Decomposition

1. Decomposition I am learning a standard method of doing a subtraction problem on paper when the numbers are too difficult to find the answer mentally. Numbers are set out directly below each other. e.g. 243 In your head - 165

2. There are 536 people at a sports game. 358 people are wearing black. How many people are not wearing black? 536 - 358 = ? Step 1: For our first example let’s expand each number and write them underneath each other. 120 400 Step 2: There are not enough ones to subtract 8. This means we must break up a ten and add it to the six. 20 16 500 + 30 + 6 Step 3: Now subtract the ones. (16 – 8 = 8). - 300 + 50 + 8 + 100 + 70 8 Step 4: There are not enough tens to subtract 50. This means we must break up a hundred and add it to the 20. Step 5: Now subtract the tens. (120 – 50 = 70) Step 6: Now subtract the hundreds. (400 – 300 = 100) Step 7: Add the bottom line together to get your answer. 536 – 358 = 178 100 + 70 + 8 = 178

3. There were 732 people in the hall. 309 people left through Door One. How many people did not leave through Door One? 732 - 309 = ? Step 1: Now let’s try the same algorithm without expanding the number. 12 Step 2: There are not enough ones to subtract 9. This means we must break up a ten and add it to the two. 2 7 3 2 - 3 0 9 Step 3: Now subtract the ones. (12 – 9 = 3) 4 2 3 Step 4: Subtract the tens. (2 tens – 0 tens = 2 tens) Notice how we just record a 2 in the tens column. Not a 20. Step 5: Subtract the hundreds. (7 hundreds – 3 hundreds = 4 hundreds) Notice how we just record a 4 in the hundreds column. Not 400. The bottom line is the answer. 423 732 – 309 = 423

4. Now try these questions on your own. You will need to use pen and paper to record your algorithm. Click again when you have completed each question and the answer will be displayed. • 642 - 238 = ? • 537 - 188 = ? • 723 - 144 = ? • 365 - 206 = ? • 552 – 206 = ? 404 349 579 159 346 Need some more practise? Try Pg60 of Teacher Tools Addition and Subtraction Book Numeracy resources