chapter 2: fractions · 2019-08-14 · proper fractions improper fractions mixed numbers fractions...

Essential Mathematics Chapter 2

20

CHAPTER 2: FRACTIONS

Chapter Objectives

By the end of this chapter, students should be able to:

Represent fractions and mixed numbers Simplify fractions Identify types of fractions Convert between improper fractions and mixed numbers Compare fractions Perform arithmetic operations with fractions and mixed numbers Solve word problems involving fractions

Contents CHAPTER 2: FRACTIONS ........................................................................................... 20

SECTION 2.1 FRACTION INTRODUCTION ............................................................. 21

A. What is a Fraction? ....................................................................................... 21

B. Fractions in Context ...................................................................................... 22

C. Equivalent Fractions ..................................................................................... 25

D. Simplifying Fractions ..................................................................................... 28

E. Proper Fractions, Improper Fractions, and Mixed Numbers ......................... 29

F. Changing Between Improper Fractions and Mixed Numbers ........................ 30

EXERCISES........................................................................................................... 32

SECTION 2.3: OPERATIONS WITH FRACTIONS.................................................... 36

A. Adding Fractions and Mixed Numbers .......................................................... 36

B. Subtracting Fractions and Mixed Numbers ................................................... 39

C. Multiplying Fractions ..................................................................................... 43

F. Divide Fractions ............................................................................................ 45

G. Multiply and Divide Mixed Numbers .............................................................. 47

H. Word Problems ............................................................................................. 49

EXERCISES........................................................................................................... 52

CHAPTER REVIEW .................................................................................................. 57


21

SECTION 2.1 FRACTION INTRODUCTION

A. What is a Fraction?

There are many ways to think of a fraction. First, a fraction can be thought of as one

quantity divided by another written by placing a horizontal bar between the two numbers

such as 1

2 . This is “1 divided by 2.” Written as

1

2 we call 1 the numerator and 2 the

denominator.

Or, we can think of fractions as a part compared to a whole such as 1 out of 2 cookies or 1

2 of the cookies.

In this lesson, we will look at a few other ways to think of fractions as well.

Officially, fractions are any numbers that can be written as 𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟

𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 but in this course,

we will consider fractions where the numerator and denominator are integers. These

special fractions where the numerator and denominator are both integers are called

rational numbers. Since rational numbers are indeed fractions, we will frequently refer to

them as “fractions” instead of “rational numbers”.

Media Lesson Language of Fractions (Duration 6:18)

View the video lesson, take notes and complete the problems below.

Each of the phrases below are one way we may indicate a fraction with words. Rewrite

the phrases below in fraction form and write the fraction word name.

Language Fraction Representation Fraction Word Name

20 divided by 6

8 out of 9

A ratio of 3 to 2

11 per 5

2 for every 7

https://www.youtube.com/watch?v=3KETMJD7AOw&feature=youtu.be

https://www.youtube.com/watch?v=3KETMJD7AOw&feature=youtu.be


22

B. Fractions in Context

Media Lesson Fractions in Context: Four Models (Duration 8:12)


In the next example, we will look at four different types of fractions in context.

1. Quotient Model (Division): Sharing equally into a number of groups

2. Part-Whole Model: A part in the numerator a whole in the denominator

3. Ratio Part to Part Model: A part in the numerator and a different part in the

denominator

4. Rate Model: Different types of units in the numerator and denominator (miles and

hours)

Represent the following as fractions. Determine whether it is a quotient, part-whole, part

to part, or rate model.

a) Three cookies are shared among 6 friends. How many cookies does each friend

get?

b) Four out of 6 people in the coffee shop have brown hair. What fraction of people

in the coffee shop have brown hair?

c) Tia won 6 games of heads or tails and lost 3 games of heads or tails. What is the

ratio of games won to games lost?

d) A snail travels 3 miles in 6 hours. What fraction of miles to hours does he travel?

What fraction of hours to miles does he travel?

https://www.youtube.com/watch?v=WpJH8Ekbd6o&feature=youtu.be


23

YOU TRY:

Represent the following as fractions.

a) Jorge bikes 12 miles in 3 hours. What fraction of miles to hours does he travel?

b) Callie has 5 pairs of blue socks and 12 pairs of grey socks. What fraction of all of her socks are blue?

