity

Metric Measures in decimal form

Addition, subtraction, multiplication and division of metric measures

Temperature

Converting temperature from Celsius to Fahrenheit

Converting temperature from Fahrenheit to Celsius Recall Exercise 1. Metric measures: A system of measuring based on the metric units. It has three main units: · The meter for length (m) · The kilogram for mass (kg) · The second for time (s)

MATHS NOTES, CLASS - 5 Examples: A kilometer is 1,000 meters A centimeter is 1/100th (one-hundredth) of a meter The Metric System had its beginnings back in 1670 by a mathematician called Gabriel Mouton. The modern version, (since 1960) is correctly called "International System of Units" or "SI" (from the French "System International"). So we should really call it "SI", but mostly people just call it "Metric". 2. Measures of Length: We can measure how long things are, or how tall, or how far apart they are. Those are all examples of length measurements. These are the most common measurements:

Millimeters: Small units of length are called millimeters.

Centimeters: When we have 10 millimeters, it can be called a centimeter. 1 centimeter = 10 millimeters

Meters: A meter is equal to 100 centimeters. 1 meter = 100 centimeters

Kilometers: A kilometer is equal to 1000 meters.

3. Measures of mass : These are the most common measurements:

Grams : Grams are the smallest

Kilograms 4. Measures of Capacity: These are the most common measurements:

Litre

Milliliter

Recall Exercise: TB; Page. No. 92 A: 1 - 8; Exercise 6.1 5. Metric measures in decimal form:

Exercise 6.1; CW: Page. No. 93 A: 1 -3; B: 1,3,5; C: 1,3,5,6; D: 1,3,4,5,8 E: 1-4 / HW: Page. No. 93 A: 1 -6; B: 2,6; C: 2,4; D: 2,4,7,8 E: 5,6 Exercise 6.2; CW: Page. No. 94, 95 A: 1 - 4; B: 1,3,5; / HW: Page. No. 94, 95 A: 5-8; B: 2,4,6-8; Exercise 6.3; CW: Page. No. 95 A: 1 -4,7,10; B: 1, 2 , 5; C: 1, 2 , 5 / HW: Page. No. 95 A: 5,6,8,9; B: 3 , 4,6-10; Exercise 6.4 6. Temperature: How hot or cold a thing is. Temperature is measured using a thermometer, usually in the Celsius or Fahrenheit scale. There are two main temperature scales: °F, the Fahrenheit Scale (used in the US), and °C, the Celsius Scale (part of the Metric System, used in most other countries)

MATHS NOTES, CLASS - 5 7. Celcius: Celsius (or "degrees Celsius", or sometimes "Centigrade") is a temperature scale. It is used to tell how hot or cold something is often written as °C. Water freezes at 0°C and boils at 100°C 8. Farenheit: A temperature scale. It is used to tell how hot or cold something is. It is often written as °F. Water freezes at 32°F and boils at 212°F. 9. Converting Celsius to Farenheit: °C to °F Multiply by 9, then divide by 5, then add 32 10. Converting Farenheit to Celsius: °F to °C Deduct 32, then multiplies by 5, then divide by 9 The table compares the two scales

11. Measuring atmosphere temperature:

Maximum Temperature: the temperature at the time of day when it is the hottest.

Minimum Temperature: the temperature at the time of day when it is the coolest. This celsius thermometer shows how we will feel at different atmospheric temperatures.

12. Measuring body temperature:

Exercise 6.4; CW: Page. No. 97 A: 1, 3, 10; B: 1,3,5 ; / HW: Page. No. 97 A: 2,4 ; B: 2,4 ---------------------------------------------------------------------------------------------------------------------------------------------------------

Chapter No: 7. Geometry Key points

Lines and line segment

Angles and vertex, arms.

Measuring an angle

Types of Angles.

Drawing an angle

Constructions using Compass and divider

Types of lines

Polygons

Types of quadrilaterals

MATHS NOTES, CLASS - 5

Properties of triangles

Types of triangles

Circle

Radius, diameter and Circumference of a circle

Arc and semicircle Recall Exercise 1. Line: A line is defined as a line of points that extends infinitely in two directions. It has one dimension, length. A line is defined as a line of points that extends infinitely in two directions. It has one dimension, length.

2. Line segment: The part of a line that connects two points. It has definite end points. Adding the word "segment" is important, because a line normally extends in both directions without end. Recall Exercise: TB; Page.no. 102 Fill in the Blanks 1-8 Exercise 7.1 3. Angle: an angle can be defined as the figure formed by two rays meeting at a common end point.( Vertex)

An angle is represented by the symbol ∠.

Here, the angle below is ∠AOB.

Angles are measured in degrees, using a protractor. Parts of an Angle: Arms: The two rays joining to form an angle are called arms of an angle. Here, OA and OB are the arms of the ∠AOB. Vertex: The common end point at which the two rays meet to form an angle is called the vertex. Here, the point O is the vertex of ∠AOB.

