Essential Mathematics
Chapter 2
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
20
Essential Mathematics
Chapter 2
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
1
1
such as . This is “1 divided by 2.” Written as we call 1 the numerator and 2 the
2
2
denominator.
Or, we can think of fractions as a part compared to a whole such as 1 out of 2 cookies or
1
of the cookies.
2
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
21
Essential Mathematics
Chapter 2
B. Fractions in Context
Media Lesson
Fractions in Context: Four Models (Duration 8:12)
View the video lesson, take notes and complete the problems below.
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?
22
Essential Mathematics
Chapter 2
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)
View the video lesson, take notes and complete the problems below.
23
Essential Mathematics
Chapter 2
Media Lesson
Fractions on a Number Line (Duration 4:15)
View the video lesson, take notes and complete the problems below.
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.
0
For example, 5 = 0.
24
Essential Mathematics
Chapter 2
C. Equivalent Fractions
Equivalent fractions are different fractions that are equal or represent the same amount.
Media Lesson
Equivalent Fractions (Duration 7:37)
View the video lesson, take notes and complete the problems below.
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
25
Essential Mathematics
Chapter 2
𝟏𝟖
𝟐𝟒
𝟑
𝟒
𝟗
𝟏𝟐
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
26
Essential Mathematics
Chapter 2
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)
View the video lesson, take notes and complete the problems below.
Fill in the missing numerator in each fraction below to create equivalent fractions.
a)
c)
1
2
4
7
=
=
b)
30
d)
49
14
16
27
45
=
=
8
5
YOU TRY:
Rewrite the given fractions as equivalent fractions given the indicated denominator.
c)
f)
3
7
=
6
11
?
21
=
?
33
d)
g)
10
12
8
12
=
=
?
120
?
24
e)
h)
5
8
3
5
=
=
?
32
?
15
27
Essential Mathematics
Chapter 2
D. Simplifying Fractions
Media Lesson
What is a Simplified Fraction (Stop at 4:28)
View the video lesson, take notes and complete the problems below.
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)
View the video lesson, take notes and complete the problems below.
To reduce fractions we _____________________ common _____________________.
24
15
48
18
28
Essential Mathematics
Chapter 2
YOU TRY:
Simplify the given fractions completely.
6
i)
8
k)
j)
32
l)
44
30
42
15
75
E. Proper Fractions, Improper Fractions, and Mixed Numbers
We use three words to describe fractions: proper, improper, and mixed.
Proper Fractions
Fractions whose
Improper Fractions
Fractions whose
Mixed Numbers
A combination of a whole
numerator is less than their numerator is greater than
number and a proper
denominator.
fraction.
or equal to its
denominator.
8
Examples: 9 𝑎𝑛𝑑
2
7
Examples:
20 3
11
6
5
, 3 , 𝑎𝑛𝑑
1
4
Examples: 1 2 𝑎𝑛𝑑 15 7
YOU TRY:
For the following decide whether the fraction is a proper fraction, improper fraction, or
mixed number.
1
11
a) 3
b)
5
4
c)
11
50
d)
15
15
29
Essential Mathematics
Chapter 2
F. Changing Between Improper Fractions and Mixed Numbers
Media Lesson
Improper Fractions and Mixed Numbers (Duration 6:48)
View the video lesson, take notes and complete the problems below.
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.
2.
3.
4.
Divide the numerator by the denominator.
Write down the whole number.
Place any remainder in the quotient over the denominator.
Simplify the fraction if needed.
Example: Convert
Example: Convert
13
5
32
6
to a mixed number.
to a mixed number.
30
Essential Mathematics
Chapter 2
 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
Example: Convert 7
3
8
into an improper fraction.
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
31
Essential Mathematics
Chapter 2
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)?
32
Essential Mathematics
Chapter 2
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
b) Given fraction:
4
3
is equivalent to the fraction: ________
5
3
5
is equivalent to the fraction: ________
Rewrite the given fractions as equivalent fractions given the indicated numerator or
denominator.
12) Rewrite
14) Rewrite
16) Rewrite
2
with a denominator of 21.
13) Rewrite
with a numerator of 20.
15) Rewrite
3
5
6
36
48
with a numerator of 9.
17) Rewrite
6
7
4
8
5
1
with a numerator of 30.
with a denominator of 2.
with a denominator of 5.
