holt algebra 1 1-2 adding and subtracting real numbers 1-2&1-3 holt algebra 1 warm up warm up...

Holt Algebra 1

1-2 Adding and Subtracting Real Numbers1-2&1-3

Holt Algebra 1

Warm Up

Lesson Presentation

Lesson Quiz

Holt Algebra 1

1-2 Adding and Subtracting Real Numbers

Warm UpSimplify.

1.

3 2. –4

Write an improper fraction to represent eachmixed number.

3. 423

143

4. 767

557

Write a mixed number to represent each improper fraction.

5. 125 2

2

56. 24

9 2

2

3

|–3| –|4|

Holt Algebra 1


Add real numbers.

Subtract real numbers.

Objectives

Holt Algebra 1


All the numbers on a number line are called realnumbers. You can use a number line to modeladdition and subtraction of real numbers.

AdditionTo model addition of a positive number, move right. To model addition of a negative number move left.

Subtraction

To model subtraction of a positive number, move left. To model subtraction of a negative number move right.

Holt Algebra 1


Example 1A: Adding and Subtracting Numberson a Number line

Add or subtract using a number line.

Start at 0. Move left to –4.

11 10 9 8 7 6 5 4 3 2 1 0

+ (–7)

–4+ (–7) = –11

To add –7, move left 7 units.

–4

–4 + (–7)

Holt Algebra 1


Check It Out! Example 1c


–5 – (–6.5) Start at 0. Move left to –5.To subtract negative 6.5 move right 6.5 units.

8 7 6 5 4 3 2 1 0

–5

–5 – (–6.5) = 1.5

1 2

– (–6.5)

Holt Algebra 1


The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|.

5 units 5 units

210123456 6543- - - - - -

|5| = 5|–5| = 5

Holt Algebra 1


Holt Algebra 1


Add.

–5 + (–7)

Check It Out! Example 2a

When the signs are the same, find the sum of the absolute values.

Both numbers are negative, so the sum is negative.

–5 + (–7) = 5 + 7

5 + 7 = 12

–12

Holt Algebra 1


Check It Out! Example 2b

Add.

–13.5 + (–22.3)

When the signs are the same, find the sum of the absolute values.

–13.5 + (–22.3)

–35.8 Both numbers are negative so,the sum is negative.

13.5 + 22.3

Holt Algebra 1



Add.

x + (–68) for x = 52 First substitute 52 for x.

x + (–68) = 52 + (–68)

68 – 52

When the signs of the numbers are different, find the difference of the absolute values.

–16Use the sign of the number with the greater absolute value. The sum is negative.

Holt Algebra 1


Two numbers are opposites if their sum is 0. A number and its opposite are on opposite sides of zero on a number line, but are the same distance from zero. They have the same absolute value.

Holt Algebra 1


A number and its opposite are additive inverses.To subtract signed numbers, you can use additiveinverses.

11 – 6 = 5 11 + (–6) = 5

Additive inverses

Subtracting 6 is the sameas adding the inverse of 6.

Subtracting a number is the same as adding theopposite of the number.

Holt Algebra 1


Holt Algebra 1


Subtract.

13 – 21


13 – 21 To subtract 21 add –21.

When the signs of the numbers are different, find the difference of the absolute values: 21 – 13 = 8.

Use the sign of the number with the greater absolute value.

–8

= 13 + (–21)

Holt Algebra 1



Subtract.

Both numbers are positive so, the sum is positive.

To subtract add .–3 12 3 1

2

When the signs of the numbers are the same, find the sum of the absolute values: = 4.3 1

212

+

4

Holt Algebra 1


x – (–12) for x = –14


Subtract.

x – (–12) = –14 – (–12) First substitute –14 for x.

–14 + (12) To subtract –12, add 12.

When the signs of the numbers are different, find the difference of the absolute values: 14 – 12 = 2.

Use the sign of the number with the greater absolute value.

–2

Holt Algebra 1



1. –2 + 9 7 2. –5 – (–3) –2

Add or subtract.

3. –23 + 42 19 4. 4.5 – (–3.7) 8.2

5.