Exercise 7.2 Types of Angles Angles can be classified on the basis of their measurements as - Acute Angles - Right Angles - Obtuse Angles - Straight Angles - Reflex Angles - Complete Angles

Exercise 7.1; TB; Page.no.103 Q.No. 1: 1-4; Q.No. 2 : 1-3; Exercise 7.2; TB; Page.no.104 A: 1; Exercise 7.3. 4. Measuring an angle by using Protractor: For measuring an angle we use Protractor. A protractor has to scales to measure i.e., inner scale and outer scale of numbers beginning from 0 going up to 180.

MATHS NOTES, CLASS - 5 Protractor has a center and baseline in it. The measurements can be read left to right and right to left.

Exercise 7.3; TB; Page.no.105 Q.No. A: 1-4 ; Q.No. B : 1-9 ; Exercise 7.4; TB; Page.no.108 Q.No. 1: 1-6 ; Exercise 7.5. 5. Drawing an angle: To draw an angle we follow the steps given below. Step I: First we draw a line segment say XY.

Step II: Now place the protractor in such a way that its straight horizontal edge is placed on XY and its centre is on X as shown in figure. Step III: Starting from zero from the right, we start reading the scale on the protractor. We mark a point at 50° mark on the paper as shown here. Step IV: Name the point marked say, O and join the points O and X with the help a scale. ∠OXY = 50°. Exercise 7.5; CW: Page.no.109 Q.No. A: 1-5 ; / HW; Page.no.109 Q.No. A: 7-12 ; Exercise 7.6 6. Construction of Line segment:

MATHS NOTES, CLASS - 5 Exercise 7.6; TB; Page.no.110 Q.No. A: 1-4 ; Exercise 7.7 7. Types of lines:

Parallel lines: Two lines in a plane are said to be parallel if they do not intersect, when extended infinitely in both the direction. Also, the distance between the two lines is the same throughout. Parallel Lines

Intersecting lines: When two lines meet at the same point we say that they are intersecting lines.

Perpendicular lines: when two intersecting lines a and b are said to be perpendicular to each other if one of the angles formed by them is a right angle. The symbol used for perpendicular lines are ┴.

Exercise 7.7; TB; Page.no.110 Q.No. A: 1-6 ; B: 1-4; Exercise 7.8 8. Polygons: Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).

Polygon (straight sides)

Not a Polygon (has a curve)

Not a Polygon (open, not closed)

Polygon comes from Greek. Poly means many and gon means angles. 9. Types of Polygons:

Regular or Irregular: A regular polygon has all angles equal and all sides equal, otherwise it is irregular

MATHS NOTES, CLASS - 5 Three sided polygons are called triangles. Tri means three. Four sided polygons are called Quadrilaterals. Quad means four. Here are different types of triangles and quadrilaterals and their properties as …

Exercise 7.8; TB; Page. No.116 A: 1 - 6; / CW: Page. No. 117 B: 1, 2, 4; C: 1, 3, 5; / HW: Page. No. 117 B: 3, 5; C: 2, 4, 6; Exercise 7.9 10.Types of Quadrilaterals:

Exercise 7.9; TB; Page. No. 119 A: 1 - 6; Exercise 7.10 11.Circles: A circle is a closed figure is bounded by a curved line.

Every point in the circle is at equal distance from the fixed point of the circle is called its “Centre”.

The distance between the centre of and any point on a circle is called its “ Radius”.

A line segment passing through the centre of a circle , whose end points lie on the circle is called the “ Diameter” of the circle. The diameter of a circle is twice the radius.the diamter of the circle is the longest distance across the circle. Diameter = 2 X Radius Radius = diameter ÷ 2

MATHS NOTES, CLASS - 5

A line segment whose end points lie on the circle is called a “Chord’. We can make number of chords in a circle from one point on the circle.

“Diameter “ is the longest chord of the circle

Exercise 7.10; TB; Page. No. 121 A: 1 – 3; / TB; Page. No. 121 B: 1-2; C: 1 – 3; / CW: Page. No. 122 D: i-v; E: i-v; Exercise 7.11 12.Arc and semicircle:

Arc: Any part of a circle is called an ‘arc’ of a circle. Usually name an arc by three points where two points are the end points and there is a point in between them.

Semicircle: half of a circle is a ‘semicircle’ and it is also an arc of the Circle.

The perimeter of a circle is called ‘circumference ‘of the circle.

𝑪𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆

𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 = 3.14 or

𝟐𝟐

𝟕

The diameter of the circle and multiply it by 3.14 or 𝟐𝟐

𝟕 to get the Circumference.

