Year 6: The four operations and the order of operations
Part of the Year 6 sats maths revision chapter. Chapter overview · whole chapter on one page
The four operations and the order of operations
This section practises the four operations, which are used in every part of the SATs. Work with the column method, from the right: add or subtract one column at a time, and carry or exchange when you need to.
Multiplication by a number with two digits uses two rows. The first row is the number times the ones digit. The second row is the number times the tens digit, with a 0 place holder. Then add the two rows.
Division asks how many groups fit. Take the groups out a digit at a time. If something is left over, that is the remainder. The remainder must always be smaller than the number you divide by.
When a calculation has more than one operation, use the order of operations: brackets first, then multiplication and division, then addition and subtraction.
Key ideas
- Add and subtract using the column method, from the right, with carries and exchanges.
- For long multiplication, multiply by the ones digit, then by the tens digit with a 0 place holder, then add the rows.
- Long division: the remainder must be smaller than the divisor.
- Order of operations: brackets, then × and ÷, then + and − (from left to right).
Key words. The sum is the answer to an addition. A carry is the 1 ten (or 1 hundred) we move into the next column. The difference is the answer to a subtraction.
Method. Add the columns from the right, and carry any 1 ten into the next column.
- Add the ones column. Add the two digits, and the carried number if there is one.6 + 7 = 13, so write 3 and carry 1
- Add the tens column. Add the two digits, and the carried number if there is one.8 + 9 + 1 carried = 18, so write 8 and carry 1
- Add the hundreds column. Add the two digits, and the carried number if there is one.4 + 5 + 1 carried = 10, so write 0 and carry 1
- Add the thousands column. Add the two digits, and the carried number if there is one.3 + 2 + 1 carried = 6, so write 6
- Write the answer. Read the column answers from left to right.6,083
Check. 6,083 − 2,597 = 3,486, so the sum is right. ✓
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it in the same column.
Method. Use the column method, one digit at a time, and check with an estimate.
- Multiply by the ones digit. Write 6 under the ones, and multiply the whole number by it.
214 × 36 ------- 1,284 + 6,420 ------- 7,704
214 × 6 = 1284 - Multiply by the tens digit, using a 0 place holder. The tens digit is worth ten times more, so write a 0 first.214 × 3 = 642, then 642 × 10 = 6420
- Add the two rows. Add the partial products to find the total.1284 + 6420 = 7,704
- Write the answer. This is the product.7,704
Check. Estimate: 200 × 40 = 8,000. The exact answer 7,704 is close to the estimate. ✓
Watch out. Keep each column lined up. Multiply the tens row by 10 by writing a 0 first.
Key words. In division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer, and the remainder is what is left over.
Method. Share the number into groups of the divisor, one digit at a time, and keep the remainder smaller than the divisor.
- Divide 47 by 23. Use the first digits that make a number at least as big as 23.
206 23 ) 4758 46 -- 1 0 - 15 138 --- 202 × 23 = 46; 47 − 46 = 1 - Divide 15 by 23. Bring down the 5 to make 15.0 × 23 = 0; 15 − 0 = 15
- Divide 158 by 23. Bring down the 8 to make 158.6 × 23 = 138; 158 − 138 = 20
- Write the answer. The last remainder is what is left over, and it must be smaller than the divisor.206 remainder 20
Check. 206 × 23 + 20 = 4,758. ✓
Watch out. The remainder must be smaller than the number you divide by. If it is not, you can take one more group.
Watch out
Common mistake: forgetting the 0 place holder. When you multiply by the tens digit, the second row is ten times bigger, so it must start one place to the left. Write the 0 first, or the answer is wrong.
Exercise 13A Practice set: the four operations (timed: about 15 minutes for 12 questions)
Non-calculatorKey words. The sum is the answer to an addition. A carry is the 1 ten (or 1 hundred) we move into the next column. The difference is the answer to a subtraction.
Method. Add the columns from the right, and carry any 1 ten into the next column.