Lesson Quiz

6. The temperature at 6:00 A.M. was –23°F.At 3:00 P.M. it was 18°F. Find the differencein the temperatures.41°F

Holt Algebra 1


Multiply real numbers. Divide real numbers.

Objectives

Holt Algebra 1


WORDS

Multiplying and Dividing Numbers with the Same Sign

If two numbers have the same sign, their product or quotient is positive.

NUMBERS 4 5 = 20

–15 ÷ (–3) = 5

Multiplying and Dividing Signed Numbers

Holt Algebra 1


WORDS

Multiplying and Dividing Numbers with Different Signs

If two numbers have different signs, their product or quotient is negative.

NUMBERS6(–3) = –18

Multiplying and Dividing Signed Numbers

–18 ÷ 2 = –9

Holt Algebra 1


Find the value of each expression.

–7The quotient of two numberswith different signs is negative.

Check It Out! Example 1a and 1b

1a. 35 (–5)

44 The product of two numberswith the same sign is positive.

1b. –11(–4)

Holt Algebra 1



–6x = –6(7) First substitute 7 for x.


1c. –6x for x = 7

= –42 The product of two numbers with different signs is negative.

Holt Algebra 1


Two numbers are reciprocals if their product is 1.A number and its reciprocal are called multiplicative inverses. To divide by a number, you can multiply by its multiplicative inverse.

Dividing by a nonzero number is the same as Multiplying by the reciprocal of the number.

Holt Algebra 1


10 ÷ 5 = 2 10 ∙ = = 215

105

Multiplicative inverses

Dividing by 5 is the same as multiplying by thereciprocal of 5, .

Holt Algebra 1


You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1.

Helpful Hint

Holt Algebra 1



Divide.

Write as an improper fraction.

To divide by , multiply by .

and have the same signs,

so the quotient is positive.

Holt Algebra 1



Divide.

Write the reciprocal of .

To divide by , multiply by .

and have different signs,

so the quotient is negative.

Holt Algebra 1



Divide.

Write as an improper fraction.

To divide by multiply by .

The signs are different so the quotient is negative.

Holt Algebra 1


No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal. Because 0 has no reciprocal, division by 0 is not possible. We say that division by zero is undefined.

Holt Algebra 1


Properties of Zero

WORDS

NUMBERS

ALGEBRA

Multiplication by ZeroThe product of any numberand 0 is 0.

13 · 0 = 0 0(–17) = 0

a · 0 = 0 0 · a = 0

Holt Algebra 1


Properties of Zero

WORDS

NUMBERS

ALGEBRA

Zero Divided by a NumberThe quotient of 0 and any nonzero number is 0.

06 = 0

0 ÷ a = 0

0 ÷ 23 = 0

0a = 0

Holt Algebra 1


Properties of Zero

WORDS

NUMBERS

ALGEBRA

Division by Zero

Division by 0 is undefined.

a ÷ 0 a0

12 ÷ 0Undefined

–5 0

Undefined

Holt Algebra 1



Divide:

Multiply by the reciprocal.

Any number multiplied by0 equals 0.

Turn into an improperfraction.

Holt Algebra 1


Check It Out! Example 3b and 3c

Divide:

3b. 0 ÷ 0

0 ÷ 0 = undefined Any number divided by 0 is undefined.

3c. (–12.350)(0)

(–12.350)(0) = 0 The product of any number and 0 is 0.

Holt Algebra 1



1. 35–7 –5 2. 2x for x = –6 – 12

Lesson Quiz

Multiply or divide if possible.

3. –3 1 34 (0)4. –21

3 5. – 034

– 12 7

0 undefined

15 miles

6. A cyclist traveled on a straight road for 1 hours at a speed of 12 mi/h. How many miles did the cyclist travel?

14

Holt Algebra 1


Homework:

Vocabulary for Sections 1-2 and 1-3

p. 17-18, #’s 17-43 Odd, 53, 55

p. 23-24, 13-61 Odd

This is a lot of problems!!! Don’t put it off!!!

holt algebra 1 1-2 adding and subtracting real numbers 1-2&1-3 holt algebra 1 warm up warm up...

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