Media Lesson Fraction Basics (Duration 4:14)


https://www.youtube.com/watch?v=jgWqSjgMAtw


24

Media Lesson Fractions on a Number Line (Duration 4:15)


It is important to note, dividing by zero is undefined. Consider dividing 5 candles among

0 people. How much does each person get? The question does not make sense because

we cannot share among 0 people. So we cannot divide by 0.

In fractions when the numerator is zero, the whole fraction is equal to zero.

For example, 05 = 0.

https://www.youtube.com/watch?v=Z0WsfO-RI8Y


25

C. Equivalent Fractions

Equivalent fractions are different fractions that are equal or represent the same amount.

Media Lesson Equivalent Fractions (Duration 7:37)


𝟏

𝟒

𝟐

𝟖

To find equivalent fractions ____________________ or ____________________ the

numerator and denominator by the same nonzero (don’t use zero) whole number.

We would only divide the numerator and denominator by a whole number that is

a ____________________ of both the numerator and denominator.

Once a fraction does not have any common factors other than 1 between the

numerator and denominator a fraction is simplified or written in lowest terms.

𝟏

𝟐

𝟐

𝟒

𝟒

𝟖

https://www.youtube.com/watch?v=d1bWAz43rMY

https://www.youtube.com/watch?v=d1bWAz43rMY&feature=youtu.be


26

𝟏𝟖

𝟐𝟒

𝟗

𝟏𝟐

𝟑

𝟒

𝟏

𝟐𝟒

𝟏

𝟏𝟐

𝟏

𝟖

𝟏

𝟔

𝟏

𝟒

𝟏

𝟑

𝟏

𝟐

1

Define: Dark Blue Rod = 1

1

Determine two equivalent fractions for each fraction below.

7

8

4

12


27

Why is finding equivalent fractions important?

It will help you when you add and subtract fractions.

Media Lesson Determine the Numerator Given Denominator (Duration 2:25)


Fill in the missing numerator in each fraction below to create equivalent fractions.

a) 1

2=

30 b)

14

16=

8

c) 4

7=

49 d)

27

45=

5

YOU TRY:

Rewrite the given fractions as equivalent fractions given the indicated denominator.

c) 3

7=

?

21

d) 10

12=

?

120

e) 5

8=

?

32

f) 6

11=

?

33

g) 8

12=

?

24

h) 3

5=

?

15

https://www.youtube.com/watch?v=9hYCsIEILB4&feature=youtu.be


28

D. Simplifying Fractions

Media Lesson What is a Simplified Fraction (Stop at 4:28)


The simplest form of a fraction is the equivalent form of the fraction where the numerator

and denominator are written as integers without any common factors besides 1. We may

also request that a fraction be written in simplest form by using the equivalent language;

simplify the fraction, reduce the fraction, or reduce the fraction completely.

a) Write the fraction number for each diagram below the figure using one circle as the

unit.

b) What do the fractions have in common?

c) Which fraction do you think is simplest and why?

A fraction is in its simplest form, or lowest terms or reduced, when it has the least

numerator and the least denominator possible.

When you are asked to simplify fractions or reduce fractions, you are being asked to

find the simplest form.

Media Lesson Reduce- Reduce Fractions (Duration 2:27)


To reduce fractions we _____________________ common _____________________.

24

15

48

18

https://www.youtube.com/watch?v=JUGAWb4rjx8&feature=youtu.be

https://www.youtube.com/watch?v=E2wReCkcMyQ

https://www.youtube.com/watch?v=JUGAWb4rjx8&feature=youtu.be


29

YOU TRY:

Simplify the given fractions completely.

i) 6

8 j)

30

42

k) 32

44

l) 15

75

E. Proper Fractions, Improper Fractions, and Mixed Numbers

We use three words to describe fractions: proper, improper, and mixed.

Proper Fractions Improper Fractions Mixed Numbers

Fractions whose

numerator is less than their

denominator.

Fractions whose

numerator is greater than

or equal to its

denominator.

A combination of a whole

number and a proper

fraction.

