Date:________________________________
Math 7 – Chapter 5 – Fraction Operations
Name: _____________________________
Class: _____________________________
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Date:________________________________
5.0 Activating Prior Knowledge
Fractions are made up of two parts, a numerator and denominator.
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
Fractions can be made into equivalents by multiplying or dividing both the numerator
and denominator by the same number.
Equivalent Fractions
Quick Review
 To find an equivalent fraction with a greater numerator and denominator,
multiply the numerator and denominator by the same number.
2
7
9
=
3
14
18
7
9
=
5
21
27
7
9
2
3
14 21
35
7
, , and
are equivalent to .
18 27
45
9
=
35
45
5
 To find an equivalent fraction with a lesser numerator and denominator,
divide the numerator and denominator by the same number.
6
36
48
=
2
6
8
6
8
6
6
36
8 is equivalent to 48.
6
36
is a simpler form of .
8
48
=
3
4
2
3
6
36
4 is equivalent to 8 and 48.
3
36
is the simplest form of .
4
48
Try these. Find two equivalent fractions for each given fraction.
1.
5
10
2.
10
15
3.
3
4
2
Date:________________________________
5.1 Using Models to Add Fractions
A fraction is a number that written as a quotient of two whole
numbers.
For example:
2 7
1
, and 2 are all fractions.
5 3
4
Fractions can be represented by pattern blocks.
yellow hexagon = 1
blue rhombus =
1
2
red trapezoid =
1
3
green triangle =
1
6
Example:
Use the pattern blocks to represent the fractions:
1.)
2
3
2.)
5
6
3.) 2
1
2
Fractions can also be represented using fraction circles. To
represent any fraction, use the bottom number (the denominator) to
determine the number of pieces in your circle and the top number
(the numerator) to determine how many of the pieces are shaded.
For example: Draw the fraction circle for
3
5
We can use these models to help add fractions.
For example: model and add
2 1
 .
3 6
3
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5.2 Using Other Models to Add Fractions
Try this:
Use either the pattern blocks or fraction circles, to model and then
add
1 3
1 
5 10
Be sure to draw out the models as part as your solution!
Notes:
Fractions can also be modeled with fraction strips. These
are strips of paper that are placed on a number line to add fractions.
Example: The fraction strip for
1
is
3
⅓
0
1
3
2
3
1
To add fraction strips, we place both fraction strips on the number line
and use equivalent fractions (fractions that have different denominators
but represent the same number) to determine the sum.
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Example:
Add.
1
3

2
8
1
0
2
3
8
1
2
1
2
1
2
 4
 or 
 8
answer:
Use this method to add
7
8
1
5
and
.
3
6
5
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5.3 Using Symbols to Add Fractions
Try This:
So far, you have learned about two methods of modeling adding
fractions. List one positive and negative thing about each modeling method.
Pattern Blocks/Fraction Circles:
Fraction Strips
Use your favorite method to add:
2 3

5 10
Notes:
Using the fraction strips, pattern blocks and fraction circles creates a
mental image on how to add fractions. However, using these models to add
fractions may not be the most effective method of adding fractions.
We can add fractions by finding the common denominator and
adding.
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Date:________________________________
Examples:
1.) Add.
3 1

5 2
2.) Add.
2 2

7 3
3.) Add.
7 2

10 3
*remember that creating the mental picture (by using pattern blocks,
fraction strips or fraction circles) of each addition statement may help you
gain a better understanding of adding fractions.
** you must leave your answer in simplest form (or lowest terms) which
means the numerator and denominator cannot have a common factor
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Date:________________________________
5.4 Using Models to Subtract Fractions
Try This:
Write a step-by-step explanation of how to add fractions that have
different denominators. Create an example and complete it using your
process.
Notes:
All of the addition models learned can be used to subtract fractions. The
only difference is that instead of adding the blocks, strips or circle pieces,
you need to subtract them.
Example: Subtract using pattern blocks.
2
1

3
6
8
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Example: Subtract using fraction circles.
3
1

8
4
Example: Subtract using fraction strips.
7
1

12
3
9
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5.5 Using Symbols to Subtract Fractions
Try This:
1
of a pizza
3
1
1
himself. His friend Eric ate of a pizza and Donna ate . How much pizza
5
4
Dave had a pizza party with some friends. He ate
was left after they were all done. Use pattern blocks, fraction circles or
fraction strips to model and solve this problem.
Notes:
As with addition, when subtracting fractions, you must have a
common denominator. Once you have found the common denominator,
you can subtract the numerators.
Example: Subtract.
1.)
11 2

12 3
10
Date:________________________________
2.)
3
5

4
8
3.)
7
1

3
6
*remember to leave your answer in simplest form
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Date:________________________________
5.6 Adding with Mixed Numbers
Try This:
The difference between two fractions is
between 0 and
9
. The smallest fraction is
12
1
. What can you say about the larger fraction? How do you
2
know?
If the smaller fraction is
1
, what is the larger fraction?
3
Notes:
Fractions can be grouped into two categories: proper fractions
(where the numerator is smaller than the denominator) and improper
fractions (where the numerator is larger than the denominator). If you have
improper fractions, you can rewrite it as a mixed number (where the
numerator is reduced to include a whole number before the fraction).
Example: Convert
8
to a mixed number.
5
12
Date:________________________________
Example: Convert 2
3
to an improper fraction.
4
2
3
1
6
Example: Using fraction circles to add 1  2 .
Notice that the whole numbers can be added separately from the
fraction portion without changing the answer. To add mixed numbers
(without using the modeling techniques), we can add the whole numbers
separately after adding the fractions. Additionally, fractions can be turned
into improper fractions and added the same as proper fractions. This is our
PREFERED METHOD.
Example: Add.
1.
4 3
1 
5 10
2.
1 1
3 1
4 3
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5.7 Subtracting with Mixed Numbers
Try This:
Nellie was in charge of a school pie sale. In the fundraiser, pies were
sold by the slice in the cafeteria at lunch. At the end of lunch, Nellie
3
8
determined how many pies were left. She saw that there was 1 apples
pies left,
2
1
1
of the cherry pie, 2 of the blueberry and of the banana
5
3
5
cream pie. How many pies are left?
Notes:
The process for subtracting mixed numbers is the same as adding
mixed numbers. You need to convert the mixed numbers into improper
fractions and then use the same process you used when subtracting proper
fractions
Example: Using fraction circles, subtract 2
7
2
1 .
10
5
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Example: Using symbols, subtract
1.)
4 1
2 1
5 3
2.)
4
3.)
2 1
2 
5 2
8
3
2
15
10
15
Date:________________________________
5.8 Chapter Review
Try This:
Write (in your own words) a procedure you can use to add or
subtract mixed numbers. Create an example and solve it using
your process. Be specific as possible and try to use the proper
terms in your explanation.
I should be able to:
 Use pattern blocks, fraction circles, fraction strips to
model addition and subtraction of simple fractions and
mixed numbers
 Add and subtraction simple fractions and mixed
numbers without using a modeling technique
 Create equivalent fractions with or without a
modeling technique
 Convert improper fractions to mixed numbers
 Convert mixed numbers to improper fractions
 Determine the common denominator of two or more
fractions
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