Simplify each of the following fractions if possible.
18)
21)
5
1
1
6
19)
22)
6
6
1
1
20)
23)
0
4
1
0
33
Essential Mathematics
Chapter 2
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
24)
25)
Common Factor
Prime Factorization
12
42
16
100
26) 5
27
63
For the following problems, convert from an improper fraction to a mixed number.
27)
28)
29)
19
5
33
10
52
7
For the following problems, convert from a mixed number to an improper fraction.
30) 1
31) 5
3
8
1
6
5
32) 10 9
Check your work with the answer key!
34
Essential Mathematics
Chapter 2
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.
35
Essential Mathematics
Chapter 2
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)
View the video lesson, take notes and complete the problems below.
Examples: Adding Fractions with Like Denominators
2 3
+
7 7
+
2 1
+
9 9
+
Media Lesson
Adding Fractions (Duration 9:10)
View the video lesson, take notes and complete the problems below.
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
5
+
2
5
=
1 2 3 4 5
36
Essential Mathematics
Chapter 2
 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.
4) Simplify, if possible.
1
2
+
1
4
=
Why do we need to have a common denominator?
ERROR!
1 1 2
+ ≠
2 4 6
1
1
1 1 3
+ =
2 4 4
2
2
3
4
1 2 3 4 5 6
2
4
1
2
3
4
1
4
1
2
3
4
3
4
1
2
3
4
Add.
3 1
+
10 5
3 1
+
4 6
3
5
5 3
+
12 8
3+
37
Essential Mathematics
Chapter 2
Media Lesson
Adding Mixed Numbers (Duration 6:35)
View the video lesson, take notes and complete the problems below.
 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.
1
2
4 +2
4
3
4
11
1 +2
5
15
7
5
3 +2
8
6
YOU TRY:
Add the following fractions and reduce your answer to the lowest terms if possible.
3
2
1
5
b) 5
+4
a) 3
+
5
3
2
6
c)
7
10
+
e) 3 + 2
1
10
d)
2
6
+
1
8
1
2
38
Essential Mathematics
Chapter 2
B. Subtracting Fractions and Mixed Numbers
Media Lesson
Ex: Subtract Fractions with Like Denominators (Duration 3:00)
View the video lesson, take notes and complete the problems below.
Examples: Subtracting Fractions with Like Denominators
7 3
−
8 8
+
4 1
−
9 9
+
Media Lesson
Subtracting Fractions Introduction (Duration 8:29)
View the video lesson, take notes and complete the problems below.
To subtract fractions with like denominators:
1) Keep the denominators the same and subtract the numerators.
2) Simplify, if possible.
1 2 3 4 5
−
3
5
−
1 2 3 4 5
1
5
=
1 2 3 4 5
=
39
Essential Mathematics
Chapter 2
 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.
4) Simplify, if possible.
3
1
Example: 4 − 2 =
1 2 3 4
−
1 2 3 4
=
1 2 3 4
Subtract.
5 7
−
6 12
7 3
−
10 8
5
1
−
12 15
2−
5
14
40
Essential Mathematics
Chapter 2
We will now look at how to subtract mixed numbers.
Media Lesson
Subtract Mixed Numbers (Duration 2:43)
View the video lesson, take notes and complete the problems below.
To subtract mixed numbers we ________________________ and work
_________________ to _________________.
4
1
9 −3
5
2
7
3
7 −2
8
4
Sometimes you need to borrow in order to subtract mixed numbers.
Media Lesson
Subtract with Borrowing (Duration 4:10)
View the video lesson, take notes and complete the problems below.
If we can’t subtract two fractions we may have to ___________________.
2
11
6 −2
5
15
9−5
3
4
41
Essential Mathematics
Chapter 2
Media Lesson
Subtracting Mixed Numbers (Duration 7:15)
View the video lesson, take notes and complete the problems below.
 To subtract mixed numbers:
1.
2.
3.
4.
Obtain a common denominator.
Check to see if you need to borrow.
Subtract the fractions and then the whole numbers.
Simplify if needed.
Subtract.
3
1
4 −2
4
4
4
11
6 −2
5
15
3
5
5 −2
8
6
7
1
1
−2
10
6
12 − 8
3
11
42
Essential Mathematics
Chapter 2
YOU TRY:
Subtract and reduce your answer to the lowest term if possible.