Examples: 8

9 𝑎𝑛𝑑

2

7 Examples:

20

6,

3

3, 𝑎𝑛𝑑

11

5 Examples: 1

1

2 𝑎𝑛𝑑 15

4

7

YOU TRY:

For the following decide whether the fraction is a proper fraction, improper fraction, or mixed number.

a) 3 1

5 b)

11

4

c) 11

50 d)

15

15


30

F. Changing Between Improper Fractions and Mixed Numbers

Media Lesson Improper Fractions and Mixed Numbers (Duration 6:48)


1. A proper fraction is fraction with a smaller numerator than denominator. Proper

fractions are ________________________.

Examples:

2. An improper fraction is a fraction which the numerator is greater or equal to the

denominator. Improper fractions are ________________________.

Examples:

3. A mixed number is a number written as the sum of an integer and a proper fraction.

Examples:

To Convert from an Improper Fraction to a Mixed Number

1. Divide the numerator by the denominator.

2. Write down the whole number.

3. Place any remainder in the quotient over the denominator.

4. Simplify the fraction if needed.

Example: Convert 13

5 to a mixed number.

Example: Convert 32

6 to a mixed number.

https://www.youtube.com/watch?v=snPPwBp6tSQ

https://www.youtube.com/watch?v=snPPwBp6tSQ


31

To Convert a Mixed Number into an Improper Fraction

1. Multiply the denominator by the whole number.

2. Take that product and add that to the numerator of the fraction.

3. Take that sum and place it over the denominator.

Example: Convert 2 3

8 into an improper fraction.

Example: Convert 7 5

12 to an improper fraction.

Why is converting a mixed number to an improper fraction important?

It will help you when we learn to multiply and divide mixed numbers!

YOU TRY:

Convert the following fractions to mixed numbers if you can.

a) 8

3 b)

15

4 c)

21

25 d)

34

10 e)

12

11


32

EXERCISES

Each of the phrases below are one way we may indicate a fraction with words.

Rewrite the phrases below in fractions from and write the fraction word name.

Language Fraction Representation Fraction Word Name

1) A ratio of 5 to 10

2) 9 for every 10

3) 4 out of 7

4) 15 per 2

5) 16 divided by 5

For each problem below, write the fraction that best describes the situation. Be

sure to reduce your result.

6) John had 12 marbles in his collection. Three of the marbles were Comet marbles.

What fraction of the marbles were Comet marbles? What fraction were NOT Comet

marbles?

7) Jorge’s family has visited 38 of the 50 states in America. What fraction of the states

have they visited?

8) In a given bag of M & M’s, 14 were yellow, 12 were green, and 20 were brown. What

fraction were yellow? Green? Brown?

9) Donna is going to swim 28 laps. She has completed 8 laps. What fraction of laps has

she completed? What fraction of her swim remains?

10) Last night you ordered a pizza to eat while watching the football game. The pizza

had 12 pieces of which you ate 6. Today, two of your friends come over to help you

finish the pizza and watch another game. What is the fraction of the LEFTOVER pizza

that each of you gets to eat (assuming equally divided)? What is the fraction of the

ORIGINAL pizza that each of you gets to eat (also assuming equally divided)?


33

11) Create two fractions equivalent to the given fraction by cutting the given

representations into a different number of equal pieces.

a) Given fraction: 3

4

3

4 is equivalent to the fraction: ________

b) Given fraction: 3

5

3

5 is equivalent to the fraction: ________

Rewrite the given fractions as equivalent fractions given the indicated numerator or

denominator.

12) Rewrite 2

3 with a denominator of 21.

13) Rewrite 6

7 with a numerator of 30.

14) Rewrite 5


15) Rewrite 4


16) Rewrite 36


17) Rewrite 5


Simplify each of the following fractions if possible.

18) 5

1 19)

6

6 20)

0

4

21) 1

6

22) 1

1 23)

1

0


34

Simplify the given fractions completely using both common factors and prime

factorization. In each case, state which method you think is easier and why.

Fraction Common Factor Prime Factorization

24) 12

42

25) 16

100

26) 5 27

63

For the following problems, convert from an improper fraction to a mixed number.

27) 19

5

28) 33

10

29) 52

7

For the following problems, convert from a mixed number to an improper fraction.

30) 1 3

8

31) 5 1

6

32) 105

9

Check your work with the answer key!


35

Online Quiz

Log on to Canvas to take the section quiz

Directions: It is very useful to save your math exercise work and use it as a chapter

test review when you study for your chapter test and final.

