Solved Examples and Worksheet for Estimation-Whole Numbers

Q1603 people attended the circus last Sunday. If the average cost of a ticket was $19, estimate the amount of money collected.

A. $12,000
B. $10,000
C. $6,000
D. $20,000

Solutions
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Step: 1
Number of people attended the circus last Sunday = 603
Step: 2
The average cost of a ticket = $19
Step: 3
Estimated amount of money collected = number of people who attended × cost of ticket
Step: 4
= 603 × 19
Step: 5
= 600 × 20
  [Round each number in the product to the nearest 10.]
Step: 6
= 12,000
  [Simplify.]
Correct Answer is :   $12,000
Q2A school is planning to take 350 students on a trip. If a bus can accommodate 22 children, about how many buses should the school arrange for if 12 teachers are accompanying them?
A. 18
B. 16
C. 25
D. 20

Solutions
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Step: 1
Total number of members in the college = 350+12 = 362
Step: 2
Round down 362 to 360 .
Step: 3
Number of people that can be accommodated in a bus = 22.
Step: 4
Round down 22 to 20.
Step: 5
Number of buses needed = Number of members of the college ÷ Number of persons a bus can accommodate.
Step: 6
36020= 18
Step: 7
About 18 buses are needed for the trip.
Correct Answer is :   18
Q3Each package contains 29 stickers. Beth bought 18 packages of stickers. To estimate the total number of stickers she multiplied 30 × 20. Would Beth's estimate be MORE or LESS than the actual product?

A. More, because she rounded both numbers down.
B. Less, because she rounded both numbers down.
C. Less, because she rounded both numbers up.
D. More, because she rounded both numbers up.

Solutions
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Step: 1
Actual total number of stickers = Number of stickers × Number of stickers in each pack
Step: 2
= 29 × 18 = 522
  [Substitute the values and multiply.]
Step: 3
Estimated number of stickers = 30 × 20 = 600
Step: 4
Beth's estimate would be more as she rounded up both the numbers.
Correct Answer is :   More, because she rounded both numbers up.
Q4In a game that Marta is playing, she scores 63 points for each target that she hits. If Marta hits 21 targets estimate the total points that she would score.
A. Marta scored less than 60 points.
B. Marta scored more than 1,200 points.
C. Marta scored about 60 points.
D. Marta scored less than 1,200 points.

Solutions
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Step: 1
Score for each target she hits is 63 points, round down to 60 points.
Step: 2
Number of targets hit is 21, round down to 20.
Step: 3
Total points she scored = Points she scores for each target × Number of targets
Step: 4
= 60 × 20 = 1200
  [Substitute the values and multiply.]
Step: 5
As we are rounding down both the values, actual total points she scored are more than estimated total points.
  [Substitute the values and multiply.]
Step: 6
So, the total points that she scored are more than 1200.
Correct Answer is :   Marta scored more than 1,200 points.
Q5A class of 59 students was divided into different groups containing 5 students in each of them. Estimate the number of groups that can be formed.

A. 10
B. 12
C. 11
D. 20

Solutions
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Step: 1
An estimate is enough to find the number of groups that can be made with 59 students.
Step: 2
Number of students in each group = 5
Step: 3
Total number of students in the class = 59
Step: 4
59 can be rounded to 60.
  [Round 59 to nearest ten.]
Step: 5
Number of groups that can be made with the given number of students = Total number of students rounded to nearest ten ÷ Number of students in each group
Step: 6
= 60 ÷ 5 = 12
  [Divide 60 by 5.]
Step: 7
Therefore, the estimated number of groups that can be formed is 12.
Correct Answer is :   12
Q6Bryan earns $140 as match fee per match. He plays between 62 and 65 matches per season. He estimated that he would earn $8300 per season. Did he underestimate or overestimate his seasonal earnings?

A. Bryan found the exact amount he will earn per week.
B. Bryan under estimated his earnings.
C. Insufficient data
D. Bryan over estimated his earnings.

Solutions
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Step: 1
Bryan earnings per match = $140
Step: 2
Number of matches he plays per season = 62 to 65 = 60
  [Round down to 60.]
Step: 3
Estimated earnings = 140 × 60 = $8400
  [Earnings per match × Number of matches he plays.]
Step: 4
Bryan's estimated earning per season = $8300
Step: 5
Bryan's estimation is less than Actual estimation.
  [$8300 < $8400.]
Step: 6
So, Bryan under estimated his seasonal earnings.
Correct Answer is :   Bryan under estimated his earnings.
Q7Each shirt costs $19. Ray wants to buy 4 shirts. To estimate the amount of money he needs, Ray should ___ .

