Multiplying and dividing by two digits; divisibility · Usually met around P4
Estimate first, then check
Round and estimate, then judge the answer.
How to do it
Method
Round and estimate, then judge the answer
38 × 21 is about 40 × 20 = 800; it is 798
Another way
Check with the inverse
798 ÷ 21 = 38
In full
Before multiplying or dividing big numbers, round them to estimate how big the answer should be. 38 × 21: 38 is about 40 and 21 about 20, and 40 × 20 = 800, so the answer is about 800. Working it out, 38 × 21 = 798, close to 800, so it is sensible; if you got 7980 or 79, you'd know a digit had been added or lost, and work it again. Division too: 1512 ÷ 28, 1512 is about 1500 and 28 about 30, 1500 ÷ 30 = 50, so the answer is about 50 (it is 54). For three digits times two, round the three-digit number to the nearest hundred and the two-digit number to the nearest ten. Another check is the inverse: check a multiplication by dividing, 798 ÷ 21 = 38; check a division by multiplying, 54 × 28 = 1512.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Estimate 46 × 52: round both to the nearest ten, and the answer is about □.
Show the answer and working
Answer: 2500
46 is about 50 and 52 about 50: 50 × 50 = 2500.
Example 2
Ming works out 415 × 53 and gets 21995. Judging by an estimate, this answer is sensible.
True or false?
Show the answer and working
Answer: True
Estimate: 415 is about 400 and 53 about 50, 400 × 50 = 20000, so the answer should be near 20000; it is 21995.
Example 3
Estimate 121 × 73 (the three-digit number to the nearest hundred, the two-digit one to the nearest ten): 121 is about □, 73 is about □, and the answer is about □.
Fill in each box
Show the answer and working
Answer: 100，70，7000
121 to the nearest hundred is 100, 73 to the nearest ten is 70: 100 × 70 = 7000.
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