Name
Reteaching
9-4
Estimating Quotients
When you are working with fractions and mixed numbers, you can
estimate using rounding and compatible numbers.
Estimate 23_56 ! 8_37 .
Estimate 31_16 ! 4_58 .
23_56 ! 8_37
Round each mixed
number to the
nearest whole
number.
24 ! 8 " 3
Divide.
30 ! 5 " 6
23_56 ! 8_37 ! 3
31_16 ! 4_58 " 6
Change 31_16 and
4_58 to the nearest
compatible whole
numbers.
Think: 31_16 and 4_58
are close to 30
and 5.
Estimate each quotient.
1. 11_12 ! 6_14
2. 19_13 ! 3_23
3. 41_79 ! 7_15
4. 35_18 ! 5_45
5. 61_38 ! 8_59
6. 72_29 ! 7_78
7. 86_34 ! 10_56
9 ! 2_
5
8. 26__
10
8
9. 11_27 ! 3_35
6 ! 7__
1
11. 47__
10
12
5 ! 5_
4
12. 60__
12
9
9 ! 2__
3
10. 7__
10
10
13. Critical Thinking Which of these two estimates is closer to the actual quotient?
How do you know?
Lisa’s estimate: 55_12 ! 6_34 " 54 ! 6 " 9
Hayden’s estimate: 55_12 ! 6_34 " 56 ! 7 " 8
14. Patrick uses wire to make wreaths. He has 31_12 feet of wire left on
a spool. Estimate how many 3_34 pieces can he cut from the longer
piece of wire.
© Pearson Education, Inc. 6
Reteaching 9-4
31_16 ! 4_58
44
Topic 9
Name
Reteaching
9-4
Estimating Quotients
When you are working with fractions and mixed numbers, you can
estimate using rounding and compatible numbers.
Estimate 23_56 ! 8_37 .
23_56 ! 8_37
Round each mixed
number to the
nearest whole
number.
24 ! 8 " 3
Divide.
23_56 ! 8_37 ! 3
4. 35_18 ! 5_45
7. 86_34 ! 10_56
9 ! 2__
3
10. 7__
10
10
30 ! 5 " 6
31_16 ! 4_58 " 6
Estimate each quotient.
1. 11_12 ! 6_14
31_16 ! 4_58
2
6
8
4
Change 31_16 and
4_58 to the nearest
compatible whole
numbers.
Think: 31_16 and 4_58
are close to 30
and 5.
Sample answers are shown.
2. 19_13 ! 3_23 5
3. 41_79 ! 7_15
5. 61_38 ! 8_59 7
6. 72_29 ! 7_78
9 ! 2_
5 9
8. 26__
9. 11_27 ! 3_35
10
8
6 ! 7__
5 ! 5_
1 7
4
11. 47__
12. 60__
10
12
12
9
6
9
3
10
13. Critical Thinking Which of these two estimates is closer to the actual quotient?
How do you know?
Lisa’s estimate: 55_12 ! 6_34 " 54 ! 6 " 9
Hayden’s estimate: 55_12 ! 6_34 " 56 ! 7 " 8
Sample answer: Hayden’s estimate is closer because he
used numbers closer to the original numbers.
14. Patrick uses wire to make wreaths. He has 31_12 feet of wire left on
a spool. Estimate how many 3_34 pieces can he cut from the longer
piece of wire.
Sample answer: About 8 pieces
© Pearson Education, Inc. 6
Reteaching 9-4
Estimate 31_16 ! 4_58 .
44
Topic 9