Estimating Calculations
At the shop till you often just need to know roughly what your basket comes to — enough
to be sure the coins in your pocket will cover it, without adding every price exactly. That quick,
good-enough sum is an estimate.
Before you work out an exact answer, you can get a quick
about right one by
rounding each number first.
Round numbers — tidy tens like 30, 40,
50 — are easy to add or multiply in your head, so the estimate takes a
moment. It won't be exactly right, but it tells you roughly what the real answer should be.
Take 38 + 43. Round each to the nearest ten:
38 \to 40 and 43 \to 40. Now the sum is
easy — 40 + 40 = 80 — so:
38 + 43 \approx 80
The wavy \approx sign means approximately equal to:
not exactly, but close. We use = for an exact answer and
\approx for an estimate. The true total here is
81, and our estimate of 80 sits right
next to it — close enough to be useful, and far quicker to work out.
Press play, then replay it: a sum like 38 + 43 appears, each number
snaps to its nearest ten on the number line, and the easy estimate lands beside the true
total so you can see how close they are.
See it: rounding on the number line
Here are two numbers sitting on a number line. Watch how each one hops to the
nearest ten — the closest tick marked with a tidy round number. Then those two tens add up in a
blink to give the estimate. Press Refresh to try a brand-new sum.
A few worked examples
The same trick works for taking away. To estimate 71 - 28, round each
number first: 71 \to 70 and 28 \to 30, then
do the easy take-away:
71 - 28 \approx 70 - 30 = 40
The exact answer is 43 — so 40 is a good guide.
And it works for times-ing too. To estimate 19 \times 21, round to
20 \times 20:
19 \times 21 \approx 20 \times 20 = 400
The exact answer is 399 — almost spot on, and much easier to do in
your head than the real multiplication.
One more sum: 48 + 31. Round to 50 + 30:
48 + 31 \approx 50 + 30 = 80
The true total is 79 — our estimate of 80 is right beside it.
Two estimating traps to dodge:
- Round FIRST, then calculate. Round each number to a tidy ten, then add (or
subtract, or multiply). Don't work out the exact answer and then round it — that isn't
estimating, that's just hiding the real answer.
- An estimate is a sensible-checker, not the answer. If you carefully add
48 + 31 and get 790, your estimate of
80 shouts that something has gone wrong — the answer should be
about 80, not ten times bigger.
You want an apple and a banana. The apple costs
19p and the banana
32p. Will the coins
in your hand — about 50p — be enough? Round:
19 \to 20 and 32 \to 30, so the cost is
about 20 + 30 = 50p. It's going to be close, so you'd better bring a
little extra! (The real total is 51p.) A quick estimate told you that
without any hard sums — that is exactly when estimating is handy.
One jar has
28 cookies and the other has
33. Roughly how many altogether? Round to
30 + 30 = 60, so about sixty. You don't need to
count every crumb to know there's enough for a class of thirty children to have one each. That's
the power of an estimate: a fast, good-enough answer when an exact one would be slow and you
don't really need it.
Because an estimate is quick, it makes a friendly check on an exact answer. Work
the sum out properly, then ask: is my answer near my estimate? If it is, you can relax.
If it's miles off, you've probably made a slip — go back and look. A quick estimate catches silly
mistakes before they cause trouble.
Khan Academy walks through using rounding to estimate sums here: