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Year 4 Maths Addition

Estimate & check addition

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Theory

Estimating and checking addition is a Year 4 maths skill: you round each number to the nearest 10 or 100, then add to get an answer that is about right. This page shows how to estimate a sum, how to tell if an exact answer is reasonable, and how to check addition with subtraction. Estimating to check answers begins in Year 3 and is built on in Year 4. Curriculum: VC2M4N07 / AC9M4N07.

An estimate is a close answer that is quick to work out. To estimate a sum, you round each number to the nearest 10 or nearest 100, then add the rounded numbers. For \(43 + 36\) you round to \(40 + 40\), so the sum is about 80.

Rounding means changing a number to the nearest ten or hundred. Look at the next digit: if it is 5 or more you round up; if it is 4 or less you round down. So \(43\) rounds down to \(40\) and \(36\) rounds up to \(40\). To round to the nearest 100, look at the tens digit instead: \(372\) rounds up to \(400\) and \(1640\) rounds down to \(1600\).

An estimate lets you check your work. An exact answer that is close to the estimate is reasonable. You can also check by subtraction, because adding and subtracting are opposites: if \(257 + 136 = 393\), then \(393 - 136\) should give back \(257\).

Rounding 58 to the nearest 10 on a number line A number line from 50 to 60 with a halfway mark at 55. A red arrow at 58 sits to the right of 55, so 58 rounds up to 60. 505560 58
58 is past the halfway mark 55, so it rounds up to 60.
Checking that 683 is reasonable using an estimate of 700 A number line from 600 to 800. The estimate 700 is shown with a navy arrow and the exact answer 683 sits just before it, so 683 is close to 700 and is reasonable. 600650700 750800 estimate 700 answer 683
For 487 + 196, the exact answer 683 is close to the estimate 500 + 200 = 700, so it is reasonable.

Estimating does not need a formula, but these facts help you round and check quickly.

\[ 5 \text{ or more} \to \text{round up} \]
5 or more → round up
\[ 4 \text{ or less} \to \text{round down} \]
4 or less → round down
\[ 43 + 36 \approx 40 + 40 = 80 \]
43+36≈40+40=80
\[ 257 + 136 = 393 \ \text{checks as} \ 393 - 136 = 257 \]
393-136=257
Reasonable means the exact answer is close to the estimate. Round two-digit numbers to the nearest 10 (look at the ones digit) and larger numbers to the nearest 100 (look at the tens digit). If both numbers round up, the estimate is a little higher than the exact sum; if both round down, it is a little lower.

How to estimate and check a sum

  1. Round each number. Round to the nearest 10 for two-digit numbers (look at the ones digit), or the nearest 100 for larger numbers (look at the tens digit).
  2. Add the rounded numbers. This gives the estimate, so the sum is about this much.
  3. Check the exact answer. Work out the exact sum and see if it is close to the estimate, or subtract one number from the total to make sure you get the other number back.
Example 1 — Estimate to the nearest 10
Estimate \(58 + 24\) by rounding each number to the nearest 10. The number line shows where 24 sits.
Rounding 24 to the nearest 10 on a number line A number line from 20 to 30 with a halfway mark at 25. A red arrow at 24 sits left of 25, so 24 rounds down to 20. 202530 24
Solution
\(58\)\(\to\)\(60\)
\(24\)\(\to\)\(20\)
\(60 + 20\)\(=\)\(80\)
60+20=80

The sum is about \(80\).

Example 2 — Estimate to the nearest 100
Estimate \(483 + 291\) by rounding each number to the nearest 100.
Solution
\(483\)\(\to\)\(500\)
\(291\)\(\to\)\(300\)
\(500 + 300\)\(=\)\(800\)
500+300=800

The sum is about \(800\).

Example 3 — Is it reasonable?
A jumper costs \(\$46\) and jeans cost \(\$52\). Priya says the total is \(\$98\). Use an estimate to check.
Solution
\(\$46\)\(\to\)\(\$50\)
\(\$52\)\(\to\)\(\$50\)
\(\$50 + \$50\)\(=\)\(\$100\)
50+50=100

\(\$98\) is close to \(\$100\), so it is reasonable.

Example 4 — Check by subtracting
Mia worked out \(346 + 218 = 564\). Check her answer using subtraction.
Solution
\(564 - 218\)\(=\)\(346\)
564-218=346

Subtracting gives back \(346\), so \(564\) is correct.

Example 5 — Three numbers
Estimate \(26 + 43 + 59\) by rounding each number to the nearest 10.
Solution
\(26\)\(\to\)\(30\)
\(43\)\(\to\)\(40\)
\(59\)\(\to\)\(60\)
\(30 + 40 + 60\)\(=\)\(130\)
30+40+60=130

The total is about \(130\). (The exact total is \(128\).)

Example 6 — Numbers in the thousands
A school fete had \(2360\) visitors on Saturday and \(1720\) on Sunday. Estimate the total by rounding each number to the nearest 100.
Solution
\(2360\)\(\to\)\(2400\)
\(1720\)\(\to\)\(1700\)
\(2400 + 1700\)\(=\)\(4100\)
2400+1700=4100

Look at the tens digit: \(6\) rounds up, \(2\) rounds down. About \(4100\) visitors.

Example 7 — Is there enough money?
Ben has \(\$70\). He wants a ball that costs \(\$39\) and a hat that costs \(\$28\).
(i) Estimate the total by rounding each price to the nearest \(\$10\).
(ii) Is the real total more or less than the estimate? Does Ben have enough?
Solution
\(\$39\)\(\to\)\(\$40\)
\(\$28\)\(\to\)\(\$30\)
\(\$40 + \$30\)\(=\)\(\$70\)
40+30=70

(i) About \(\$70\).
(ii) Both prices were rounded up, so the real total is a little less than \(\$70\). Ben has enough (the exact total is \(\$67\)).

Common pitfalls

Round the numbers, not the answer. Watch out for adding first. Round \(43\) and \(36\) to \(40\) and \(40\), then add. Do not add first to get \(79\) and round that.
An estimate is not exact. Say the sum is "about 80", not "\(= 80\)". The exact answer can be a little more or a little less.
Check that the answer is close. If the exact answer is far from the estimate, you have probably made a mistake and should work it out again.

Frequently asked questions

How do you estimate a sum by rounding?

Round each number to the nearest 10 or nearest 100, then add the rounded numbers. For example, \(43 + 36\) rounds to \(40 + 40\), which is about \(80\).

What does estimate mean in maths?

An estimate is a close answer that is quick to work out. It is not exact, so we say the sum is about a number rather than equal to it.

How do you check if an addition answer is reasonable?

Estimate the sum by rounding, then compare. If the exact answer is close to the estimate it is reasonable. If it is far away, check your working for a mistake.

How do you check addition using subtraction?

Adding and subtracting are opposites. If \(257 + 136 = 393\), then \(393 - 136\) should give back \(257\). If it does, the addition is correct.

Do you round to the nearest 10 or 100 when estimating?

Use the nearest 10 for two-digit numbers and the nearest 100 for larger numbers in the hundreds. Rounding to a bigger place gives a rougher but quicker estimate.

Why is my estimate different from the exact answer?

An estimate uses rounded numbers, so it is only close, not exact. If you round both numbers up the estimate is a little high, and if you round both down it is a little low.

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