Exercise 7.11; CW: Page. No. 123 A, B, C, D: 1 - 6; Exercise 7.12 13. Construction of Circles:

Exercise 7.12; CW: Page. No. 124 Q.No 1 - 8; ---------------------------------------------------------------------------------------------------------------------------------------------------------

Chapter No: 8. Area and volume Key points

Perimeter and Area

Areas of irregular shapes

Area by formula

Volume of 3 dimensional shapes

Volume of irregular objects

MATHS NOTES, CLASS - 5 Recall Exercise 1. Perimeter: The perimeter of a figure is the total distance around the edge of the figure. 2. Areas of irregular shapes: Place a square cm grid on the shape and count the number of squares within the curve. When half a square or more is covered, count it as a full square. Do not count less than half a square. Recall Exercise; TB; Page.no. 127 A: 1-3; Page.no. 128 A: 1-3 Exercise 8.1; TB; Page.no. 130 A: 1-5; B: 1-3; Exercise 8.2

3. Area by formula:

Area of a square = S X S = 𝑆2 Area of a rectangle = Length X breadth 4. Perimeter by formula: Perimeter of a square = 4 X S Perimeter of a rectangle = 2 x (l + b) Exercise 8.2; TB; Page.no. 133 A: 1-5; B: 1-6; / CW: Page.no. 134 C: 1-3; D: 1 - 2; E: 1-6; F: 1-6; Exercise 8.3

5. Volume: the volume of an object is the amount of space it occupies. 6. Volume of a cuboid = l X b X h 7. Volume of a cube = S X S X S Exercise 8.3. CW: Page.no. 135 Story Sums 1-10; Exercise 8.4. TB; Page.no. 137 A: 1-6; Page.no. 138 B: 1-2; Exercise 8.5. CW: Page.no. 138 C: 1(a-h); D: 2(a-d); Exercise 8.6 CW: Page.no. 138,139 Story Sums 1-7;

--------------------------------------------------------------------------------------------------------------------------------------------------------- Chapter No: 9. Percentages

Key Points Exercise 9.1 1. Percentages:

The term ‘per cent’ means one out of a hundred.

Percentages are used to describe parts of a whole – the whole being made up of a hundred equal parts.

The percentage symbol % is used commonly to show that the number is a percentage Exercise 9.1; TB; Page. No. 143 A: 1-3; Page. No. 144 B: 1-3; Exercise 9.2; CW; Page. No. 144 1-18; Exercise 9.3; CW; Page. No. 145 1-15; Exercise 9.4; CW; Page. No. 145 1-10; Exercise 9.5; CW; Page. No. 146 1-10; Exercise 9.6

2. Percentages as decimals:

a percent is a fraction of a whole it can be written as a decimal.

To write a percentage as a decimal simply divides it by 100.

To convert fractions into a percentage multiply by 100.

To convert percentage into fractions divides it by 100.

To convert decimal into fractions multiply by 100. 3. To find a percentage of a number, write the percentage as a fraction and multiply by the number. Exercise 9.6; CW; Page. No. 146 1-10; Exercise 9.7; Class Work Page. No. 147 A: 1-5; B: 1-5; C: 1-5; Exercise 9.8; CW: Page. No. 148 A: 1, 7, 8, 10; B: 1, 4, 5; / HW: Page. No. 148 A: 2-6,9; B: 2,3,6; Exercise 9.9; CW: Page. No. 148,149 Story Sums 1-10; Exercise 9.10; CW: Page. No. 149 Story Sums 1-7;

---------------------------------------------------------------------------------------------------------------------------------------------------------

MATHS NOTES, CLASS - 5 Chapter No: 10.Money in Everyday Life

Topics to Revise

Conversion of rupees to paisa/paisa to rupees.

Addition ,subtraction ,multiplication and division of money

Profit and Loss

Cost price , selling price

Profit percentage and loss percentage Key points Recall Exercise 1. The money is used in our country is rupee; 2. to convert rupees into paise multiply by 100; 3. Converting rupees to paise is also very simple by removing the decimal point; 4. Converting paise to rupees is put a decimal point 2 places from the right. 5. Profit and Loss : The price at which something is bought is called ‘Cost Price.’ The price at which it is sold is called a ‘Selling price’ The gain in money is called ‘profit.’ If cost price is more than selling price then is said to be ‘Loss’. IMPORTANT FORMULAE Profit = (S.P.) - (C.P.) Loss = (C.P.) - (S.P.)

Loss or gain is always depends on C.P.

If S.P,C.P. and Profit are given To find C.P C.P. = S.P. - Profit To find S.P S.P. = Profit + C.P. If S.P,C.P. and Loss are given To find C.P C.P. = Loss + S.P. To find S.P S.P. = C.P. - Profit Profit Percentage and Loss percentage:

1.

2.

MATHS NOTES, CLASS - 5

Exercise 10.1; CW; Page.no. 152 A: 1-3 B: 1-4; Page.no. 153 C: 1-4 D: 1-8; E: 1-8; Exercise 10.2; CW; Page.no. 156 A: 1-4 B: 1-4; C: 1-4; Page.no. 157 D: 1-6 B: 1-4; Exercise 10.3; CW; Page.no. 157 A: 1-4 / CW; Page.no. 158 B: 1-4; C: 1-10; Exercise 10.4; TB: Page.no. 160 A: 1-6 B: 1-6; / CW; Page.no. 161 C: 1-6; Exercise 10.5; TB: Page.no. 161 A: 1-4;

--------------------------------------------------------------------------------------------------------------------------------------------------------- Chapter No: 11.Time

Key points Recall Exercise 1. Time:

Time is the ongoing sequence of events taking place. The past, present and future.

