35 × 56 is estimated as 30 × 50. How does the estimate, 1,500, compare with the exact value? A. Too small B. Exactly equal C. Too big D. Can't tell Choose the right answer

A. Too small. 35 became 30 and 56 became 50: both moved the same way, so the product moves that way too.

Estimate 3,584 ÷ 9 with a compatible number: change 3,584 to the nearest whole hundred that 9 divides, and the estimate is □.

400. 3,584 ≈ 3,600, and 3,600 ÷ 9 = 400.

Take each number to 1 significant figure to estimate 8,658 ÷ 46: □

180. 8,658 ≈ 9,000 and 46 ≈ 50, so 9,000 ÷ 50 = 180.

Approximation & estimation · Ages 12–13

Estimation strategies

1 s.f., front-end or compatible numbers; then over or under.

How to do it

Method

1 s.f., front-end or compatible numbers; then over or under

382 × 47 ≈ 400 × 50 = 20,000 (an overestimate)

Another way

Compatible numbers

4,213 ÷ 7 ≈ 4,200 ÷ 7 = 600

In full

An estimate is a quick, rough answer, used to check that a calculation is sensible. One way: rounding. Take each number to 1 significant figure, then work it out: 382 × 47 ≈ 400 × 50 = 20,000. Another: front-end. Add the leading digits first, then adjust: 389 + 612 + 245 has hundreds 300 + 600 + 200 = 1,100, and the rest, 89 + 12 + 45, is about 150, so about 1,250. A third: compatible numbers, changed to ones that are easy to work with: 4,213 ÷ 7 ≈ 4,200 ÷ 7 = 600. Over or under? Adding or multiplying, with every number rounded up the estimate is too big; all rounded down, too small. Subtracting and dividing turn it round: a bigger first number or a smaller number taken away makes the difference too big, and a bigger divisor makes the quotient smaller.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
35 × 56 is estimated as 30 × 50. How does the estimate, 1,500, compare with the exact value?
- A. Too small
- B. Exactly equal
- C. Too big
- D. Can't tell
Choose the right answer
Show the answer and working
Answer: A. Too small
35 became 30 and 56 became 50: both moved the same way, so the product moves that way too.
Example 2
Estimate 3,584 ÷ 9 with a compatible number: change 3,584 to the nearest whole hundred that 9 divides, and the estimate is .
Show the answer and working
Answer: 400
3,584 ≈ 3,600, and 3,600 ÷ 9 = 400.
Example 3
Take each number to 1 significant figure to estimate 8,658 ÷ 46:
Show the answer and working
Answer: 180
8,658 ≈ 9,000 and 46 ≈ 50, so 9,000 ÷ 50 = 180.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Round each number to the nearest hundred to estimate 103 + 881:
Answer:
2.64 × 88 is estimated as 70 × 90. How does the estimate, 6,300, compare with the exact value?
- A. Exactly equal
- B. Too big
- C. Can't tell
- D. Too small
Choose the right answer
Answer:
3.A front-end estimate of 887 + 698 + 866: the hundreds first make ; the tens and ones left, added and taken to the nearest hundred, make ; the estimate is .
Fill in each blank
Answer:
4.Taking 1 significant figure, about how much is 77 × 780?
- A. 640,000
- B. 64,000
- C. 6,400
- D. 880
Choose the right answer
Answer:
5.Take each number to 1 significant figure to estimate 8,669 ÷ 89:
Answer:

All the answers

1. 1000
2. B. Too big
3. 2200, 300, 2500
4. B. 64,000
5. 100

Free worksheet: Estimation strategiesWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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