Name
Reteaching
7-6
Subtracting Mixed Numbers
To subtract mixed numbers, the fractional parts must have the same
denominator. Use one of these methods:
Step 1
Step 2
Find 8_13 2 5_45
Use the LCD to write
equivalent fractions.
Estimate:
5
8_13 5 8__
15
82652
Step 3
Step 4
5
Rename 8__
to show
15
more fifteenths so you
can subtract.
5
8 __
12
5 _45 5 5__
15
Subtract and simplify if
possible.
20
8
12 5 2__
7__
2 5__
15
15
15
15
5
15
7 __
1 __
15
15
20
__
7
15
Find 3_12 – 1 _58
Write each mixed
number as an improper
fraction.
Estimate:
42252
3_12 5 _72
Use the LCD to
rewrite the improper
fractions with the
same denominator.
28
7 5 __
_
2
8
13
__
13
1 _58 5 __
8
8
9 2 2_
3 5
1. 5__
5
10
4. 4_23 2 2 5
5 2 3_
3 5
7. 6__
16
4
10. 7_78 2 2_34 5
13. 7_34 2 2_78 5
3
3__
10
_
2 23
9
2__
16
_
1
58
4_78
3 5
7 2 8_
2. 11__
16
8
7 5
5. 4_14 2 __
12
7 5
8. 8 2 4__
10
11. 3_13 2 1_79 5
14. 3_79 2 1_13 5
1
3__
16
_
323
3
3__
10
_
159
2_49
3. 9_23 2 9_16 5
_
1
2
13
2__
14
_
1
13 5
13
2_15 2 __
15
_
1
12_38 2 5_18 5 7 4
_
3
12_18 2 5_38 5 6 4
13 5
6. 5_67 2 2__
14
9.
12.
15.
16. Number Sense How do you know if you need to rename the first
number in a subtraction problem involving mixed numbers?
If the fractional part of the first number is less
than the fractional part of the second number,
you will have to rename the first number to
subtract.
58
Topic 7
© Pearson Education, Inc. 6
Reteaching 7-6
Find each difference. Simplify if possible.
Subtract and simplify if
possible.
Use this
28
13
__
2 __
5
8
8
method
15
__
when the
5
8
mixed
1_78
numbers
are small.
Name
Practice
7-6
Subtracting Mixed Numbers
Find each difference. Simplify if possible.
1. 2_35 1_15 9 3. 5_58 1__
16
15 4 5. 6__
16
7. 9 7_58 9. 6_89 1_23 1_25
1
4__
16
__
215
16
1_38
5_29
2. 1_49 _89 4. 12 4_56 3 7 2_
6. 3__
12
4
8. 15_16 8_23 5 10. 2_37 1__
14
_
5
9
7_16
_
5
6
6_12
1
1__
14
11. In which of the exercises above do you have to rename the first
mixed number to show more fractional parts before subtracting?
Exercises 2, 4, 6, 7, and 8
The table at the right shows the lengths of
various carpentry nails.
12. How much longer is a 30d nail than a 5d nail?
2_34 in. longer
_
1 in. longer
2
5d
1_34
9d
2_34
12d
3_14
30d
4_12
Practice 7-6
13. How much longer is a 12d nail than a 9d nail?
Carpentry Nails
Length
Size
(inches)
14. To subtract 4_56 from 10_13 , which of the following must the mixed
number 10_13 first be renamed as?
A 9_23
B 9_46
C 9_86
© Pearson Education, Inc. 6
D 10_26
15. Writing to Explain Jack says that once you have a common
denominator you are ready to subtract two mixed numbers. What
other step might be necessary before you can subtract? Give an
example.
Sample answer:
The larger number may need to be renamed.
For example, 3_14 ⴚ 1_12 ⴝ 3_14 ⴚ 1_24 ⴝ 2_54 ⴚ 1_24 .
Topic 7
59