The basic unit of time is the second. There are also minutes, hours, days, weeks, months and years.

We can measure time using clocks. 2. Time - AM/PM vs 24 Hour Clock:

Normally time is shown as Hours : Minutes

There are 24 Hours in a Day and 60 Minutes in each Hour.

Example: 10:25 means 10 Hours and 25 Minutes 3. Showing the Time:

There are two main ways to show the time: "24 Hour Clock" or "AM/PM": I. 24 Hour Clock: the time is shown as how many hours and minutes since midnight.

II. AM/PM (or "12 Hour Clock"): III. The day is split into:

The 12 Hours running from Midnight to Noon (the AM hours), and

The other 12 Hours running from Noon to Midnight (the PM hours). IV. Midnight and Noon:

"12 AM" and "12 PM" can cause confusion, so we prefer "12 Midnight" and "12 Noon". Recall Exercise: TB: Page.no. 1651: a, b; 2: a-e; 3: a-d; 4: a-d; Page.no.166 5: a, b; 6: a-d; 7: a-d; Exercise 11.1

V. Adding and Subtracting Time:

Add or Subtract the hours and minutes separately.

But you may need to do some adjusting if the minutes end up 60 or more, or less than zero! VI. Adding Times: Follow these steps:

MATHS NOTES, CLASS - 5 Add the hours Add the minutes If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours Easy example: What are 2:45 + 1:10? Add the Hours: 2+1 = 3 Add the Minutes: 45+10 = 55 The minutes are OK, so the answer is 3:55 Hard example: What is 2:45 + 1:20? Add the Hours: 2+1 = 3 Add the Minutes: 45+20 = 65 The minutes are 60 or more, so subtract 60 from minutes (65−60 = 5 Minutes) and add 1 to Hours (3+1 = 4 Hours) The answer is 4:0

VII. Subtracting Times: Follow these steps: Subtract the hours Subtract the minutes If the minutes are negative, add 60 to the minutes and subtract 1 from hours. Easy example: What is 4:10 - 1:05? Subtract the Hours: 4−1 = 3 Subtract the Minutes: 10−5 = 5 The minutes are OK, so the answer is 3:05 Hard example: What is 4:10 - 1:35? Subtract the Hours: 4−1 = 3 Subtract the Minutes: 10−35 = −25 The minutes are less than 0, so: add 60 to Minutes (−25+60 = 60−25 = 35 Minutes) and subtract 1 from Hours (3−1 = 2 Hours) The answer is 2:35

VIII. 24-Hour Clock When Hours end up less than zero: add 24 When hours end up more than 23: subtract 24 Example: What is 16:20 + 9:35? Add the Hours: 16+9 = 25 Add the Minutes: 20+35 = 55 The minutes are OK The hours are more than 23, so subtract 24: 25−24 = 1 The answer is 1:55 of the next day. Example: What is 4:10 − 6:15? Subtract the Hours: 4−6 = −2 Subtract the Minutes: 10−15 = −5 The minutes are less than 0, so: add 60 to Minutes: −5+60 = 60−5 = 55 Minutes and subtract 1 from Hours: −2−1 = −3 Hours The hours are less than 0, so add 24: −3+24 = 24−3 = 21 The answer is 21:55 of the previous day.

IX. 12-Hour Clock (AM/PM): For 12-Hour Clock it is best to convert to 24-Hour Clock, do the calculations then convert back. Example: What is 3:20 PM − 16:05? 3:20 PM is 15:20 Subtract the Hours: 15−16 = −1 Subtract the Minutes: 20−5 = 15 The minutes are OK The hours are less than 1, so add 24: −1+24 = 24−1 = 23

MATHS NOTES, CLASS - 5 The answer is 23:15, which is 11:15 PM of the previous day. There are different units of time. Second, minute, hour, day, week, month and year are the units of time. These have the following relations between each: 60 seconds = 1 minute or 1 minute = 60 seconds 60 minutes = 1 hour or 1 hour = 60 minutes 24 hours = 1 day (day + night); 7 days = 1 week; 12 months = 1 year; 52 weeks = 1 year; 365 days or 366 days make a year; these are the relations between units of time. We say time like this: 1 hour = 60 minutes or 60 minutes = 1 hour 1 minute = 60 seconds or 60 seconds = 1 minute 1 hour = 60 minutes = 60 x 60 or 3600 seconds Exercise 11.1: CW: Page.no.167 A: 1-6; B: 1-4; C: 1-4; Page.no.168 D: 1-4; E: 1-4; F: 1-4; Exercise 11.2 There are twelve months in a year: All the months have different numbers of days. These are the number of days each month has: (i) January = 31 days (ii) February = 28/29 days (iii) March = 31 days (iv) April = 30 days (v) May = 31 days (vi) June = 30 days (vii) July = 31 days (viii) August = 31 days (ix) September = 30 days (x) October = 31 days (xi) November = 30 days (xii) December = 31 days Thus 7 months have 31 days each; 4 months have 30 days each, only the month of February has 28 days ordinarily. But in a leap year, the month of February has 29 days. In an ordinary year, the numbers of days are (7 x 31) + (4 x 30) + (1 x 28) = 217 + 120 + 28 = 365 days. But a leap year (in which February is of 29 days) has 217 + 120 + 29 = 366 days. How to Remember You can remember how many days in each month using this rhyme:

