Estimating Sums
Before you calculate a sum precisely, estimating gives you a target to aim at. If your exact answer is far from the estimate, you know to check your working.
Rounding to Estimate a Sum
Round each addend to an appropriate degree of accuracy, then add the rounded values. The level of rounding depends on how precise your estimate needs to be.
| Calculation | Round to nearest 10 | Estimate | Exact answer |
|---|---|---|---|
| 47 + 63 | 50 + 60 | 110 | 110 |
| 83 + 28 | 80 + 30 | 110 | 111 |
| 194 + 307 | 200 + 300 | 500 | 501 |
Front-End Estimation for Sums
Take the leading digit of each number, replace the rest with zeros, then add.
5,728 + 3,415: front-end gives 5,000 + 3,000 = 8,000 (exact: 9,143)
Front-end estimation is fast but less accurate than rounding. Add the next digits for a refined estimate:
Refined: 5,700 + 3,400 = 9,100 (very close to 9,143)
Checking Reasonableness
An estimate tells you the approximate size of your answer. If the exact and estimated answers differ by more than about 10%, investigate.
If you calculate 47 + 38 = 175, your estimate of 50+40=90 immediately reveals an error.
When Is an Estimate Sufficient?
- Checking whether you have enough money before buying.
- Planning quantities for a project.
- Quick calculations during conversations.
- Checking a calculator result.
Key Takeaways
- Rounding before adding is the most common estimation method.
- Front-end estimation is faster but less precise.
- Always compare your estimated and exact answers.
- Use ≈ to signal that a value is an estimate.
Practice Questions
- Estimate 68 + 45 by rounding to the nearest 10.
- Use front-end estimation for 4,356 + 2,789.
- A student calculates 312 + 489 = 1201. Use estimation to show this is wrong.
- Estimate the total of 23 + 47 + 52 + 18.
- A recipe needs 375 g flour and 248 g sugar. Estimate the total weight of dry ingredients.