1) Write each question on the screen down to for your record

2) Solve the problem step by step below each question

3) Double check your work to see whether your answer make sense

4) Enter your answer in the answer box in Canvas. Make sure you click on the

“Preview” button to make sure you enter the right format before you submit your

answer. If you are not sure how to enter your answer with the correct format, ask

your instructor.

5) If you did not answer the question correctly, solve the question again from the

beginning below your 1st attempt. Sometimes, it is better to start a problem again

from the beginning and compare your steps with your 1st attempt to figure out your

mistake.

6) Insert your work at the end of each section in your workbook so that you can use it

to study for your chapter test later.

https://rsccd.instructure.com/



36

SECTION 2.3: OPERATIONS WITH FRACTIONS

A. Adding Fractions and Mixed Numbers

To add and subtract fractions you need to have like denominators. Sometimes like

denominators are called common denominators.

Media Lesson Ex: Add Fractions with Like Denominators (Duration 2:36)


Examples: Adding Fractions with Like Denominators

2

7+

3

7

+

2

9+

1

9

+

Media Lesson Adding Fractions (Duration 9:10)


To add fractions with like denominators:

1) Add the numerators, keeping the same denominator.

2) Simplify, if possible.

1 2 3 4 5 + 1 2 3 4 5 = 1 2 3 4 5

1

5 +

2

5 =

https://www.youtube.com/watch?v=GTkY34kl6Kw

https://www.youtube.com/watch?v=d53wePmJZFY

https://www.youtube.com/watch?v=d53wePmJZFY


37

To add fractions with unlike denominators:

1) Find the least common multiple of the denominators. That number is the least

common denominator, LCD.

2) Create equivalent fractions with the common denominator.

3) Add the numerators, keeping the same denominator.


1

2 +

1

4 =

Why do we need to have a common denominator?

ERROR! 1

2+

1

4≠

2

6

1

2+

1

4=

3

4

1 2 2

4 1 2 3 4

1 2 3 4 1

4 1 2 3 4

1 2 3 4 5 6 3

4 1 2 3 4

Add. 3

10+

1

5

3

4+

1

6

3 +3

5

5

12+

3

8


38

Media Lesson Adding Mixed Numbers (Duration 6:35)


To add mixed numbers:

1. Obtain a common denominator.

2. Add.

3. If the sum has an improper fraction, convert it to a mixed number and add it to

the whole number.

4. Simplify if possible.

Add.

41

4+ 2

2

3

14

5+ 2

11

15

37

8+ 2

5

6

YOU TRY:

Add the following fractions and reduce your answer to the lowest terms if possible.

a) 3 1

2 +

5

6 b) 5

3

5 +4

2

3

c) 7

10+

1

10 d)

2

6+

1

8

e) 3 + 2 1

2

https://www.youtube.com/watch?v=f5a28iu-V6E

https://www.youtube.com/watch?v=f5a28iu-V6E


39

B. Subtracting Fractions and Mixed Numbers

Media Lesson Ex: Subtract Fractions with Like Denominators (Duration 3:00)


Examples: Subtracting Fractions with Like Denominators

7

8−

3

8

+

4

9−

1

9

+

Media Lesson Subtracting Fractions Introduction (Duration 8:29)


To subtract fractions with like denominators:

1) Keep the denominators the same and subtract the numerators.


1

2

3

4

5

−

1

2

3

4

5

=

1

2

3

4

5

3

5

− 1

5

=

https://www.youtube.com/watch?v=7CeAQcpOJw0

https://www.youtube.com/watch?v=43LQU9whwWM

https://www.youtube.com/watch?v=43LQU9whwWM


40

To subtract fractions with unlike denominators:

1) Find the least common multiple of the denominators. That number is the least

common denominator, LCD.

2) Crate equivalent fractions with the common denominator.

3) Keep the denominator the same and subtract the numerators.


Example: 3

4−

1

2=

1

2

3

4

−

1

2

3

4

=

1

2

3

4

Subtract.

5

6−

7

12

7

10−

3

8

5

12−

1

15

2 −5

14


41

We will now look at how to subtract mixed numbers.

