Fraction Subtraction (with Models)
Subtracting fractions requires a firm understanding of the meaning
of a fraction’s numerator (the number of fractional parts at hand) and
denominator (the number of fractional parts in the whole) as well as
facility in naming equivalent fractions. When two or more fractions have
like denominators, the problem solver subtracts the numerators: that is,
the problem solver subtracts the number of fractional parts at hand. The
number of fractional parts in the whole—the denominator—does
not change.
As is the case with adding fractions, subtracting fractions that have unlike
denominators requires an additional step. The problem solver must first
rename the fractions so that they have like denominators.
Build Understanding
Subtraction
Review the process of finding common multiples and common denominators.
5 - __
3 - __
1 and __
2.
Ask students to find common denominators for problems like __
6
3
4
3
Using page 39, explain that when subtracting fractions with different
denominators, students will need to find a common multiple of the
denominators, or a common denominator. Then, they will rename the fractions
as equivalent fractions having common denominators. Remind students
that renaming fractions will be easier if they use the smallest common
denominator. Use questions like the following to guide students through
the examples:
• To subtract fractions having the same denominator, what do you do to the
numerators? (You subtract them.) What do you do to the denominator?
(Nothing. It stays the same.)
5 and __
1 ? (12)
• In Example 2, what is a common denominator of __
6
4
5 so that it has a denominator of 12, which number
• When renaming __
6
will you multiply by the denominator? (2, because 6 * 2 = 12)
Error Alert Watch for students who multiply incorrectly when they find
common denominators. Stress the need to multiply both the numerator and
the denominator by the same number.
2
1. _5
Check Understanding
1
2. _2
Divide the class into groups of 3 and ask each group to solve the problem
3 . Have one member of the group draw a diagram of the problem. Have
1 - ___
__
2
10
the other members use the algorithm. The group members then compare the
answers to make sure they are the same. If they are not the same, have the
group members correct the error. Circulate around the room checking students’
work. When you are reasonably certain that most of your students understand
the algorithm, assign the “Check Your Understanding ” exercises at the bottom
of page 39. (See answers in margin.)
2
3. _9
5
4. __
12
1
5. _8
Copyright © Wright Group/McGraw-Hill
Page 39
Answer Key
1
6. _2
1
7. __
24
1
8. __
48
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Teacher Notes
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Name
Date
Time
Fraction Subtraction (with Models)
Check that the addends have like denominators.
Then subtract the numerators to find the difference.
The denominator does not change.
The denominators are the same.
Subtract the numerators.
Example 2
The denominators are not the same.
Copyright © Wright Group/McGraw-Hill
Rename each fraction with a
common denominator.
Subtract the numerators.
Subtraction
6
_
7
2
- _7
4
_
7
Example 1
5
_
6
1
-_
4
5
5∗2
10
_
= ____ = __
6
6∗2
12
1∗3
3
- _1 = ____ = __
4∗3
12
4
7
__
12
Check Your Understanding
Solve the following problems.
4
2
1. _5 - _5
7
3
2. _8 - _8
7
5
3. _9 - _9
2
1
4. _3 - _4
1
3
5. _2 - _8
3
1
6. _5 - __
10
7
5
7. _8 - _6
11
2
-_
8. __
16
3
Write your answers on a separate sheet of paper.
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Student Practice
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