1
1
2
b) 3 −
a) 3 −
2
5
5
2
2
c) 9 9 − 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)
View the video lesson, take notes and complete the problems below.
With multiplication __________________ we can __________________ before
multiplying.
To reduce we _______________________ any common factors in the
__________________ and __________________.
6 14
∙
35 9
25 21
∙
49 10
43
Essential Mathematics
Chapter 2
Media Lesson
Multiply Fractions with Whole Numbers (Only do first example)
View the video lesson, take notes and complete the problems below.
To make a whole number a fraction, ____________________________.
14
∙ 10
15
Media Lesson
Multiplying Fractions: An Explanation (Duration 5:05)
View the video lesson, take notes and complete the problems below.
2 4
× =
3 5
44
Essential Mathematics
Chapter 2
YOU TRY:
Multiply. If possible, simplify and express your answer a mixed number.
2 3
12 35
a) ∙
b)
∙
3 4
25 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)
View the video lesson, take notes and complete the problems below.
Reciprocal:
If we multiply reciprocals the answer will always be __________.
Find the reciprocal.
7
3
9
45
Essential Mathematics
Chapter 2
 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)
View the video lesson, take notes and complete the problems below.
Example: Divide and simplify.
8 16
÷
27 9
2 5
÷
3 2
Media Lesson
Divide with Whole Numbers and Fractions (Duration 2:23)
View the video lesson, take notes and complete the problems below.
Whole numbers can be made into fractions by putting them over ________.
Example 1:
Example 2:
7
28 ÷
8
4
÷ 14
9
46
Essential Mathematics
Chapter 2
YOU TRY:
Divide. If possible, simplify and express your answer a mixed number.
4
1
3
b) 8 ÷
a) ÷
5
2
5
What is the reciprocal of
c)
3
7
3
5
What is the reciprocal of
?
÷5
d)
What is the reciprocal of 5 ?
1
9
÷
4
5
?
1
3
What is the reciprocal of
1
3
?
G. Multiply and Divide Mixed Numbers
Media Lesson
Mixed Numbers- Multiply and Divide (Duration 5:00)
View the video lesson, take notes and complete the problems below.
To multiply or divide mixed numbers we will first change to a _____________________
then we will _____________________ then we will _____________________.
1 5
4 ∙2
8 6
1
5
9 ÷2
3
6
47
Essential Mathematics
Chapter 2
Media Lesson
Example: Division Involving Mixed Numbers (Duration 3:47)
View the video lesson, take notes and complete the problems below.
Example: Divide and simplify.
8÷2
1
2
5
3
4 ÷2
6
4
YOU TRY:
Solve. If possible, simplify your answer and express as a mixed number.
1
1
3
2
a) 3 ∙ 1
b) 1 ÷ 1
5
9
5
3
c)
1
1
6
2
1 ÷4
d)
2
1
3
9
3 ÷
48
Essential Mathematics
Chapter 2
H. Word Problems
Media Lesson
Adding Fractions Word Problem (Duration 5:46)
View the video lesson, take notes and complete the problems below.
Cindy and Michael need 1 gallon of orange paint for the giant cardboard pumpkin they
2
1
are making for Halloween. Cindy has of a gallon of red paint. Michael has of a gallon
5
2
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)
View the video lesson, take notes and complete the problems below.
Silvia is growing tomato plants and studying their heights. Here is her data:
Tomato Type
Beefsteak
Roma
Cherry
Height (feet)
1
3
4
7
2
8
1
3
2
What is the difference between the heights of the Beefsteak and Roma tomato plants?
49
Essential Mathematics
Chapter 2
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.
1
7
1×2
7
3 −2 =3
−2
4
8
4×2
8
2
7
=3 −2
8
8
10
7
= 2 −2
8
8
3
=
𝑓𝑒𝑒𝑡
8
𝐿𝑒𝑡 𝑢𝑠 𝑓𝑖𝑟𝑠𝑡 𝑔𝑒𝑡 𝑎 𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
𝑊𝑒 𝑤𝑖𝑙𝑙 𝑛𝑒𝑒𝑑 𝑡𝑜 𝑏𝑜𝑟𝑟𝑜𝑤 𝑡𝑜 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡
𝑊𝑒 𝑐𝑎𝑛 𝑛𝑜𝑤 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡 𝑟𝑖𝑔ℎ𝑡 𝑡𝑜 𝑙𝑒𝑓𝑡
Media Lesson
Multiply Fractions Word Problem (Duration 3:38)
View the video lesson, take notes and complete the problems below.
