Name
Reteaching
8-2
Estimating Products
When you are working with fractions and mixed numbers, you can estimate using
rounding, compatible numbers, or compatible benchmark fractions.
3 ! 21 ≈ 6
__
10
Think: 20 ÷ 10 " 2.
3 ! 12 using a compatible
Estimate __
10
benchmark fraction.
3 to a compatible
3 ! 12
__
Round __
10
10
3 is
benchmark fraction. Since __
10
1
_
close to 4 and 4 is a factor of
1 ! 12 " 3
_
twelve, use _14 .
4
3 ! 12 ≈ 3
__
10
Think: 12 # 4 " 3.
1 ! 3 " 3.
3 ! 2 " 6.
Estimate each product by using compatible numbers or benchmark fractions.
1. _16 ! 19 "
2.
4 ! 10 "
_
7
3. _58 ! 23 "
4. 31 ! _25 "
7 ! 18 "
5. __
12
9 ! 90 "
6. __
16
7. 43 ! _27 "
5 "
8. 35 ! __
12
9. 16 ! _49 "
Estimate each product by rounding each factor to the nearest whole number.
10. 6_23 ! 5_18 ‡ Round 6_23 :
11. 10_29 ! 4_56 "
Round 5_18:
12. 2_78 ! 3_34 =
Multiply:
4 "
13. 4_15 ! 2__
10
14. Reasonableness Carlotta estimated that _37 ! 20 is about _37 ! 14 " 6. Is her estimate
reasonable? Why or why not?
6 ! 18 shown below different? Is one
15. Critical Thinking Why are the estimates of __
10
estimate better than the other?
6 ! 18 ≈ __
6 × 20 " 12
__
10
10
6 × 18 ≈ _
1 ! 18 " 9.
__
10
2
© Pearson Education, Inc. 6
Reteaching 8-2
3 ! 21 using a whole number
Estimate __
10
that is compatible with the denominator.
3 ! 21
__
Change 21 to the nearest
10
whole number that is
compatible with 10.
3 ! 20 " 6
__
10
24
Topic 8
Name
Reteaching
8-2
Estimating Products
When you are working with fractions and mixed numbers, you can estimate using
rounding, compatible numbers, or compatible benchmark fractions.
3 ! 21 ≈ 6
__
10
Think: 20 ÷ 10 " 2.
3 ! 12 using a compatible
Estimate __
10
benchmark fraction.
3 to a compatible
3 ! 12
__
Round __
10
10
3 is
benchmark fraction. Since __
10
‚
‚
1
_
close to 4 and 4 is a factor of
1 ! 12 " 3
_
twelve, use _14 .
4
3 ! 12 ≈ 3
__
10
Think: 12 # 4 " 3.
1 ! 3 " 3.
3 ! 2 " 6.
Sample answers are shown.
Estimate each product by using compatible numbers or benchmark fractions.
1. _16 ! 19 "
4. 31 ! _25 "
7. 43 ! _27 "
3
12
12
2.
4 ! 10 "
_
7
7 ! 18 "
5. __
12
5 "
8. 35 ! __
12
5
9
15
3. _58 ! 23 "
9 ! 90 "
6. __
16
9. 16 ! _49 "
15
45
8
Estimate each product by rounding each factor to the nearest whole number.
10. 6_23 ! 5_18 ‡ Round 6_23 :
11. 10_29 ! 4_56 "
50
7
Round 5_18:
12. 2_78 ! 3_34 =
12
5
Multiply:
35
4 "
13. 4_15 ! 2__
10
8
14. Reasonableness Carlotta estimated that _37 ! 20 is about _37 ! 14 " 6. Is her estimate
reasonable? Why or why not?
No, a better
choice for a number compatible to
__
3
20 is 21: 7 ! 21 " 9.
6 ! 18 shown below different? Is one
15. Critical Thinking Why are the estimates of __
10
estimate better than the other?
6 ! 18 ≈ __
6 × 20 " 12
__
10
10
6 × 18 ≈ _
1 ! 18 " 9.
__
10
2
Sample answer: The first estimate uses a
compatible whole number to estimate and the
second uses a compatible benchmark fraction.
Both are reasonable ways to estimate, and in this
case, one method is not better than the other.
24
Topic 8
© Pearson Education, Inc. 6
Reteaching 8-2
3 ! 21 using a whole number
Estimate __
10
that is compatible with the denominator.
3 ! 21
__
Change 21 to the nearest
10
whole number that is
‚
‚
compatible with 10.
3 ! 20 " 6
__
10