Step-by-step Maths Level 3: Subtracting 2-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 2-digit numbers with exchange
Some 2-digit subtractions need exchange. Check the ones first. If the top ones are fewer, exchange a ten for ten ones.
Write the new tens and ones in the columns, then take away.
Key ideas
- Check the ones first.
- Exchange a ten for ten ones when you need to.
- Take the ones away, then the tens.
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.73 over 38
- Exchange 1 ten for 10 ones. The ones on top (3) are fewer than the ones below (8), so we need more ones.7 tens become 6 tens, and the ones go from 3 to 13
- Subtract the ones. 13 - 8 = 5.13 - 8 = 5
- Subtract the tens. 6 - 3 = 3.6 - 3 = 3
- Write the answer. Read the columns from left to right.35
Check. Check: 35 + 38 = 73.
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.64 over 27
- Exchange 1 ten for 10 ones. The ones on top (4) are fewer than the ones below (7), so we need more ones.6 tens become 5 tens, and the ones go from 4 to 14
- Subtract the ones. 14 - 7 = 7.14 - 7 = 7
- Subtract the tens. 5 - 2 = 3.5 - 2 = 3
- Write the answer. Read the columns from left to right.37
Check. Check: 37 + 27 = 64.
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.92 over 47
- Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (7), so we need more ones.9 tens become 8 tens, and the ones go from 2 to 12
- Subtract the ones. 12 - 7 = 5.12 - 7 = 5
- Subtract the tens. 8 - 4 = 4.8 - 4 = 4
- Write the answer. Read the columns from left to right.45
Check. Check: 45 + 47 = 92.
Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.
Watch out
Watch out. After you exchange, the top tens are one less. 73 - 38 is 35, not 45.
Exam tip
Grown-up tip. Ask: “Are the ones on top big enough? If not, which ten can we break?”
Exercise 5B Practice: 2-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.30 over 18
- Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (8), so we need more ones.3 tens become 2 tens, and the ones go from 0 to 10
- Subtract the ones. 10 - 8 = 2.10 - 8 = 2
- Subtract the tens. 2 - 1 = 1.2 - 1 = 1
- Write the answer. Read the columns from left to right.12
Check. Check: 12 + 18 = 30.
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.72 over 68
- Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (8), so we need more ones.7 tens become 6 tens, and the ones go from 2 to 12
- Subtract the ones. 12 - 8 = 4.12 - 8 = 4
- Subtract the tens. 6 - 6 = 0.6 - 6 = 0
- Write the answer. Read the columns from left to right.4
Check. Check: 4 + 68 = 72.
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.94 over 29
- Exchange 1 ten for 10 ones. The ones on top (4) are fewer than the ones below (9), so we need more ones.9 tens become 8 tens, and the ones go from 4 to 14
- Subtract the ones. 14 - 9 = 5.14 - 9 = 5
- Subtract the tens. 8 - 2 = 6.8 - 2 = 6
- Write the answer. Read the columns from left to right.65
Check. Check: 65 + 29 = 94.
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.44 over 36
- Exchange 1 ten for 10 ones. The ones on top (4) are fewer than the ones below (6), so we need more ones.4 tens become 3 tens, and the ones go from 4 to 14
- Subtract the ones. 14 - 6 = 8.14 - 6 = 8
- Subtract the tens. 3 - 3 = 0.3 - 3 = 0
- Write the answer. Read the columns from left to right.8
Check. Check: 8 + 36 = 44.
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.53 over 45
- Exchange 1 ten for 10 ones. The ones on top (3) are fewer than the ones below (5), so we need more ones.5 tens become 4 tens, and the ones go from 3 to 13
- Subtract the ones. 13 - 5 = 8.13 - 5 = 8
- Subtract the tens. 4 - 4 = 0.4 - 4 = 0
- Write the answer. Read the columns from left to right.8
Check. Check: 8 + 45 = 53.
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.82 over 36
- 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 - 3 = 4.7 - 3 = 4
- Write the answer. Read the columns from left to right.46
Check. Check: 46 + 36 = 82.
