โ˜ฐ Year plan ยท Mathematics

Dividing decimals: powers of ten, models and estimates

Week 11 ยท Dividing decimals ยท 3 lessons
3

Estimating decimal quotients

Discover Mathematics P5: Term 1, Unit 5, Lessons 11โ€“14
GoalRound to friendly numbers to estimate a decimal quotient and use the estimate to check where the decimal point goes.
New words
estimate ยท an answer that is close to the exact one, found quicklycompatible numbers ยท numbers close to the real ones that divide easily, such as 42 and 6reasonable ยท close enough to the estimate to make sense
Explanation

To estimate 41.7 รท 6, change 41.7 to a nearby number that 6 divides exactly. 42 is close to 41.7 and 42 รท 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 รท 4 = 0.46, the estimate 20 รท 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?

DivisionCompatible numbersEstimate
41.7 รท 642 รท 67
7.9 รท 48 รท 42
18.4 รท 420 รท 45
Worked examples
ExactRoundedQuotient
19.8 รท 520 รท 54
A tank holds 19.8 L and is filled by 5 equal jugs. Round 19.8 to 20: 20 รท 5 = 4. Each jug holds about 4 L. The exact answer is 3.96 L, which is close to 4.
Estimate 25.8 รท 5.1. Round 25.8 to 25 and 5.1 to 5: 25 รท 5 = 5. The answer is about 5.
โ˜…Check
Estimate first. Then the exact answer must be close to the estimate.
Karim says 18.4 รท 4 = 0.46. Estimate: 20 รท 4 = 5. His answer is far from 5, so the point is in the wrong place. The correct answer is 4.6, and 4 ร— 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 รท 9 with compatible numbers.
2
Which compatible numbers would you use for 48.9 รท 7? What is the estimate?
3
Which is reasonable for 35.2 รท 8: 0.44, 4.4 or 44?
4
Estimate how much each of 6 friends pays if the bill is 47.5 LE.
5
Estimate 6.1 รท 0.3 by using 6 รท 0.3 and tenths.