Discover Mathematics P5: Term 1, Unit 5, Lessons 11–14
GoalRound to friendly numbers to estimate a decimal quotient and use the estimate to check where the decimal point goes.
New words
estimate · an answer that is close to the exact one, found quicklycompatible numbers · numbers close to the real ones that divide easily, such as 42 and 6reasonable · close enough to the estimate to make sense
Explanation
To estimate 41.7 ÷ 6, change 41.7 to a nearby number that 6 divides exactly. 42 is close to 41.7 and 42 ÷ 6 = 7, so the answer is about 7. Choose compatible numbers by thinking of the multiplication facts of the divisor. Estimates also catch mistakes with the decimal point: if a child writes 18.4 ÷ 4 = 0.46, the estimate 20 ÷ 4 = 5 shows that 0.46 is far too small, and the right answer 4.6 is close to 5. Always finish by asking: is my answer close to my estimate?
Division
Compatible numbers
Estimate
41.7 ÷ 6
42 ÷ 6
7
7.9 ÷ 4
8 ÷ 4
2
18.4 ÷ 4
20 ÷ 4
5
Worked examples
Exact
Rounded
Quotient
19.8 ÷ 5
20 ÷ 5
4
A tank holds 19.8 L and is filled by 5 equal jugs. Round 19.8 to 20: 20 ÷ 5 = 4. Each jug holds about 4 L. The exact answer is 3.96 L, which is close to 4.
Estimate 25.8 ÷ 5.1. Round 25.8 to 25 and 5.1 to 5: 25 ÷ 5 = 5. The answer is about 5.
★Check
Estimate first. Then the exact answer must be close to the estimate.
Karim says 18.4 ÷ 4 = 0.46. Estimate: 20 ÷ 4 = 5. His answer is far from 5, so the point is in the wrong place. The correct answer is 4.6, and 4 × 4.6 = 18.4.
Class activity
Estimate it first. Ask a grown-up to read prices or measurements from a shopping receipt or a kitchen scale (for example 29.7 kg shared by 10 children, or 35.2 LE shared by 8). Before calculating, the child says the compatible numbers and the estimate. Then use a calculator for the exact answer and decide if it is reasonable.
Practice
1
Estimate 27.6 ÷ 9 with compatible numbers.
27.6 is close to 27 and 27 ÷ 9 = 3, so about 3.
2
Which compatible numbers would you use for 48.9 ÷ 7? What is the estimate?
49 ÷ 7 = 7, so about 7.
3
Which is reasonable for 35.2 ÷ 8: 0.44, 4.4 or 44?
32 ÷ 8 = 4, so 4.4 is reasonable. (8 × 4.4 = 35.2.)
4
Estimate how much each of 6 friends pays if the bill is 47.5 LE.
48 ÷ 6 = 8, so about 8 LE each.
5
Estimate 6.1 ÷ 0.3 by using 6 ÷ 0.3 and tenths.
6 = 60 tenths and 0.3 = 3 tenths. 60 ÷ 3 = 20, so about 20.