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.63 over 37
- Exchange 1 ten for 10 ones. The ones on top (3) are fewer than the ones below (7), so we need more ones.6 tens become 5 tens, and the ones go from 3 to 13
- Subtract the ones. 13 - 7 = 6.13 - 7 = 6
- Subtract the tens. 5 - 3 = 2.5 - 3 = 2
- Write the answer. Read the columns from left to right.26
Check. Check: 26 + 37 = 63.
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.50 over 23
- Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (3), so we need more ones.5 tens become 4 tens, and the ones go from 0 to 10
- Subtract the ones. 10 - 3 = 7.10 - 3 = 7
- Subtract the tens. 4 - 2 = 2.4 - 2 = 2
- Write the answer. Read the columns from left to right.27
Check. Check: 27 + 23 = 50.
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.90 over 42
- Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (2), so we need more ones.9 tens become 8 tens, and the ones go from 0 to 10
- Subtract the ones. 10 - 2 = 8.10 - 2 = 8
- Subtract the tens. 8 - 4 = 4.8 - 4 = 4
- Write the answer. Read the columns from left to right.48
Check. Check: 48 + 42 = 90.
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.51 over 36
- Exchange 1 ten for 10 ones. The ones on top (1) are fewer than the ones below (6), so we need more ones.5 tens become 4 tens, and the ones go from 1 to 11
- Subtract the ones. 11 - 6 = 5.11 - 6 = 5
- Subtract the tens. 4 - 3 = 1.4 - 3 = 1
- Write the answer. Read the columns from left to right.15
Check. Check: 15 + 36 = 51.
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.62 over 16
- Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (6), so we need more ones.6 tens become 5 tens, and the ones go from 2 to 12
- Subtract the ones. 12 - 6 = 6.12 - 6 = 6
- Subtract the tens. 5 - 1 = 4.5 - 1 = 4
- Write the answer. Read the columns from left to right.46
Check. Check: 46 + 16 = 62.
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.97 over 19
- Exchange 1 ten for 10 ones. The ones on top (7) are fewer than the ones below (9), so we need more ones.9 tens become 8 tens, and the ones go from 7 to 17
- Subtract the ones. 17 - 9 = 8.17 - 9 = 8
- Subtract the tens. 8 - 1 = 7.8 - 1 = 7
- Write the answer. Read the columns from left to right.78
Check. Check: 78 + 19 = 97.
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.83 over 54
- Exchange 1 ten for 10 ones. The ones on top (3) are fewer than the ones below (4), so we need more ones.8 tens become 7 tens, and the ones go from 3 to 13
- Subtract the ones. 13 - 4 = 9.13 - 4 = 9
- Subtract the tens. 7 - 5 = 2.7 - 5 = 2
- Write the answer. Read the columns from left to right.29
Check. Check: 29 + 54 = 83.
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.43 over 37
- Exchange 1 ten for 10 ones. The ones on top (3) are fewer than the ones below (7), so we need more ones.4 tens become 3 tens, and the ones go from 3 to 13
- Subtract the ones. 13 - 7 = 6.13 - 7 = 6
- Subtract the tens. 3 - 3 = 0.3 - 3 = 0
- Write the answer. Read the columns from left to right.6
Check. Check: 6 + 37 = 43.
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.30 over 26
- Exchange 1 ten for 10 ones. The ones on top (0) are fewer than the ones below (6), so we need more ones.3 tens become 2 tens, and the ones go from 0 to 10
- Subtract the ones. 10 - 6 = 4.10 - 6 = 4
- Subtract the tens. 2 - 2 = 0.2 - 2 = 0
- Write the answer. Read the columns from left to right.4
Check. Check: 4 + 26 = 30.
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.52 over 14
- Exchange 1 ten for 10 ones. The ones on top (2) are fewer than the ones below (4), so we need more ones.5 tens become 4 tens, and the ones go from 2 to 12
- Subtract the ones. 12 - 4 = 8.12 - 4 = 8
- Subtract the tens. 4 - 1 = 3.4 - 1 = 3
- Write the answer. Read the columns from left to right.38
Check. Check: 38 + 14 = 52.
Watch out. Exchange a ten for ten ones when the ones on top are too small. Then take away.