Step-by-step Maths Level 3: Subtracting 3-digit numbers with exchange
Part of the Step-by-step Maths Level 3 subtracting within 1000 chapter. Chapter overview · whole chapter on one page
Subtracting 3-digit numbers with exchange
When the tens on top are too small, exchange a hundred for ten tens. When the hundreds are used up, the number in the hundreds goes down by one.
Line up the columns. Work from the ones, then the tens, then the hundreds.
Key ideas
- Line up the columns.
- Exchange a ten for ten ones if the ones are too small.
- Exchange a hundred for ten tens if the tens are too small.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.432 over 187
- Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (7), so we need more ones.3 tens become 2 tens, and the ones go from 2 to 12
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (8 tens), so we need more tens.4 hundreds become 3 hundreds, and 2 tens become 12 tens
- Subtract the ones. 12 - 7 = 5.12 - 7 = 5
- Subtract the tens. 12 - 8 = 4.12 - 8 = 4
- Subtract the hundreds. 3 - 1 = 2.3 - 1 = 2
- Write the answer. Read the columns from left to right.245
Check. Check: 245 + 187 = 432.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.500 over 286
- Exchange 1 hundred for 10 tens. There are no tens to take from, so we first change a hundred into tens.5 hundreds and 0 tens become 4 hundreds and 10 tens
- Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (6), so we need more ones.10 tens become 9 tens, and the ones go from 0 to 10
- Subtract the ones. 10 - 6 = 4.10 - 6 = 4
- Subtract the tens. 9 - 8 = 1.9 - 8 = 1
- Subtract the hundreds. 4 - 2 = 2.4 - 2 = 2
- Write the answer. Read the columns from left to right.214
Check. Check: 214 + 286 = 500.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.604 over 258
- Exchange 1 hundred for 10 tens. There are no tens to take from, so we first change a hundred into tens.6 hundreds and 0 tens become 5 hundreds and 10 tens
- Exchange 1 ten for 10 ones. The ones on top (4) are fewer than the ones below (8), so we need more ones.10 tens become 9 tens, and the ones go from 4 to 14
- Subtract the ones. 14 - 8 = 6.14 - 8 = 6
- Subtract the tens. 9 - 5 = 4.9 - 5 = 4
- Subtract the hundreds. 5 - 2 = 3.5 - 2 = 3
- Write the answer. Read the columns from left to right.346
Check. Check: 346 + 258 = 604.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Watch out
Watch out. 500 - 286 needs two exchanges: a hundred becomes ten tens, then a ten becomes ten ones. The answer is 214.
Exam tip
Grown-up tip. Draw the columns on squared paper. Ask the child to say each exchange out loud before writing it.
Exercise 5C Practice: 3-digit numbers with exchange
Non-calculatorMethod. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.315 over 199
- Exchange 1 ten for 10 ones. The ones on top (5) are fewer than the ones below (9), so we need more ones.1 tens become 0 tens, and the ones go from 5 to 15
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (9 tens), so we need more tens.3 hundreds become 2 hundreds, and 0 tens become 10 tens
- Subtract the ones. 15 - 9 = 6.15 - 9 = 6
- Subtract the tens. 10 - 9 = 1.10 - 9 = 1
- Subtract the hundreds. 2 - 1 = 1.2 - 1 = 1
- Write the answer. Read the columns from left to right.116
Check. Check: 116 + 199 = 315.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.541 over 512
- Exchange 1 ten for 10 ones. The ones on top (1) are fewer than the ones below (2), so we need more ones.4 tens become 3 tens, and the ones go from 1 to 11
- Subtract the ones. 11 - 2 = 9.11 - 2 = 9
- Subtract the tens. 3 - 1 = 2.3 - 1 = 2
- Subtract the hundreds. 5 - 5 = 0.5 - 5 = 0
- Write the answer. Read the columns from left to right.29
Check. Check: 29 + 512 = 541.
Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.382 over 46
- Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (6), so we need more ones.8 tens become 7 tens, and the ones go from 2 to 12
- Subtract the ones. 12 - 6 = 6.12 - 6 = 6
- Subtract the tens. 7 - 4 = 3.7 - 4 = 3
- Subtract the hundreds. 3 - 0 = 3.3 - 0 = 3
- Write the answer. Read the columns from left to right.336
Check. Check: 336 + 46 = 382.
Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.150 over 137
- Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (7), so we need more ones.5 tens become 4 tens, and the ones go from 0 to 10
- Subtract the ones. 10 - 7 = 3.10 - 7 = 3
- Subtract the tens. 4 - 3 = 1.4 - 3 = 1
- Subtract the hundreds. 1 - 1 = 0.1 - 1 = 0
- Write the answer. Read the columns from left to right.13
Check. Check: 13 + 137 = 150.
Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.536 over 271
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (7 tens), so we need more tens.5 hundreds become 4 hundreds, and 3 tens become 13 tens
- Subtract the ones. 6 - 1 = 5.6 - 1 = 5
- Subtract the tens. 13 - 7 = 6.13 - 7 = 6
- Subtract the hundreds. 4 - 2 = 2.4 - 2 = 2
- Write the answer. Read the columns from left to right.265
Check. Check: 265 + 271 = 536.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.382 over 173
- Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (3), so we need more ones.8 tens become 7 tens, and the ones go from 2 to 12
- Subtract the ones. 12 - 3 = 9.12 - 3 = 9
- Subtract the tens. 7 - 7 = 0.7 - 7 = 0
- Subtract the hundreds. 3 - 1 = 2.3 - 1 = 2
- Write the answer. Read the columns from left to right.209
Check. Check: 209 + 173 = 382.
Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.320 over 171
- Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (1), so we need more ones.2 tens become 1 tens, and the ones go from 0 to 10
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (7 tens), so we need more tens.3 hundreds become 2 hundreds, and 1 tens become 11 tens
- Subtract the ones. 10 - 1 = 9.10 - 1 = 9
- Subtract the tens. 11 - 7 = 4.11 - 7 = 4
- Subtract the hundreds. 2 - 1 = 1.2 - 1 = 1
- Write the answer. Read the columns from left to right.149
Check. Check: 149 + 171 = 320.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.238 over 147
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (4 tens), so we need more tens.2 hundreds become 1 hundreds, and 3 tens become 13 tens
- Subtract the ones. 8 - 7 = 1.8 - 7 = 1
- Subtract the tens. 13 - 4 = 9.13 - 4 = 9
- Subtract the hundreds. 1 - 1 = 0.1 - 1 = 0
- Write the answer. Read the columns from left to right.91
Check. Check: 91 + 147 = 238.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.391 over 109
- Exchange 1 ten for 10 ones. The ones on top (1) are fewer than the ones below (9), so we need more ones.9 tens become 8 tens, and the ones go from 1 to 11
- Subtract the ones. 11 - 9 = 2.11 - 9 = 2
- Subtract the tens. 8 - 0 = 8.8 - 0 = 8
- Subtract the hundreds. 3 - 1 = 2.3 - 1 = 2
- Write the answer. Read the columns from left to right.282
Check. Check: 282 + 109 = 391.
Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.427 over 378
- Exchange 1 ten for 10 ones. The ones on top (7) are fewer than the ones below (8), so we need more ones.2 tens become 1 tens, and the ones go from 7 to 17
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (7 tens), so we need more tens.4 hundreds become 3 hundreds, and 1 tens become 11 tens
- Subtract the ones. 17 - 8 = 9.17 - 8 = 9
- Subtract the tens. 11 - 7 = 4.11 - 7 = 4
- Subtract the hundreds. 3 - 3 = 0.3 - 3 = 0
- Write the answer. Read the columns from left to right.49
Check. Check: 49 + 378 = 427.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.373 over 93
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (9 tens), so we need more tens.3 hundreds become 2 hundreds, and 7 tens become 17 tens
- Subtract the ones. 3 - 3 = 0.3 - 3 = 0
- Subtract the tens. 17 - 9 = 8.17 - 9 = 8
- Subtract the hundreds. 2 - 0 = 2.2 - 0 = 2
- Write the answer. Read the columns from left to right.280
Check. Check: 280 + 93 = 373.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.518 over 490
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (9 tens), so we need more tens.5 hundreds become 4 hundreds, and 1 tens become 11 tens
- Subtract the ones. 8 - 0 = 8.8 - 0 = 8
- Subtract the tens. 11 - 9 = 2.11 - 9 = 2
- Subtract the hundreds. 4 - 4 = 0.4 - 4 = 0
- Write the answer. Read the columns from left to right.28
Check. Check: 28 + 490 = 518.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.368 over 298
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (9 tens), so we need more tens.3 hundreds become 2 hundreds, and 6 tens become 16 tens
- Subtract the ones. 8 - 8 = 0.8 - 8 = 0
- Subtract the tens. 16 - 9 = 7.16 - 9 = 7
- Subtract the hundreds. 2 - 2 = 0.2 - 2 = 0
- Write the answer. Read the columns from left to right.70
Check. Check: 70 + 298 = 368.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.352 over 176
- Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (6), so we need more ones.5 tens become 4 tens, and the ones go from 2 to 12
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (7 tens), so we need more tens.3 hundreds become 2 hundreds, and 4 tens become 14 tens
- Subtract the ones. 12 - 6 = 6.12 - 6 = 6
- Subtract the tens. 14 - 7 = 7.14 - 7 = 7
- Subtract the hundreds. 2 - 1 = 1.2 - 1 = 1
- Write the answer. Read the columns from left to right.176
Check. Check: 176 + 176 = 352.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.827 over 131
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (3 tens), so we need more tens.8 hundreds become 7 hundreds, and 2 tens become 12 tens
- Subtract the ones. 7 - 1 = 6.7 - 1 = 6
- Subtract the tens. 12 - 3 = 9.12 - 3 = 9
- Subtract the hundreds. 7 - 1 = 6.7 - 1 = 6
- Write the answer. Read the columns from left to right.696
Check. Check: 696 + 131 = 827.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.
Method. Subtract the ones first. If the top digit is too small, exchange from the next column, then subtract.
- Write the numbers in columns. Keep the ones under the ones and the tens under the tens.864 over 375
- Exchange 1 ten for 10 ones. The ones on top (4) are fewer than the ones below (5), so we need more ones.6 tens become 5 tens, and the ones go from 4 to 14
- Exchange 1 hundred for 10 tens. The tens on top are fewer than the tens below (7 tens), so we need more tens.8 hundreds become 7 hundreds, and 5 tens become 15 tens
- Subtract the ones. 14 - 5 = 9.14 - 5 = 9
- Subtract the tens. 15 - 7 = 8.15 - 7 = 8
- Subtract the hundreds. 7 - 3 = 4.7 - 3 = 4
- Write the answer. Read the columns from left to right.489
Check. Check: 489 + 375 = 864.
Watch out. When a column is too small, exchange one from the column to its left. Ten ones make one ten, ten tens make one hundred.