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Adding & subtracting

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Addition & subtraction

Adding & Subtracting Whole Numbers

We add and subtract every day — working out totals when we shop, or change when we pay. Here you will estimate first, then use a written method that splits numbers into hundreds, tens and ones.

hundreds4= 400tens7= 70ones2= 2472 = 400 + 70 + 2

Always estimate first

Before you calculate, make a quick estimate by rounding each number to the nearest hundred. For 235 + 174, think 200 + 200 = 400. Your real answer should be close to 400. Estimating helps you spot mistakes.

Decompose, then compose

Decompose means split each number into hundreds, tens and ones. For 235 + 174: 235 = 200 + 30 + 5 and 174 = 100 + 70 + 4. Add the hundreds, the tens and the ones: 300 + 100 + 9. Then compose (put together) the parts to get 409.

Subtract the same way

For 459 - 318, decompose both numbers and subtract each place: 400 - 300 = 100, 50 - 10 = 40, 9 - 8 = 1. Compose the parts: 100 + 40 + 1 = 141.

Regroup when you need to

Sometimes a part is too small to subtract from. For 424 - 179, the ones 4 - 9 will not work, so regroup: rewrite 424 as 300 + 110 + 14. Now subtract: 300 - 100 = 200, 110 - 70 = 40, 14 - 9 = 5. Compose: 200 + 40 + 5 = 245.

Worked examples

Written addition

  1. Estimate: 200 + 200 = 400.
  2. Decompose: 235 = 200 + 30 + 5 and 174 = 100 + 70 + 4.
  3. Add each place: 300 + 100 + 9.
  4. Compose the parts: 300 + 100 + 9 = 409.

Answer: 235 + 174 = 409.

Written subtraction

  1. Estimate: 500 - 300 = 200.
  2. Decompose: 459 = 400 + 50 + 9 and 318 = 300 + 10 + 8.
  3. Subtract each place: 100 + 40 + 1.
  4. Compose the parts: 100 + 40 + 1 = 141.

Answer: 459 - 318 = 141.

Subtraction with regrouping

  1. Estimate: 400 - 200 = 200.
  2. The ones 4 - 9 will not work, so regroup 424 as 300 + 110 + 14.
  3. Subtract each place: 200 + 40 + 5.
  4. Compose the parts: 200 + 40 + 5 = 245.

Answer: 424 - 179 = 245.

Where you see this in real life

  • Adding the mass of two pieces of fruit on a scale.
  • Working out how many more chairs are needed for a concert.
  • Counting a stamp collection after adding new stamps.
  • Finding how much change you get after paying for shopping.

Key words

Estimate
A quick, close answer found by rounding before you calculate.
Decompose
To split a number into hundreds, tens and ones.
Compose
To put the parts back together to make the answer.
Regroup
To move a hundred or ten so you can subtract a place.
Difference
The result of subtracting one number from another.
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