Media Lesson Subtract Mixed Numbers (Duration 2:43)


To subtract mixed numbers we ________________________ and work

_________________ to _________________.

94

5− 3

1

2 7

7

8− 2

3

4

Sometimes you need to borrow in order to subtract mixed numbers.

Media Lesson Subtract with Borrowing (Duration 4:10)


If we can’t subtract two fractions we may have to ___________________.

62

5− 2

11

15 9 − 5

3

4

https://www.youtube.com/watch?v=el8tqAKElJg

https://www.youtube.com/watch?v=0Z3ZD3YilIA


42

Media Lesson Subtracting Mixed Numbers (Duration 7:15)


To subtract mixed numbers:

1. Obtain a common denominator.

2. Check to see if you need to borrow.

3. Subtract the fractions and then the whole numbers.

4. Simplify if needed.

Subtract.

43

4− 2

1

4 6

4

5− 2

11

15

53

8− 2

5

6

71

10− 2

1

6

12 − 83

11

https://www.youtube.com/watch?v=tVrelLu6K6k

https://www.youtube.com/watch?v=tVrelLu6K6k


43

YOU TRY:

Subtract and reduce your answer to the lowest term if possible.

a) 3 − 2

5

b) 3 1

2−

1

5

c) 9 29 − 2

2

3 d) 6

4

6 − 3

5

6

C. Multiplying Fractions

When we multiply or divide fractions, we do not need a common denominator.

To multiply fractions:

1. Multiply the numerators and multiply the denominators.

2. Simplify, if possible.

We can alternatively cancel common factors before multiplying.

Media Lesson Multiply Fractions with Reducing(Duration 3:26)


With multiplication __________________ we can __________________ before

multiplying.

To reduce we _______________________ any common factors in the

__________________ and __________________.

6

35∙

14

9

25

49∙

21

10

https://www.youtube.com/watch?v=BgH5xbvBJwo


44

Media Lesson Multiply Fractions with Whole Numbers (Only do first example)


To make a whole number a fraction, ____________________________.

14

15∙ 10

Media Lesson Multiplying Fractions: An Explanation (Duration 5:05)


2

3×

4

5=

https://www.youtube.com/watch?v=xClgvKmbioY

https://www.youtube.com/watch?v=x6xtezhuCZ4


45

YOU TRY:

Multiply. If possible, simplify and express your answer a mixed number.

a) 2

3∙

3

4 b)

12

25∙

35

48

c) 7

8 ∙ 5

d) 12 ∙ 1

9

F. Divide Fractions

To divide fractions we will be using a reciprocal.

Media Lesson Reciprocals (Duration 2:01)


Reciprocal:

If we multiply reciprocals the answer will always be __________.

Find the reciprocal.

7

3

9

https://www.youtube.com/watch?v=MPeR4kdd-Xw


46

To divide fractions:

1. Change the second fraction to its reciprocal.

2. Simplify or cancel common factors if possible.

3. Multiply.

Media Lesson Example 1: Division Involving Fractions (Duration 3:06)


Example: Divide and simplify.

2

3÷

5

2

8

27÷

16

9

Media Lesson Divide with Whole Numbers and Fractions (Duration 2:23)


Whole numbers can be made into fractions by putting them over ________.

Example 1:

28 ÷7

8

Example 2: 4

9÷ 14

https://www.youtube.com/watch?v=IAp_EFhzJSs

https://www.youtube.com/watch?v=OprakkMKkS4

https://www.youtube.com/watch?v=IAp_EFhzJSs


47

YOU TRY:

Divide. If possible, simplify and express your answer a mixed number.

a) 1

2÷

3

5

What is the reciprocal of 3

5 ?

b) 8 ÷ 4

5


5 ?

c) 3

7 ÷ 5

What is the reciprocal of 5 ?

d) 1

9÷

1

3


3 ?

G. Multiply and Divide Mixed Numbers

Media Lesson Mixed Numbers- Multiply and Divide (Duration 5:00)


To multiply or divide mixed numbers we will first change to a _____________________

then we will _____________________ then we will _____________________.

41

8∙ 2

5

6

91

3÷ 2

5

6

https://www.youtube.com/watch?v=aV6gYM4cEJs


48

Media Lesson Example: Division Involving Mixed Numbers (Duration 3:47)


Example: Divide and simplify.