30 days has September, April, June and November. All the rest have 31 Except February alone, Which has 28 days clear And 29 in each leap year.

Or you can use the "knuckle method":

MATHS NOTES, CLASS - 5 A knuckle is "31 days", and in between each knuckle it isn't. Where your hands meet, the two knuckles are "July, August", which both have 31 days. (Note: the last knuckle isn't used)

X. Convert the units of time into seconds, minutes, hours, days, months and year. Consider the following examples on units of time: 1. Convert the following: (i) 7 days 6 hours into hours. Solution: 1 day = 24 hours Therefore, 7 days 6 hours = (7 x 24) hours + 6 hours = 168 hours + 6 hours = 174 hours (ii) 6 hours 40 minutes into minutes. Solution: 1 hour = 60 minutes Therefore, 6 hours + 40 minutes = (6 x 60) minutes + 40 minutes = (360 + 40) minutes = 400 minutes (iii) 4 minutes 25 seconds into seconds. Solution: 1 minute = 60 seconds Therefore, 4 minutes 25 seconds = (4 x 60) seconds + 25 seconds = (240 + 25) seconds = 265 seconds 2. Convert the following: (i) 5 years 9 months into months. Solution: 1 year =12 months Therefore, 5 years 9 months = (5 x 12) months + 9 months = (60 + 9) months = 69 months (ii) 4 months 10 days into days. Solution: 1 month = 30 days Therefore, 4 months 10 days = (4 x 30) + 10 days = 120 + 10 = 130 days (iii) 7 weeks 6 days into days. Solution: 1 week = 7 days Therefore, 7 weeks 6 days = (7 x 7) days + 6 days = (49 + 6) days = 55 days iv) 1 year into seconds. Solution: 1 year = 365 days, 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds therefore, 1 year = 365 x 24 x 60 x 60 = 31536000 seconds 3. Convert the following: (i) 800 hours into days and hours. Solution: 24 hours = 1 day Therefore, 800 hours = 800 ÷ 24 days = 33 days 8 hour (ii) 750 minutes into hours and minutes. Solution: 60 minutes = 1 hour 750 minutes = 750 ÷ 60 hours = 12 hours 30 minutes

MATHS NOTES, CLASS - 5 (iii) 900 seconds into minutes and seconds. Solution: 60 seconds = 1 minute Therefore, 900 seconds = (900 ÷ 60) minutes

= 15 minutes 4. Convert the following: (i) 80 months into years and months. Solution: (i) 12 months = 1 year 80 months = (80 ÷ 12) years = 6 years 6 months

(ii) 210 weeks into years and weeks. Solution: 52 weeks = 1 year 210 weeks = 210 ÷ 52 = 4 years 2 weeks

(iii) 530 days into weeks and days. Solution: 7 days = 1 week 530 days = 530 ÷ 7 = 75 weeks 5 days

Exercise 11.2: CW: Page. No. 169 A: 1, 4, 5; B: 1, 4, 5, 6; C: Story sums / HW: Page. No. 169 A: 2, 3, 6; C: 2, 3; Exercise 11.3: CW: Page. No.170 A: 1-3; B: 1-3; C: 1-3; Exercise 11.4: TB: Page. No.172, 173 Chart A, B;

--------------------------------------------------------------------------------------------------------------------------------------------------------- Chapter No: 12. Representing information in Graphical Form

Key points Recall Exercise 1. Data: Data is a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. 2. Qualitative vs Quantitative

Data can be qualitative or quantitative.

Qualitative data is descriptive information (it describes something)

Quantitative data is numerical information (numbers)

