Written subtraction across a zero

What you will learn

• Use adjacent place-value exchanges, including across a zero, in three-digit subtraction

Models used: place-value charts, number sentences, bar models, stories.

Before you start

• Add and subtract numbers up to three digits

Exchange, then subtract

Work out 402 − 187.

1. Line up ones under ones and tens under tens. Start on the right.

   402 − 187

   	hundreds	tens	ones
   First number	4	0	2
   −	1	8	7
   Answer	?	?	?

2. Exchange 1 hundred for 10 tens. The top number still has the same value.

   1 hundred = 10 tens

   	hundreds	tens	ones
   First number	43	010	2
   −	1	8	7
   Answer	?	?	?

   1 hundred⇄10 tens

3. Exchange 1 ten for 10 ones. The top number still has the same value.

   1 ten = 10 ones

   	hundreds	tens	ones
   First number	43	09	212
   −	1	8	7
   Answer	?	?	?

   1 ten⇄10 ones

4. Now subtract the ones. Write 5 in this column.

   12 − 7 = 5

   	hundreds	tens	ones
   First number	43	09	212
   −	1	8	7
   Answer	?	?	5

5. Now subtract the tens. Write 1 in this column.

   9 − 8 = 1

   	hundreds	tens	ones
   First number	43	09	212
   −	1	8	7
   Answer	?	1	5

6. Now subtract the hundreds. Write 2 in this column.

   3 − 1 = 2

   	hundreds	tens	ones
   First number	43	09	212
   −	1	8	7
   Answer	2	1	5

7. Read the answer from left to right. Add back the amount taken away to check.

   215 + 187 = 402

   	hundreds	tens	ones
   First number	43	09	212
   −	1	8	7
   Answer	2	1	5

Worked example: Fill one answer box at a time

Work out 503 − 268.

1. Line up ones under ones and tens under tens. Start on the right.

   503 − 268

   	hundreds	tens	ones
   First number	5	0	3
   −	2	6	8
   Answer	?	?	?

2. Exchange 1 hundred for 10 tens. The top number still has the same value.

   1 hundred = 10 tens

   	hundreds	tens	ones
   First number	54	010	3
   −	2	6	8
   Answer	?	?	?

   1 hundred⇄10 tens

3. Exchange 1 ten for 10 ones. The top number still has the same value.

   1 ten = 10 ones

   	hundreds	tens	ones
   First number	54	09	313
   −	2	6	8
   Answer	?	?	?

   1 ten⇄10 ones

4. Work in the highlighted column.

   	hundreds	tens	ones
   First number	54	09	313
   −	2	6	8
   Answer	?	?	?

   What digit belongs in the ones column?

   5

5. Work in the highlighted column.

   	hundreds	tens	ones
   First number	54	09	313
   −	2	6	8
   Answer	?	?	5

   What digit belongs in the tens column?

   3

6. Work in the highlighted column.

   	hundreds	tens	ones
   First number	54	09	313
   −	2	6	8
   Answer	?	3	5

   What digit belongs in the hundreds column?

   2

7. Read the answer from left to right. Add back the amount taken away to check.

   235 + 268 = 503

   	hundreds	tens	ones
   First number	54	09	313
   −	2	6	8
   Answer	2	3	5

Common mistakes to discuss

• Swap subtraction digits. Keep the order. Exchange from the next place when the top digit is too small.
• Change only one column. Each exchange reduces the next place by one and adds ten to the place beside it.

Check your understanding

• Keep the starting value unchanged when exchanging.
• Work across a zero by exchanging through the next place.
• Check the difference with addition.

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.