Discover Mathematics P5: Term 1, Unit 1, Lessons 6–9
GoalEstimate a sum of decimals by rounding, and use the estimate to check an answer.
New words
estimate · a careful guess that is close to the exact answerreasonable · makes sense because it is close to the estimate
Explanation
An estimate tells us about how big an answer should be. To estimate a sum, round every number to the same easy place and add the rounded numbers. For 4.87 + 2.14 + 6.5 round to the nearest whole number: 5 + 2 + 7 = 14. The exact sum is 13.51, which is close to 14, so the answer is reasonable. Rounding to the nearest tenth gives a closer estimate but takes longer. The estimate also protects us from big mistakes, such as a misplaced decimal point: if the exact answer were 135.1 or 1.351, the estimate 14 would show at once that something is wrong. Always estimate first, then add exactly, then compare.
Number
4.87
2.14
6.5
Sum
Rounded
5
2
7
14
Exact
4.87
2.14
6.5
13.51
Worked examples
Mariam buys 2.75 kg of tomatoes, 1.9 kg of onions and 3.2 kg of potatoes. Her bag can carry 8 kg. Estimate: 3 + 2 + 3 = 8. This is too close to decide, so we add exactly: 2.75 + 1.9 + 3.2 = 7.85 kg. It is less than 8 kg, so the bag can carry it.
Number
12.6
7.35
Sum
Rounded to tenths
12.6
7.4
20
Exact
12.6
7.35
19.95
Estimate 12.6 + 7.35 by rounding to the nearest tenth: 12.6 + 7.4 = 20. The exact sum is 19.95. The estimate is only 0.05 too big, which is a very good estimate.
✓Tip
Round, add, then ask: is my exact answer close to the estimate?
Karim adds 14.6 + 3.75 and gets 52.1. Estimate: 15 + 4 = 19. The answer 52.1 is far from 19, so it cannot be right. He lined the digits up on the right instead of lining up the decimal points. The correct sum is 14.6 + 3.75 = 18.35.
Class activity
Shop estimates. Take a shop leaflet or write five prices such as 7.95, 12.5, 3.25, 19.75 and 4.4 LE on paper. Choose three prices, round each to the nearest whole pound and estimate the total. Then add exactly and see how close the estimate was. Try to get within 1 LE.
Practice
1
Estimate 7.9 + 4.2 by rounding to the nearest whole number.
8 + 4 = 12.
2
Estimate 23.46 + 18.7 by rounding to the nearest whole number. The exact sum is 42.16. Is it reasonable?
23 + 19 = 42. The exact sum 42.16 is close to 42, so it is reasonable.
3
A pair of sandals costs 119.75 LE and a bag costs 84.5 LE. Round each price to the nearest whole LE and estimate the cost of both.
120 + 85 = 205 LE. (84.5 rounds up to 85.)
4
Hana says 6.38 + 2.95 = 93.3. Use an estimate to show she is wrong.
6 + 3 = 9, so the sum is about 9. The correct answer is 9.33; she put the point in the wrong place.
5
Estimate 3.84 + 5.17 by rounding to the nearest tenth.
