What is an estimate?
An estimate is an answer that is close enough to be useful, found without counting every item or doing the exact calculation. People estimate all the time: How long will this take? About how much will this cost? Is there enough pizza?
Estimating is not the same as guessing. A guess can be wild; an estimate uses information and reasoning.
Estimating quantities
Use a benchmark
A benchmark is an amount you already know. If you know what 10 jelly beans look like, you can imagine how many groups of 10 fill a jar.
Example: One handful of rice fills a tenth of a bag. The bag holds about 10 handfuls.
Count a part, then multiply
Count the items in a small section, then multiply by the number of sections.
Example: A crowd photo has a grid of 20 equal squares. One square has about 30 people. Estimate: 20 × 30 = about 600 people.
Estimating calculations
Rounding
Round each number, then calculate.
- 289 + 412 ≈ 300 + 400 = 700 (exact: 701)
- 48 × 6 ≈ 50 × 6 = 300 (exact: 288)
Front-end estimation
Front-end estimation keeps only the first digit of each number and replaces the rest with zeros.
- 437 + 268 + 315 ≈ 400 + 200 + 300 = 900 (exact: 1,020)
It’s fast but may be low, so you can adjust by looking at the leftover parts.
Compatible numbers
Compatible numbers are numbers that work nicely together.
- 247 ÷ 5 → 250 ÷ 5 = 50
- 23 + 78 → 25 + 75 = 100
Choose numbers close to the real ones that make the maths easy.
Over or under?
Notice whether your estimate is too high or too low:
| Strategy | Example | Estimate is |
|---|---|---|
| Round 48 up to 50 | 48 × 6 → 300 | a little high |
| Front-end on 437 + 268 | 900 | low (we dropped the tens and ones) |
This matters in real life. When checking whether you have enough money, round prices up so you don’t come up short.
Worked examples
Example 1: About how many are in a jar if 10 fill one row and there are 5 rows?
10 × 5 = about 50.
Example 2: Estimate 612 − 289.
Round: 600 − 300 = about 300 (exact: 323).
Example 3: You have $20. You want items costing $4.85, $7.10 and $6.95. Do you have enough?
Round up: $5 + $8 + $7 = $20. Your total is at most $20, so yes. (Exact: $18.90.)
Common mistakes
- Treating an estimate as if it must be exact. Close is the goal.
- Guessing wildly without a strategy.
- Not checking whether an estimate is high or low when that matters.
- Rounding so roughly that the estimate is useless. Rounding 349 + 351 to the nearest thousand gives 0 + 0!
Try it yourself
- Estimate 398 + 205.
- Estimate 31 × 9.
- Use compatible numbers to estimate 362 ÷ 9.
- A page has about 12 lines of 10 words. About how many words on 8 pages?
Answers: 1) about 600 2) about 270 (30 × 9) 3) about 40 (360 ÷ 9) 4) about 960 (120 × 8), or about 1,000
Quick recap
- An estimate is a reasonable answer that is close enough.
- Use benchmarks, rounding, front-end estimation or compatible numbers.
- Think about whether your estimate is high or low.