Grouping & estimating
Add lists smartly and estimate before you calculate.
Best in your head · no pen, no calculator why?
Opens at level 11. You're level 1. You can read and practice here now.
the idea
Two habits make long calculations safer.
Group before you add. In a list, look for two numbers whose endings make a round hundred, like 275 and 125, and add those first. The order never changes the total, so pick the order that carries least.
Estimate. Round the numbers and calculate with the rounded ones. An estimate is not the exact answer, so when a question says how to round, give the rounded result. Estimates also catch the most common slip: an answer 10 times too big or too small.
techniques
Pair the round hundreds
- Look at the last two digits of each number.
- Find two whose endings make 100, like 75 and 25, or 40 and 60.
- Add that pair first, then add the rest.
worked example
340 + 215 + 160
- 40 and 60 make 100, so pair 340 and 160.
- 340 + 160 = 500.
- 500 + 215 = 715.
Answer: 715
Round as the question says
- Round each number the way the question says: to the nearest ten, or the nearest hundred.
- For the nearest ten, look at the ones digit: 5 or more rounds up, less rounds down.
- If the question offers a friendlier pair of numbers, use that pair.
- Calculate with the rounded numbers and give that result, not the exact one.
worked example
Estimate 38 × 62 by rounding each factor to the nearest ten.
- 38 rounds to 40, and 62 rounds to 60.
- 40 × 60 = 2,400.
Answer: 2,400
Count the digits
- For a product, round each number to its first digit, multiply those digits, then add the zeros.
- For a division, multiply the divisor by 10, 100 and 1,000 to see which two the number falls between.
- Pick the choice that fits. The others are off by about 10 times or more.
worked example
Which is closest to 63 × 288: about 1,800, about 18,000 or about 180,000?
- Round to first digits: 60 × 300.
- 6 × 3 = 18, then three zeros: 18,000.
Answer: 18,000
watch out for
- Giving the exact answer when the question asks for an estimate.
- Dropping the hundred carried from a pair. 275 + 125 is 400, not 300.
- Adding or losing a zero. 40 × 400 is 16,000: 4 × 4 = 16, then three zeros.
practice
Group into hundreds
worked example
850 + 530 + 450
Answer: 1,830
- Pair the friendly numbers first: 850 + 450 = 1,300, then add 530: 1,830.
Estimate by rounding
worked example
Estimate 8,130 ÷ 91 using 8,100 ÷ 90.
Answer: 90
- Use the friendly pair: 8,100 ÷ 90 = 810 ÷ 9 = 90.
Right size?
worked example
Which is closest to 50 × 5,636?
- about 2,800,000
- about 28,000,000
- about 280,000
- about 28,000
Answer: about 280,000
- Round each number to its leading digit: 50 × 6,000 = 300,000.
- The exact 281,800 is about 280,000; the other choices are about 10 times too small, or 10 or 100 times too big.