A. round down 19 to 15.
B. round up 19 to 20.
C. round down 19 to 10.
D. round down 19 to 18.

Solutions
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Step: 1
To estimate how much money Ray needs, he should first approximate the amount $19.
Step: 2
Approximating $19 can be done using a number line as shown below.
Step: 3
Represent the number 19 on a number line.
Step: 4
From the number line, 19 is closer to 20 than 10, 15, or 18.
Step: 5
So, Ray should round up 19 to 20.
Correct Answer is :   round up 19 to 20.
Q8Arthur deposited $423 in his bank account last month and he deposited $978 this month. Estimate the total amount that Arthur deposited.

A. $1,500
B. $1,200
C. $1,300
D. $1,400

Solutions
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Step: 1
Round down 423 to the nearest hundred = 400
Step: 2
Round up 978 to the nearest hundred = 1000
Step: 3
400 + 1000 = 1,400
  [Add the rounded values.]
Step: 4
So, the amount in Arthur's account is about $1,400.
Correct Answer is :   $1,400
Q9To estimate the product of 37 and 25, Carl multiplied 40 × 30. Which of these statement is true?

A. Estimation of the product of 37 and 25 equals the exact answer.
B. Estimation of the product of 37 and 25 is greater than the exact answer.
C. Estimation of the product of 37 and 25 is less than the exact answer.

Solutions
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Step: 1
The product 37 × 25 is
Step: 2
37
×25
185
74
925
Step: 3
So, the product of 37 and 25 is 925.
Step: 4
The product 40 × 30 is
Step: 5
40
× 30
0000
120
1200
  [Carl′s estimation for 37 × 25 is 40 × 30.]
Step: 6
So, the product of 40 × 30 is 1200.
Step: 7
The product of 40 × 30 is greater than the product of 37 × 25.
  [1200 > 925.]
Step: 8
So, the statement 'Estimation of the product 37 and 25 is greater than the exact answer' is true.
Correct Answer is :   Estimation of the product of 37 and 25 is greater than the exact answer.
Q10During the past 8 weeks, Anna spent between $22 and $38 for magazines each week. Which could be the total amount that he spent on the magazines for the past 8 weeks?

A. between $20 and $40
B. between $160 and $360
C. less than $160

Solutions
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Step: 1
As Anna spent minimum of $22 each week, its nearest value to tens is $20.
Step: 2
Maximum amount spent by her is $38 and its nearest value to tens is $40.
Step: 3
For 8 weeks, Anna's minimum expenses are $20 × 8 = $160.
Step: 4
For 8 weeks, Anna's maximum expenses are $40 × 8 = $320.
Step: 5
Therefore, among the choices, between $160 and $360 is correct.
Correct Answer is :   between $160 and $360
Q11Lehman puts oranges in cartons in his shop. He puts 43 to 49 oranges in each carton. Which could be the total number of oranges he puts in 10 cartons?

A. between 400 and 500
B. less than 200
C. between 200 and 300

Solutions
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Step: 1
As Lehman puts a minimum of 43 oranges in each carton, its nearest value to tens is 40.
Step: 2
He puts a maximum of 49 oranges in each carton and its nearest value to tens is 50.
Step: 3
In 10 cartons, the minimum number of oranges kept by Lehman is 40 × 10 = 400.
Step: 4
In 10 cartons, the maximum number of oranges kept by Lehman is 50 × 10 = 500.
Step: 5
Therefore, Lehman puts between 400 and 500 oranges in 10 cartons.
Correct Answer is :   between 400 and 500
Q12Jessica can type 11 pages in an hour and she has 21 hours to complete the job. Which of the following can she use to find the best estimate of the number of pages she can type?
A. divide 10 and 20
B. add 10 and 20
C. multiply 20 and 10
D. Subtract 20 and 10

Solutions
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Step: 1
Number of pages she can type = Number of pages can be typed in an hour × Number of hours
Step: 2
= 10 × 20
  [Round down 11 to nearest whole number 10 and 21 to nearest whole number 20.]
Step: 3
The best estimate of the number of pages she can type can be found by multiplying 20 and 10.
Correct Answer is :   multiply 20 and 10

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