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)
View the video lesson, take notes and complete the problems below.
1
1
You can ride your bike 5 of a mile per minute. If it takes you 3 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)
50
Essential Mathematics
Chapter 2
Media Lesson
Divide Fractions Word Problem (Duration 2:07)
View the video lesson, take notes and complete the problems below.
A baby’s T-shirt requires
4
5
yards of fabric. How many T-shirts can be made from 48
yards?
51
Essential Mathematics
Chapter 2
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
of a carrot cake last night and
6
one whole carrot cake did Tom have?
2) Ava walked
3
2
6
of a carrot cake today. How much of
of a mile to the store and then ran another
8
How far did she travel in total?
3)
3
4
+
7
8
of a mile to school.
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)
6)
8)
10)
5
8
+
2
10
5
−
5)
8
+
9−
4
4
3
10
5
6
1
3
7)
9)
11)
4
3
−
7
22
5
7
2
3
1
3
5
+
+
+
22
4
9
3
5
52
Essential Mathematics
12)
3
4
+
Chapter 2
5
13)
6
1
2
4
3
5 −2
Divide or multiply. Simplify your answer if possible. If your answer is an improper
fraction convert it to a mixed number.
14)
16)
18)
20)
1 3
∙
15)
∙1
17)
6 5
3
8
1
2
3
5
3 ∙2
18
5
÷
19)
9
21)
15
1
5
3
7
22)
4 ÷
24)
1 ÷4
23)
1
2
3
3
25)
8
9
∙
9 12
3
8
∙0
1 1
1 ∙
2 2
12
÷
5
5
6
1
3
3
7
5 ÷4
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 10 2 miles one day and 12 1 miles the second day and 8 1 miles the third day,
3
4
5
how far did I drive?
53
Essential Mathematics
Chapter 2
1
28) Melody bought a 2-liter bottle of soda at the store. If she drank of the bottle and her
8
2
brother drank of the bottle, how much of the bottle is left?
7
29) James brought a small bag of carrots for lunch. There are 6 carrots in the bag. Is it
2
5
possible for him to eat of the bag for a morning snack and of the bag at lunch?
6
6
Why or why not?
30) Maureen went on a 3 day, 50 mile biking trip. The first day she biked 21 2 miles. The
3
3
second day she biked 17 miles. How many miles did she bike on the 3rd day?
8
31) Scott bought a 5 lb bag of cookies at the bakery. He ate 2 of a bag and his sister
5
2
ate
of a bag. What fraction of the bag did they eat? What fraction of the bag
9
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 of the human body is water weight how much water weight
7
is present in a person weighing 182 pounds?
34) If, while training for a marathon, you ran 920 miles in 3
1
months, how many miles
2
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
as many points as your first test. How many points did you earn on your second
5
math test?
54
Essential Mathematics
Chapter 2
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!
55
Essential Mathematics
Chapter 2
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.
56
Essential Mathematics
Chapter 2
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
57
Essential Mathematics
Chapter 2
Change from an improper fraction to a mixed number.
1)
12
2)
5
23
6
Change from a mixed number to an improper fraction.
3)
2
1
4)
3
4
3
4
Simplify the following fractions.
5)
7)
9)
11)
5
6)
20
20
8)
25
32
10)
48
36
12)
72
12
42
4
10
54
72
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
1
3
3
4
15)
1 ÷
17)
4−
19)
21)
2
3
14)
×
16)
4
18)
5
4
20)
5
1
1
5
2
2 ×4
22)
5
9
+1
3×
6
7
÷
7∙
1
2
1
6
7
8
7
3
3
5
×3
1
3
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Essential Mathematics
23)
25)
27)
29)
3
4 ÷2
24)
5
3
5
3
7
+
+
1
26)
5
2
21
1
1
2
3
7 −2
Chapter 2
2
3
÷
11
12
1
6
+
5
12
5
4
6
9
1
1
5
4
28)
8 +7
30)
7 −3
59