8 ÷ 21

2 4

5

6÷ 2

3

4

YOU TRY:

Solve. If possible, simplify your answer and express as a mixed number.

a) 31

5∙ 1

1

9 b) 1

3

5÷ 1

2

3

c) 11

6÷ 4

1

2 d) 3

2

3÷

1

9

https://www.youtube.com/watch?v=x1coIlZoFag


49

H. Word Problems

Media Lesson Adding Fractions Word Problem (Duration 5:46)


Cindy and Michael need 1 gallon of orange paint for the giant cardboard pumpkin they

are making for Halloween. Cindy has 2

5 of a gallon of red paint. Michael has

1

2 of a gallon

of yellow paint. If they mix their paint together, will they have the 1 gallon they need?

Media Lesson Subtract Fractions Word Problem (Duration 3:18)


Silvia is growing tomato plants and studying their heights. Here is her data:

Tomato Type Height (feet)

Beefsteak 31

4

Roma 27

8

Cherry 31

2

What is the difference between the heights of the Beefsteak and Roma tomato plants?

https://www.youtube.com/watch?v=PKh5B9xyzSc

https://www.youtube.com/watch?v=5fK8HEYNRuQ


50

In the video the mixed numbers were converted to improper fractions. Another way to

find the difference is to subtract the mixed numbers as they are.

31

4− 2

7

8= 3

1 × 2

4 × 2− 2

7

8 𝐿𝑒𝑡 𝑢𝑠 𝑓𝑖𝑟𝑠𝑡 𝑔𝑒𝑡 𝑎 𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟

= 32

8− 2

7

8 𝑊𝑒 𝑤𝑖𝑙𝑙 𝑛𝑒𝑒𝑑 𝑡𝑜 𝑏𝑜𝑟𝑟𝑜𝑤 𝑡𝑜 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡

= 210

8− 2

7

8 𝑊𝑒 𝑐𝑎𝑛 𝑛𝑜𝑤 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡 𝑟𝑖𝑔ℎ𝑡 𝑡𝑜 𝑙𝑒𝑓𝑡

= 3

8 𝑓𝑒𝑒𝑡

Media Lesson Multiply Fractions Word Problem (Duration 3:38)


A recipe for banana oat muffins calls for 3

4 cup of old-fashioned oats. You are making

1

2

of the recipe. How much oats should you use?

Media Lesson Multiply Fractions Word Problems (Duration 3:50)


You can ride your bike 1

5 of a mile per minute. If it takes you 3

1

3 minutes to get to your

friend’s house, how many miles away does your friend live?

(FOCUS ON THE SECOND METHOD TO SOLVE THIS)

https://www.youtube.com/watch?v=YJgIGwTysk0

https://www.youtube.com/watch?v=tfjQVtOyoaQ


51

Media Lesson Divide Fractions Word Problem (Duration 2:07)


A baby’s T-shirt requires 4

5 yards of fabric. How many T-shirts can be made from 48

yards?

https://www.youtube.com/watch?v=PQsgXNggV7Q


52

EXERCISES

Use the diagrams given to represent the values in the addition problem and find the

sum. Then perform the operation algebraically.

1) Tom had 1

6 of a carrot cake last night and

2

6 of a carrot cake today. How much of

one whole carrot cake did Tom have?

2) Ava walked 3

8 of a mile to the store and then ran another

7

8 of a mile to school.

How far did she travel in total?

3) 3

4+

2

4

Add or subtract each of the following. Be sure to leave your answer in simplest

form. If your answer is an improper fraction convert it to a mixed number.

4) 5

8+

4

8

5) 4

3−

1

3

6) 2

10+

3

10

7) 7

22+

5

22

8) 9 −5

6

9) 5

7+

4

9

10) 4

5−

1

3

11) 2

3+

3

5


53

12) 3

4+

5

6

13) 51

4− 2

2

3

Divide or multiply. Simplify your answer if possible. If your answer is an improper

fraction convert it to a mixed number.

14) 1

6∙

3

5 15)

8

9∙

9

12

16) 3

8∙ 1

17) 3

8∙ 0

18) 31

3∙ 2

2

5

19) 11

2∙

1

2

20) 18

5÷

9

15

21) 12

5÷

5

6

22) 41

3÷

5

7

23) 51

3÷ 4

3

7

24) 11

3÷ 4

2

3

25) 11

12÷

22

7

Solve the following problems. When necessary, write your final answer as both

mixed numbers and improper fractions in simplest form.

26) If Josh ate 1

4 of a pizza, what fraction of the pizza is left?

27) If I drove 102

3 miles one day and 12

1

4 miles the second day and 8

1

5 miles the third day,

how far did I drive?


54

28) Melody bought a 2-liter bottle of soda at the store. If she drank 1

8 of the bottle and her

brother drank 2

7 of the bottle, how much of the bottle is left?

29) James brought a small bag of carrots for lunch. There are 6 carrots in the bag. Is it

possible for him to eat 2

6 of the bag for a morning snack and

5

6 of the bag at lunch?

Why or why not?

30) Maureen went on a 3 day, 50 mile biking trip. The first day she biked 221

3 miles. The

second day she biked 317

8 miles. How many miles did she bike on the 3rd day?

31) Scott bought a 5 lb bag of cookies at the bakery. He ate 2

5 of a bag and his sister

ate 2

9 of a bag. What fraction of the bag did they eat? What fraction of the bag

remains?

32) Suppose your school costs for this term were $2500 and financial aid covered 3

4 of

that amount. How much did financial aid cover?

33) If, on average, about 4

7 of the human body is water weight how much water weight

is present in a person weighing 182 pounds?

34) If, while training for a marathon, you ran 920 miles in 3 1

2 months, how many miles

did you run each month? (Assume you ran the same amount each month)

35) On your first math test, you earned 75 points. On your second math test, you earned 6

5 as many points as your first test. How many points did you earn on your second

math test?


55

36) You are serving cake at a party at your home. There are 12 people in total and 2 3

4

cakes. (You ate some before they got there!). If the cakes are shared equally among the 12 guests, what fraction of a cake will each guest receive?

Check your work with the answer key!


56

Online Quiz

Log on to Canvas to take the section quiz

Directions: It is very useful to save your math exercise work and use it as a chapter

test review when you study for your chapter test and final.

7) Write each question on the screen down to for your record

8) Solve the problem step by step below each question

9) Double check your work to see whether your answer make sense

10) Enter your answer in the answer box in Canvas. Make sure you click on the

“Preview” button to make sure you enter the right format before you submit your

answer. If you are not sure how to enter your answer with the correct format, ask

your instructor.

11) If you did not answer the question correctly, solve the question again from the

beginning below your 1st attempt. Sometimes, it is better to start a problem again

from the beginning and compare your steps with your 1st attempt to figure out your

mistake.

12) Insert your work at the end of each section in your workbook so that you can use it

to study for your chapter test later.




57

CHAPTER REVIEW

KEY TERMS AND CONCEPTS

Look for the following terms and concepts as you work through the workbook. In the space below, explain the meaning of each of these concepts and terms in your own words. Provide examples that are not identical to those in the text or in the media lesson.

Numerator

Denominator

Equivalent Fraction

Simplest Form

Lowest Terms

Reduce

Simplify

Proper Fraction

Improper Fraction

Mixed Number

Like Denominators

Common Denominators

Reciprocal

Borrow


58

Change from an improper fraction to a mixed number.

1) 12

5 2)

23

6

Change from a mixed number to an improper fraction.

3) 21

3

4) 43

4

Simplify the following fractions.

5) 5

20

6) 12

42

7) 20

25

8) 4

10

9) 32

48 10)

54

72

11) 36

72 12)

18

30

Solve the following. Simplify your answer if applicable. If your answer is improper fraction

convert it to a mixed number.

13) 1

4−

2

7 14)

5

9+ 1

1

6

15) 11

3÷

3

4

16) 3 ×7

8

17) 4 −4

5

18) 6

7÷

7

3

19) 2

3×

4

5 20) 7 ∙

3

5

21) 21

5× 4

1

2

22) 1

2× 3

1

3


59

23) 43

5÷ 2

24) 2

3÷

1

6

25) 3

5+

1

5

26) 11

12+

5

12

27) 3

7+

2

21

28) 85

6+ 7

4

9

29) 71

2− 2

1

3

30) 71

5− 3

1

4

chapter 2: fractions · 2019-08-14 · proper fractions improper fractions mixed numbers fractions...

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