Fraction Addition (with Models)
Addition
Fraction addition 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 adding two or more fractions with like denominators, the problem
solver simply adds the numerators or the number of fractional parts in
each addend. The denominator that shows the number of fractional parts
in the whole does not change.
When adding fractions that have unlike denominators, the problem solver
must first rename the addends using a common denominator.
Build Understanding
Review the process of finding common multiples. Have students list a few
multiples of 4 (4, 8, 12, 16, 20, 24) and 6 (6, 12, 18, 24, 30, 36). Then ask them to
circle any numbers that are on both lists. Tell students that the circled numbers
are common multiples of 4 and 6. If necessary, have students find common
multiples of other number pairs, such as 4 and 10, 6 and 8, and 6 and 9.
Using page 21, explain that when adding fractions with different
denominators, students will need to find a common multiple of the
denominators, or a common denominator. Then, they will rename these
fractions using this common denominator. You may want to explain that
renaming fractions will be easier if students use the smallest common
denominator. Use questions like the following to guide students through
the examples:
• If you add fractions with the same denominator, what do you do to
the numerators? (You add them.) What do you do to the denominator?
(Nothing. It stays the same.)
Page 21
Answer Key
6
1. _7
3 with a denominator of 12, which number will you
• To rename __
4
multiply each part of the fraction by? (3, because 4 * 3 = 12)
3
2. _4
Error Alert
7
4. __
12
Watch for students who add denominators. If it helps these
students, tell them to draw a diagram for each problem. This will help them
see the denominator as the number of fractional parts in the whole. Also,
watch for students who have difficulty finding common denominators. Explain
to students that an easy way to find a common denominator of two fractions is
to find the product of the two denominators.
5
5. _8
Check Understanding
2
3. 1 _3
Divide the class into groups of 3 and ask each group to solve the problem
1 + __
2 . Have one member of the group draw a diagram of the problem. Have
__
2
5
the other members use the algorithm. The group members then compare
their answers to make sure they are the same. If they are not the same, have
the group members correct the error. When you are reasonably certain that
most of your students understand the algorithm, assign the “Check Your
Understanding ” exercises at the bottom of page 21. (See answers in margin.)
5
6. _6
17
7. __
24
1
8. 1 __
24
20
Copyright © Wright Group/McGraw-Hill
3 ? (12)
1 and __
• In Example 2, what is a common denominator of __
3
4
1 with a denominator of 12, which number will you
• To rename __
3
multiply each part of the fraction by? (4, because 3 * 4 = 12)
Teacher Notes
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Name
Date
Time
Fraction Addition (with Models)
1
_
5
3
+ _5
4
_
5
Example 1
The denominators are the same.
Add the numerators.
The denominators are not the same.
Copyright © Wright Group/McGraw-Hill
3
1
_
+_
5
5
1
_
3
3
+_
4
Example 2
Rename both fractions as
equivalent fractions having
a common denominator.
Addition
Check that the addends have like denominators.
Then add the numerators to find the sum.
The denominator does not change.
1
1∗4
4
_
= ____ = __
3
3∗4
12
3
3∗3
9
+ _ = ____ = __
4
4∗3
12
13
__
12
3
13
1
1
_
+ _ = __, or 1__
3
4
12
12
Add the numerators.
Check Your Understanding
Solve the following problems.
4
2
1. _7 + _7
1
1
5. _2 + _8
5
1
2. _8 + _8
2
1
6. _3 + _6
5
5
3. _6 + _6
3
1
7. _3 + _8
Write your answers on a separate sheet of paper.
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21
1
1
4. _3 + _4
5
5
8. _8 + __
12
Student Practice
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