MATHS NOTES, CLASS - 5 Data can be collected in many ways. The simplest way is direct observation. Example: Counting Cars 3. Raw data: A collection of observations gathered initially is called raw data. 4. Range: The difference between the highest and the lowest values of the observations in a data is called the range of the data. Recall Exercise: TB: Page.no. 179 Q.No. 1: Graph; .no. 180 Q.No. 2: Graph; Exercise 12.1 5. Statistics: It is the science which deals with the collection, presentation, analysis and interpretation of numerical data. Example: Given below are the marks (out of 100) in mathematics obtained by 20 students of a class in an annual examination. 23 75 56 42 70 84 12 61 40 63 87 58 35 80 14 63 49 72 66 61 Arrange the above data in ascending order and find (i) the lowest marks obtained, (ii) The highest marks obtained, (iii) The range of the given data. Solution: Arranging the above data in ascending order, we get: 14 23 35 40 42 49 51 56 58 61 63 63 66 70 72 75 80 84 87 92 from the above data analysis, we make the following observations. (i) Lowest marks obtained = 14. (ii) Highest marks obtained = 92. (iii) Range of the given data = (92 - 14) = 78. 6. Representation of Tabular Data: the representation of tabular data and their format. When Mrs. Singh, the new Maths teacher came to the class, she wanted to know how everybody had done in the last Maths test. She noted down everyone’s marks. In other words, she collected data about the marks scored in mathematics. Roll No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Marks 62 78 80 62 85 58 90 62 70 85 55 70 90 85 75 80 78 90 80 75 55

MATHS NOTES, CLASS - 5 22 23 24 25 26 27 28 29 30

98 58 62 62 85 55 98 50 55

Notice that this data is not in any particular order. Such data is called raw data. It is usually not very easy to get useful information from raw data. To understand the performance of students better Mrs. Singh first arranged the marks in ascending order. This is how the arranged data looked. 50, 55, 55, 55, 55, 58, 58, 62, 62, 62, 62, 62, 70, 70, 75, 75, 78, 78, 80, 80, 80, 85, 85, 85, 85, 90, 90, 90, 98, 98. She could now easily count the number of students who got a particular mark. To make this data more useful she arranged it in a tabular format.

Marks Obtained 50 55 58 62 70 75 78 80 85 90 98

No. Of Students 2 4 2 4 2 2 2 3 4 3 1

Looking at this table, Mrs. Singh could easily answer the following: (i) What was the highest mark? Ans: (98) (ii) What was the lowest mark? Ans: (50) (iii) What was the mark obtained by the largest number of student? Ans: (62) 7. Pictograph: A Pictograph is a way of showing data using images. Each image stands for a certain number of things. It is a fun and interesting way to show data. But it is not very accurate. 8. Bar graph: A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. In other words, A Bar Graph (also called Bar Chart) is a graphical display of data using bars of different heights. It is a really good way to show relative sizes: we can see which types of movie are most liked, and which are least liked, at a glance. We can use bar graphs to show the relative sizes of many things, such as what type of car people have, how many customers a shop has on different days and so on. 9. Pie Chart or circle Graph: a special chart that uses "pie slices" to show relative sizes of data. It is a really good way to show relative sizes: it is easy to see which movie types are most liked, and which are least liked, at a glance. First, put your data into a table (like above), then add up all the values to get a total: Next, divide each value by the total and multiply by 100 to get a percent Now to figure out how many degrees for each "pie slice" A Full Circle has 360 degrees, so we do this calculation: Now you are ready to start drawing! Draw a circle. You can use pie charts to show the relative sizes of many things, such as: what type of car people have, How many customers a shop has on different days and so on. how popular are different breeds of dogs Exercise 12.1: CW: Page.no. 180 Q.No. 1, 2, 3; Page.no. 181 Q.No. 5-8; / GB: Page.no. 180 Q.No. 4: Exercise 12.2 10. Line Graph: a graph that shows information that is connected in some way (such as change over time) Important: Make sure to have: A Title Vertical scale with tick marks and labels

MATHS NOTES, CLASS - 5 Horizontal scale with tick marks and labels Data points connected by lines Exercise 12.2: TB: Page.no. 183 Q.No. 1, 2 ---------------------------------------------------------------------------------------------------------------------------------------------------------

Chapter No: 13. Symmetry, Patterns, Nets and Maps Key points

Symmetry

Lines of Symmetry

Quarter and half Turns

Triangular and Square Numbers

Patterns

Number Patterns Recall Exercise 1. Symmetry:

Symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip or slide.

For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first.

There can also be symmetry in one object, such as a face.

If you draw a line of symmetry down the center of your face, you can see that the left side is a mirror image of the right side.

Not all objects have symmetry;

If an object is not symmetrical, it is called asymmetric. 2. Reflection Symmetry:

Sometimes called line symmetry or mirror symmetry, reflection symmetry is when an object is reflected across a line, like looking in a mirror.

The face mentioned is an example of reflection symmetry.

The line of symmetry does not have to be vertical; it can go in any direction. Also, certain objects, like a square or a circle, can have many lines of symmetry. Recall Exercise: TB: Page.no. 187 1: a – d; 2: a – c; Page.no. 188 3: a – d; 4: a – c; 5: a – b; Exercise 13.1 Turning shapes 3. Line of Symmetry:

The reflection in this lake also has symmetry, but in this case the Line of Symmetry runs left-to-right.

It is not perfect symmetry, as the image is changed a little by the lake surface.

The Line of Symmetry can be in any direction (not just up-down or left-right). 4. Rotational Symmetry: A shape has Rotational Symmetry when it still looks the same after some rotation. How many times it matches as we go once around is called the Order. Rotation" means turning around a center.

