﻿ Estimating Products and Quotients Worksheet | Problems & Solutions

Estimating Products and Quotients Worksheet

Estimating Products and Quotients Worksheet
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1.
Round each factor to the nearest whole number to estimate the quotient of 95.24 ÷ 18.73.
 a. 6 b. 7 c. 8 d. 5

Solution:

95.24 ÷ 18.73
[Original numerical expression.]

= 95 ÷ 19
[Round 95.24 to the nearest whole number 95 and 18.73 to the nearest whole number 19.]

= 5
[Divide.]

2.
Estimate the product of 39.84 and 5.24. Round to the nearest whole number.
 a. 195 b. 190 c. 234 d. 200

Solution:

39.84 × 5.24
[Original factors.]

39.84 when rounded to nearest whole number becomes 40.
[The digit in the tenths place is 8, which is greater than 5. So, round up the whole number.]

5.24 when rounded to the nearest whole number becomes 5.
[The digit in the tenths place is 2, which is less than 5. So, round down the whole number.]

40 × 5
[Replace the original factors with their rounded values.]

= 200
[Multiply.]

So, the estimated product of 39.84 and 5.24 = 200.

3.
Estimate the quotient of 54.21 ÷ 17.95. Round to the nearest whole number.
 a. 3 b. 4 c. 5 d. 6

Solution:

54.21 ÷ 17.95
[Original numerical expression.]

= 54 ÷ 18
[Round 54.21 to the nearest whole number 54 and 17.95 to the nearest whole number 18.]

= 3
[Divide.]

4.
Between which two numbers does the quotient of 100.98 ÷ 9 lie?
 a. 9 and 10 b. 12 and 13 c. 10 and 11 d. 11 and 12

Solution:

100.98 ÷ 9
[Original numerical expression.]

= 99 ÷ 9
[Use compatible number such as 99 for 100.98.]

= 11
[Divide.]

As 100.98 is greater than 99, the quotient of 100.98 ÷ 9 will also be greater than 11.

So, the quotient of 100.98 ÷ 9 lies between the numbers 11 and 12.

5.
Estimate the product of 13.4 and 1.4 after rounding each of them to its nearest whole number.
 a. 9 b. 13 c. 17 d. 19

Solution:

13.4 x 1.4
[Original factors.]

13 x 1
[Rounding 13.4 to the nearest whole number 13 and 1.4 to the nearest whole number 1.]

= 13
[Multiply.]

6.
Estimate the product of 0.77 and 97.43 by rounding each factor to the nearest whole number.
 a. 99 b. 96 c. 97 d. 98

Solution:

0.77 × 97.43
[Original factors.]

1 × 97
[Rounding 0.77 to the nearest whole number 1 and 97.43 to the nearest whole number 97.]

97
[Multiply.]

The estimated product of 0.77 and 97.43 after rounding each factor to the nearest whole number is 97.

7.
Estimate the product of 2.37 and 4.97 by rounding each factor to the nearest whole number.
 a. 8 b. 15 c. 10 d. 12

Solution:

2.37 x 4.97
[Original factors.]

2.00 x 5.00
[Round 2.37 to the nearest whole number 2.00 and 4.97 to the nearest whole number 5.00.]

10
[Multiply.]

The value of 2.37 x 4.97 after being rounded is 10.

8.
Estimate the product of 21.23 and 3.23 after rounding each factor to the nearest whole number.
 a. 58 b. 61 c. 63 d. 68

Solution:

21.23 × 3.23
[Original factors.]

= 21 × 3
[Round 21.23 to the nearest whole number 21 and 3.23 to the nearest whole number 3.]

= 63
[Multiply.]

9.
Round 2.33 and 1.85 to their nearest whole numbers and estimate their product.
 a. 4 b. -4 c. 9 d. -1

Solution:

2.33 x 1.85
[Original factors.]

= 2 x 2
[Round 2.33 to the nearest whole number 2 and 1.85 to the nearest whole number 2.]

= 4
[Multiply.]

10.
Estimate the product of 68.9 and 43.1 using compatible numbers.
 a. 2800 b. 2810 c. 2820 d. 2780

Solution:

Compatible numbers are numbers that are easy to compute mentally.

68.9 × 43.1
[Original factors.]

= 70 × 40
[Use compatible numbers such as 70 for 68.9 and 40 for 43.1.]

= 2800
[Multiply.]

The estimated product of 68.9 and 43.1 using compatible numbers = 2800.