Mixed-Number Subtraction
A mixed number names one or more wholes and a fractional part of a
1 names 5 wholes and __
1
whole. For example, the mixed number 5__
2
2
of another whole. Therefore, when problem solvers subtract mixed
numbers, they combine the process of subtracting whole numbers and the
process of subtracting fractions.
When subtracting mixed numbers, most people prefer to subtract the
fractions first because this makes the process a bit less cumbersome when
renaming is required. However, problem solvers with good number sense
may approach such problems in either way.
Build Understanding
Subtraction
1 . On the
Ask students to draw a picture that shows 2 __
3
board, draw the picture on the right and write the
1 can be written
fractions below it. Explain that 2 __
1 +
3
3
1
4
1 as
__
__
__
as 1 + 3 + 3 , or 1 3 . Then have students rename 3 __
5
5 + __
6 and 1 __
5 . Give students problems
1 = 2 __
1 as __
4 + __
1 = __
2 + __
5
5
5
4
4
4
4
to try on their own.
—3—
3
+
—1—
3
1—4—
3
Using page 41, explain that when subtracting mixed numbers, students will
need to rename the minuend (the top number) if the minuend is a whole
number or if the fraction part of the minuend is smaller than the fraction part
of the subtrahend. In Example 1, students must rename the whole number.
Example 2 requires students first to rename the fractions so that they have
a common denominator and then rename the minuend so that subtraction
is possible. Use questions like the following to guide students through the
examples:
3 , so that it has the
• In Example 1, how is the minuend (5) renamed? (as 4 __
3
2
__
same denominator as the subtrahend 2 3 )
Page 41
Answer Key
3
1. 2 __
8
6 + __
8 .)
2 ? (You rename it as 6 + __
2 , or 6 __
• How do you rename 7 __
6
6
6
6
• In Examples 1 and 2, do you need to simplify the difference? (No.
The difference is already in simplest form.)
2
2. _5
1 as 2 __
6
Watch for students who rename a minuend like 2 __
5
5
6
5
__
__
instead of 1 5 . Remind students that they are renaming 2 as 1 5 . Crossing out
Error Alert
4
3. 2 __
7
the 2 and writing a 1 above it, similar to the way students regroup to subtract
whole numbers, might be helpful. Also, make sure students simplify the
difference if necessary after they are done subtracting.
1
4. 1 __
4
5
5. _8
Check Understanding
Copyright © Wright Group/McGraw-Hill
1 and __
1 ? (6)
• In Example 2, what is the common denominator of __
3
2
2 ) again?
• In Example 2, why do you need to rename the minuend (7 __
6
3
2
__
__
(because 6 in the minuend is smaller than 6 in the subtrahend)
1 on the board. Have a volunteer go to the board and solve the
Write 7 − 4 __
5
2 − 4 __
1,
problem. Repeat the process with the following problems: 7 __
5
5
1
2
1
1
__
__
__
__
7 5 − 4 5 , and 7 5 − 4 3 . Continue until you are reasonably certain that most
of your students understand the algorithms. Then assign the “Check Your
Understanding ” exercises at the bottom of page 41. (See answers in margin.)
1
6. 3 __
2
5
7. __
12
7
8. 1 __
24
40
Teacher Notes
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Name
Date
Time
Mixed-Number Subtraction
Use what you know about subtracting whole numbers and fractions
to subtract mixed numbers. Check for like denominators when you
subtract the fractions. Simplify the difference if necessary.
2
5 - 2 _3
Example 1
3
4 _3
Rename the whole number.
2
- 2_
3
Subtract the whole numbers.
1
1
1
7 _3 - 5 _2
Example 2
2
7 _6
Rename the fractions so that they
have a common denominator.
Rename the minuend so that
you can subtract.
Copyright © Wright Group/McGraw-Hill
Subtraction
2 _3
Subtract the fractions.
Simplify the difference if necessary.
3
- 5_
6
8
6 _6
Subtract the fractions.
3
- 5_
6
Subtract the whole numbers.
Simplify the difference if necessary.
5
1 _6
Check Your Understanding
Solve the following problems.
5
3
5
3
1. 4 - 1 _8
2. 1 - _5
3
5. 2 _8 - 1 _4
1
5
6. 6 _3 - 2 _6
1
2
_
7. 1 __
-1
12
3
Write your answers on a separate sheet of paper.
EM3_ALRH_Part 1_004-082_PDF.indd41
1
3. 3 _7 - 1 _7
41
1
1
4. 10 _2 - 9 _4
1
7
8. 8 _6 - 6 _8
Student Practice
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