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Year 4 Maths Subtraction

Estimate & check subtraction

20 practice questions 0 video lessons Theory + worked examples

A quick estimate shows whether a difference is about right before you trust the exact answer. In Tasmanian Year 4 maths this subtopic rounds numbers to estimate subtractions and to check results (Australian Curriculum AC9M4N07).

Students round to the nearest 10 or 100, so \(94 - 37\) is about \(90 - 40 = 50\), and pick the only sensible answer from a list. They check a subtraction by adding back, compare an estimate with the exact difference, and explain why it came out higher or lower. Money left after shopping, how many more fans came on one day and distances driven by a truck are the everyday links. It is part of Year 4 Subtraction.

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Theory

Estimating and checking subtraction is a Year 4 maths skill: round each number to the nearest 10 or 100, then subtract the rounded numbers to get a quick estimate of the difference. This page shows how to round, how to use an estimate to check that an answer is reasonable, and how to check a subtraction with inverse addition.

An estimate is a quick, close answer, not the exact one. To estimate a subtraction, round each number to the nearest 10 or the nearest 100, then subtract the rounded numbers. For \(86 - 41\), round to \(90 - 40 = 50\), so the difference is about 50.

To round, look at the digit in the next place. If it is 4 or less, round down; if it is 5 or more, round up. So 86 rounds up to 90 and 41 rounds down to 40. A number exactly halfway, like 65, rounds up to 70.

An estimate lets you check that an exact answer is reasonable: the exact answer should land close to the estimate. You can also check a subtraction with addition, because they are opposites. Add the difference and the number you took away, and you should get back the number you started with.

Number line rounding 86 to the nearest 10 A number line from 80 to 90 with a halfway mark at 85. A red arrow points to 86, which is right of 85, so 86 rounds up to 90. 808590 86
86 is right of the halfway mark 85, so it rounds up to 90.
Number line rounding 827 to the nearest 100 A number line from 800 to 900 with a halfway mark at 850. A red arrow points to 827, which is left of 850, so 827 rounds down to 800. 800850900 827
827 is left of the halfway mark 850, so it rounds down to 800.

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

\[ 90 - 40 = 50 \]
90-40=50
\[ \text{difference} + \text{number subtracted} = \text{starting number} \]
difference+number subtracted=starting number
\[ 255 + 176 = 431 \]
255+176=431
Rounding rule. Look at the digit in the next place. If it is 4 or less, round down; if it is 5 or more, round up. So \(65\) rounds to \(70\) and \(827\) rounds to \(800\).
Which digit do I look at? To round to the nearest 10, look at the ones digit: \(357 - 142\) is about \(360 - 140 = 220\) (exact \(215\)). To round to the nearest 100, look at the tens digit, even in a four-digit number: \(3640 - 1270\) is about \(3600 - 1300 = 2300\). Money works the same way: \(\$96 - \$52\) is about \(\$100 - \$50 = \$50\).
Is the estimate higher or lower? If the first number was rounded up and the number taken away was rounded down, the estimate is higher than the exact answer. If it is the other way round, the estimate is lower. For \(86 - 41\), \(86\) went up and \(41\) went down, so the estimate \(50\) is higher than the exact \(45\), by \(50 - 45 = 5\).

How to estimate and check a subtraction

  1. Round each number. Round both numbers to the nearest 10, or to the nearest 100 for larger numbers.
  2. Subtract the rounded numbers. Take one rounded number from the other to get your estimate of the difference.
  3. Check it is reasonable. Work out the exact answer, or add the difference back on, and make sure it lands close to your estimate.
Example 1 — Estimate to nearest 10
Estimate \(86 - 41\) by rounding each number to the nearest 10.
Solution
\(86\)\(\to\)\(90\)
\(41\)\(\to\)\(40\)
\(90 - 40\)\(=\)\(50\)
90-40=50

The difference is about \(50\).

Example 2 — Estimate to nearest 100
Estimate \(827 - 361\) by rounding each number to the nearest 100.
Solution
\(827\)\(\to\)\(800\)
\(361\)\(\to\)\(400\)
\(800 - 400\)\(=\)\(400\)
800-400=400

The difference is about \(400\). (The exact answer is \(466\).)

Example 3 — Is it reasonable?
Maya worked out \(934 - 382 = 552\). Use an estimate to check her answer.
Solution
\(934\)\(\to\)\(900\)
\(382\)\(\to\)\(400\)
\(900 - 400\)\(=\)\(500\)
900-400=500

\(552\) is close to \(500\), so it is reasonable.

Example 4 — Check with addition
Check whether \(431 - 176 = 255\) is correct by using addition.
Solution
\(255 + 176\)\(=\)\(431\)
255+176=431

Adding the difference and the number taken away gives back \(431\), so \(255\) is correct.

Common pitfalls

Round before you subtract. Watch out for subtracting first and rounding after. Round each number to the nearest 10 or 100, then subtract the rounded numbers.
An estimate is not the exact answer. It only tells you if an answer looks about right. For \(86 - 41\) the estimate is \(50\), but the exact answer is \(45\).
A halfway number rounds up. A \(5\) in the next place rounds up, so \(65\) rounds to \(70\) and \(350\) rounds to \(400\).

Frequently asked questions

How do you estimate a subtraction?

Round each number to the nearest 10 or 100, then subtract the rounded numbers. For \(86 - 41\), round to \(90 - 40\), which is about \(50\).

How do you round a number to the nearest 10?

Look at the ones digit. If it is 4 or less, round down to the lower ten. If it is 5 or more, round up to the higher ten. So \(86\) rounds up to \(90\) and \(41\) rounds down to \(40\).

How does estimating help you check a subtraction?

The exact answer should land close to the estimate. If your answer is far from the estimate, you have probably made a mistake and should work it out again.

How do you check a subtraction is correct?

Add the difference and the number you took away. If you get back the number you started with, the subtraction is correct. For \(431 - 176 = 255\), add \(255 + 176\) to get \(431\).

Is an estimate the same as the exact answer?

No. An estimate is a quick, close answer, not the exact one. For \(86 - 41\) the estimate is \(50\) but the exact answer is \(45\). The estimate just shows if an answer looks about right.

What does a reasonable answer mean in maths?

A reasonable answer is one that is close to a sensible estimate. If you estimate about \(500\) and your answer is \(552\), that is reasonable. An answer like \(52\) or \(952\) would not be.

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