The distance from the center to any point on the shape stays the same.

Every point makes a circle around the center:

This rotation can be: (a) clockwise (b) anticlockwise

The fixed about which the figure is rotated is called centre of rotation.

The angle of turning during rotation is called the angle of rotation.

A quarter turn means a rotation of 90°

A half turn means a rotation of 180°

A full turn means a rotation of 360° Exercise 13.2: TB: Page.no. 191 1: a – d; 2: a – d; 3: a – d; Exercise 13.3: TB: Page.no. 192 1: a – d; Page.no. 193 2: a – d; Exercise 13.4 Number Patterns 5. Triangular numbers: A number that can make a triangular dot pattern. Example: 1, 3, 6, 10 and 15 are triangular numbers.

MATHS NOTES, CLASS - 5

6. Common number patterns: Numbers can have interesting patterns. Here we list the most common patterns and how they are made. 7. Arithmetic Sequences: An Arithmetic Sequence is made by adding the same value each time. Example: 1, 4, 7, 10, 13, 16, 19, 22, 25... This sequence has a difference of 3 between each number. The pattern is continued by adding 3 to the last number each time, like this: Examples: 3, 8, 13, 18, 23, 28, 33, 38...

This sequence has a difference of 5 between each number.

The pattern is continued by adding 5 to the last number each time, like this:

The value added each time is called the "common difference" 8. Geometric Sequences: A Geometric Sequence is made by multiplying by the same value each time. Example: 1, 3, 9, 27, 81, 243...

This sequence has a factor of 3 between each number.

The pattern is continued by multiplying by 3 each time, like this:

What we multiply by each time is called the "common ratio". 9. Square Numbers: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81... They are the squares of whole numbers: 0 (=0×0) 1 (=1×1) 4 (=2×2) 9 (=3×3) 16 (=4×4) etc... 1. Cube Numbers: 1, 8, 27, 64, 125, 216, 343, 512, 729... They are the cubes of the counting numbers (they start at 1): 1 (=1×1×1) 8 (=2×2×2) 27 (=3×3×3) 64 (=4×4×4) etc... Exercise 13.4: TB: Page.no. 194 1: a – e; Page.no. 195 4: a – e; 5: a-c; / CW: Page.no. 195 Q.No. 2, 3; Exercise 13.5

Nets of the solids: A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure.

A solid may have different nets.

Nets are helpful when we need to find the surface area of the solids.

Nets of Prisms, Pyramids, Cylinders and Cones Here are some examples of nets of solids: Prism, Pyramid, Cylinder and Cone.

MATHS NOTES, CLASS - 5 Exercise 13.5 TB: Page.no. 199 Q.No. 1: Matching; Page.no. 200 Q.No. 2-5 : Choose a shape; Exercise 13.6 TB: Page.no. 202 Q.No. 1-5: Map;

--------------------------------------------------------------------------------------------------------------------------------------------------------- Chapter No: 14. Algebra

Key points

Algebra

Variables and constants

Literal Numbers

Expressions

Equations , Terms and Operators

Algebraic Expressions Recall Exercise 1. Algebra: Using both the numbers and symbols into the equation to find the unknown values and then solving it is called ‘’ Algebra”. Example: finding the perimeter of a square where side = 4 cm The formula for perimeter of a square is P = 4 X S where side S = 4 cm Now, Perimeter of a square P = 4 X S (here we are using number and symbol also) P= 4 X 4 cm = 16 cm (assigned the value s = 4cm) 2. Constants: A fixed value. A constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants. 3. Variable A variable is a symbol, commonly a single letter that represents a number, called the value of the variable. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable. Exercise 14.1 4. Equation: An equation says that two things are equal. It will have an equals sign "=" like this: 𝑥 + 2 = 6 That equation says: what is on the left (x + 2) is equal to what is on the right (6). So an equation is like a statement "this equals that". 5. Parts of an Equation: There are names for different parts Here we have an equation that says 4x − 7 equals 5, and all its parts: 4 is a coefficient of x x is a variable 7 and 5 are constants ‘- ‘is an operator. Exercise 14.1: Text Book: Page.no. 208 Q.No. 1-8 Exercise 14.2 6. Coefficient: A Coefficient is a number used to multiply a variable. Example: 4X: 4x means 4 times x, so 4 is a coefficient Exercise 14.2: Text Book: Page.no. 208 Q.No. 1-10; Exercise 14.3 6. Operator: An Operator is a symbol (such as +, ×, etc.) that shows an operation 7. Term: A Term is either a single number or a variable, or numbers and variables multiplied together. 8. Expression: A Term is either a single number or a variable, or numbers and variables multiplied together. 9. Literal numbers: Literal numbers the letters used in Algebra are called Variables or simply literals. According to the definition of algebra, premising that the signs +, -, × and ÷ are used with the same meaning as in Arithmetic. Also, the following sign and symbols are frequently used in algebra and have the same meanings = Means, "is equal to" ≠ Means, "is not equal to" < Means, "is less than" > Means, "Is greater than" ≮ Means, "is not less than"

MATHS NOTES, CLASS - 5 ≯ Means, "is not greater than" ∴ Means, "Therefore" 10. Addition of Literals: Examples:

Suppose we are asked to find the sum of two numbers, say 3 and 5. The sum of 3 and 5 is denoted by 3 + 5.

