The mathematical skill of estimating involves the use of rounding in order to determine the results of a math problem.
Estimating helps you to solve a math problem without having to do the full operations of addition, subtraction, multiplication, or division.
Look at the following examples.
Estimating Multiplication
(1) What is the best estimate of the following: 883 × 5.9 = ?
A. 3,200
B. 4,000
C. 4,800
D. 5,400
E. 6,200
Tip: Remember that you need to look at the answer choices first of all to see how to round.
Solution: From the answer choices, we can see that we need to round to the nearest hundred.
For numbers that are less than 50 on the last two digits, we need to round down to the nearest hundred.
On the other hand, for numbers that are 50 or more on the last two digits, we need to round up to the nearest hundred.
STEP 1: Round the provided numbers up or down.
883 is rounded up to 900.
5.9 is rounded up to 6.
STEP 2: Then do the operation.
900 × 6 = 5,400
So, the correct answer is D.
Estimating Division
(2) Estimate the result of the following: 12,300 ÷ 3.8 = ?
A. 2,000
B. 3,000
C. 4,000
D. 5,000
E. 6,000
Solution: From the answer choices, we can see that we need to round to the nearest thousand.
For numbers that are less than 500 on the last three digits, we need to round down to the nearest thousand.
If the last three digits are 500 or more, we need to round up to the nearest thousand.
STEP 1: Round the provided numbers up or down.
12,300 is rounded down to 12,000.
3.8 is rounded up to 4.
STEP 2: Then do the operation.
12,000 ÷ 4 = 3,000
So, the correct answer is B.
You may also see estimation problems involving addition or subtraction.
Very often, these types of problems are provided as a practical problem in narrative form like examples 3 and 4 below.
Estimating Addition
(3) A museum counts its visitors every day. On Monday it had 3,102 visitors. On Tuesday it had 1,535 visitors, and on Wednesday it had 2,893 visitors.
Which number below represents the best estimate of the amount of visitors to the museum in total for the three days?
A. 6,100
B. 6,500
C. 7,200
D. 7,500
E. 7,800
Solution: We need to round to the amount of visitors for each day to the nearest hundred.
STEP 1: Round the provided numbers up or down.
3,102 is rounded down to 3,100.
1,535 is rounded down to 1,500.
2.893 is rounded up to 2,900.
STEP 2: Then do the operation.
3,100 + 1,500 + 2,900 = 7,500
So, the correct answer is D.
Estimating Subtraction
(4) The highest point in Jones County is 13,179 feet above sea level. The lowest point in Jones Country is 1,232 feet above sea level. Which number below represents the best estimate of the difference in height between the highest and lowest points in Jones County?
A. 12,000
B. 13,000
C. 14,000
D. 15,000
E. 16,000
Solution: We need to round to the amount of visitors for each day to the nearest thousand.
STEP 1: Round the provided numbers up or down.
13, 179 is rounded down to 13,000.
1,232 is rounded down to 1,000.
STEP 2: Then do the operation.
13,000 – 1,000 = 12,000
So, the correct answer is A.