1
Which estimate is closer?
Discover Mathematics P2: Term 2, Lessons 81–90
GoalEstimate sums and differences in two ways and see which estimate is closer to the exact answer.
New words
estimate · a number close to the exact answerexact answer · the answer you get when you add or subtract carefullycloser · with a smaller gap from the exact answer
Explanation
There are two ways to estimate. Front-end estimation keeps the tens digit and makes the ones zero. Rounding changes each number to the nearest ten. For 47 + 39: front-end gives 40 + 30 = 70. Rounding gives 50 + 40 = 90. The exact answer is 86. The gap for 70 is 16 and the gap for 90 is only 4, so the rounding estimate is closer. Rounding is often closer because it looks at the ones digit too. An estimate is useful to check that your exact answer is sensible.
| Method | Estimate | How far from 86? |
|---|---|---|
| Front-end | 40 + 30 = 70 | 16 |
| Rounding | 50 + 40 = 90 | 4 |
Worked examples
47 + 39 = 86. Rounding gives 90, a gap of 4. Front-end gives 70, a gap of 16. Rounding is closer.
31 + 22 = 53. Front-end: 30 + 20 = 50. Rounding: 30 + 20 = 50. Both estimates are the same, a gap of 3.
67 − 21 = 46. Front-end: 60 − 20 = 40, a gap of 6. Rounding: 70 − 20 = 50, a gap of 4. Rounding is closer.
Class activity
Two guesses. Pick two numbers such as 56 and 23. Estimate their sum with front-end estimation and then by rounding. Add them exactly. Which guess is closer? Try three more pairs and keep a score.
Practice
1
Use front-end estimation for 56 + 23.
50 + 20 = 70.
2
Round the numbers in 56 + 23 and estimate again.
60 + 20 = 80.
3
The exact answer to 56 + 23 is 79. Which estimate is closer?
Rounding. 80 is 1 away from 79 and 70 is 9 away.
4
Estimate 93 − 41 with front-end estimation.
90 − 40 = 50. (The exact answer is 52.)
5
Round to the nearest ten to estimate 236 + 140.
240 + 140 = 380. (The exact answer is 376.)