Exactly in the same way, the sum of the literal y and a number 7 is denoted by y + 7 and is read as ‘y plus 7’. y + 7 can also be read as ‘7 more than y or increase y by 7’.

Similarly, y more than a literal x is written as x + y. We can also read x + y as the sum of x and y.

(x + y) + z means that the sum of literals x and y is added to the literal z x + (y + z) means that the literal x is added to the sum of literals y and z.

Sum of two literal numbers m and n is written as m + n.

The sum of m and m is written as m + m = 2m.

Sum of m, n and 5 is written as = m + n + 5. 11. Subtraction of Literals: Examples:

In the above way the subtraction of literals also takes place

If we are asked to subtract 5 from 7, then we write 7 – 5.

Exactly in the same way, when we are asked to subtract a number say 3 from a literal h, We write h – 3 and is read as ‘h minus 3’. Note that h – 3 can also be read as ‘3 less than a literal number h’. Similarly, if b is subtracted from a, we write a – b. We can also read a – b as ‘b less than a’. If a subtracted from b, then we write b – a. (a – b) – c means that b is subtracted from a and then c is to be subtracted from the result. We can also say that c is subtracted from the difference of b from a. 12. Multiplication of Literals: Multiplication of literals obeys all operation of multiplication of numbers. In arithmetic, we studied multiplication as the repeated addition. For example, 5 + 5 + 5 + 5 is called 4 times 5 and it is written as 4 × 5. Similarly, if a is a literal, then a + a + a + a is 4 times a and is written as 4 × a. Sometimes, the sign of multiplication is confused with the letter x. To avoid such as confusion we omit the sign of multiplication between a number and a literal or between two literals. Thus, when there is no sign between a literal and a number of two literals, it is understand that the two are multiplied. Thus, y + y + y + y + y = 5 × y = 5y Similarly, the product of literals a and b is written as ab. It should be noted that the product of the type y × 4 is not written as y4. Conventionally, we written it as 4y. 13. Division of Literals:

Division of literals obeys all operation of division of numbers.

We have studied that the division sign ‘÷’ read as ‘by’ between two numbers means that the number on the left of the division sign is to be divided by the number on the right. For example: 15 ÷ 3 means that the number 15 on the left of the division sign is to be divided by the number 3 on the right of division sign. In the case of literal numbers also x ÷ y read as ‘x by y’ means that the literal x is to be divided by the literal y and is written as x/y. Thus 25 divided by a is written as 25/a and y divided by 5 written as y/5. It should be noted that 1/5 of y or y divided by 5 is also written as y/5. Similarly, x divided by 10 is x/10. Quotient of 5 by z is 5/z. 14. Powers of Literal Numbers: The powers of literal numbers are the repeated product of a number with itself is written in the exponential form. Example:

MATHS NOTES, CLASS - 5 3 × 3 = 32 3 × 3 × 3 = 33 3 × 3 × 3 × 3 × 3 = 35 Since a literal number represent a number. Therefore, the repeated product of a number with itself in the exponential form is also applicable to literals. 15. Algebraic expressions: in Algebraic expressions the terms are separated by ‘+’or ‘-‘sign and forms an equation along with variables and constants. Example:

My school name is SISA Kendra is an Expression in English.

8 – 6 is an arithmetic expression.

Similarly, a + b is an algebraic expression. Where a and b are the terms of algebraic Expressions.

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression. Exercise 14.3: TB: Page.no. 210 A: 1-10 / CW: Page.no. 210 B: 1-5; C: Q.NOs. 1, 2, 3: a-e; Exercise 14.4 16. like terms unlike terms: Like terms: The terms having the same literal (variable) with same exponents are called like terms. Example: 1) 12x and -5x 2) 4x 2 and ½ x 2 Unlike terms: The terms having the same variable with different exponents or different variable with same exponents are called unlike terms. Example: 1) 5x and 5y 2) 2x 2 and 3y 2 Addition and subtraction of Algebraic Expressions with Like and Unlike terms 1) 7x +4 and 3x -1 = (7x + 4) + (3x -1) = 7x + 4 + 3x -1 [ Marking of like terms] = 10x + 3

2) Subtract -7x from 5x Solution: = 5x – ( -7x) = 5x + 7x = 12x Exercise 14.4: TB: Page.no. 211 A: 1-9 ; B: 1-5; Exercise 14.5: TB: Page.no. 212 A: 1-5; B: 1-5; / CW: Page.no. 212 C: 1-5; ---------------------------------------------------------------------------------------------------------------------------------------------------------