- Add the ones column. Add the two digits, and the carried number if there is one.8 + 5 = 13, so write 3 and carry 1
- Add the tens column. Add the two digits, and the carried number if there is one.1 + 6 + 1 carried = 8, so write 8
- Add the hundreds column. Add the two digits, and the carried number if there is one.7 + 2 = 9, so write 9
- Add the thousands column. Add the two digits, and the carried number if there is one.4 + 3 = 7, so write 7
- Write the answer. Read the column answers from left to right.7,983
Check. 7,983 − 3,265 = 4,718, so the sum is right. ✓
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it in the same column.
Key words. The sum is the answer to an addition. A carry is the 1 ten (or 1 hundred) we move into the next column. The difference is the answer to a subtraction.
Method. Subtract the columns from the right. Exchange 1 from the next column when the top digit is too small.
- Subtract the ones column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.4 is too small for 8, so exchange 1 ten: 14 − 8 = 6
- Subtract the tens column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.0 - 1 (lent) gives -1, so exchange 1 ten: 9 − 7 = 2
- Subtract the hundreds column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.0 - 1 (lent) gives -1, so exchange 1 ten: 9 − 6 = 3
- Subtract the thousands column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.8 - 1 (lent) − 3 = 4
- Write the answer. Read the answer from the bottom row.4,326
Check. 4,326 + 3,678 = 8,004, so the difference is right. ✓
Watch out. Exchange 1 from the next column, which is worth 10 of the column you are working in. Watch for zeros in the top number.
Key words. The sum is the answer to an addition. A carry is the 1 ten (or 1 hundred) we move into the next column. The difference is the answer to a subtraction.
Method. Subtract the columns from the right. Exchange 1 from the next column when the top digit is too small.
- Subtract the ones column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.0 is too small for 7, so exchange 1 ten: 10 − 7 = 3
- Subtract the tens column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.0 - 1 (lent) gives -1, so exchange 1 ten: 9 − 5 = 4
- Subtract the hundreds column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.0 - 1 (lent) gives -1, so exchange 1 ten: 9 − 4 = 5
- Subtract the thousands column. Take the bottom digit from the top digit. If the top digit is too small, exchange 1 from the next column.6 - 1 (lent) − 2 = 3
- Write the answer. Read the answer from the bottom row.3,543
Check. 3,543 + 2,457 = 6,000, so the difference is right. ✓
Watch out. Exchange 1 from the next column, which is worth 10 of the column you are working in. Watch for zeros in the top number.
Method. Use the column method, one digit at a time, and check with an estimate.
- Multiply the ones digit. Multiply this digit, and add the carried number from the column before.7 × 6 = 42, so write 2 and carry 4
- Multiply the tens digit. Multiply this digit, and add the carried number from the column before.4 × 6 + 4 carried = 28, so write 8 and carry 2
- Write the carried number at the front. Nothing is left to multiply, so the carried number is written in front.2
- Write the answer. This is the product.282
Check. Estimate: 50 × 6 = 300. The exact answer 282 is smaller than the estimate, because we rounded both numbers up. ✓
Watch out. Keep each column lined up. Multiply the tens row by 10 by writing a 0 first.
Method. Use the column method, one digit at a time, and check with an estimate.
- Multiply the ones digit. Multiply this digit, and add the carried number from the column before.8 × 7 = 56, so write 6 and carry 5
- Multiply the tens digit. Multiply this digit, and add the carried number from the column before.0 × 7 + 5 carried = 5, so write 5
- Multiply the hundreds digit. Multiply this digit, and add the carried number from the column before.3 × 7 = 21, so write 1 and carry 2
- Write the carried number at the front. Nothing is left to multiply, so the carried number is written in front.2
- Write the answer. This is the product.2,156
Check. Estimate: 300 × 7 = 2,100. The exact answer 2,156 is bigger than the estimate, because we rounded both numbers down. ✓
Watch out. Keep each column lined up. Multiply the tens row by 10 by writing a 0 first.
Key words. In division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer, and the remainder is what is left over.
Method. Share the number into groups of the divisor, one digit at a time, and keep the remainder smaller than the divisor.
- Divide 43 by 6. Use the first digits that make a number at least as big as 6.7 × 6 = 42; 43 − 42 = 1
- Divide 12 by 6. Bring down the 2 to make 12.2 × 6 = 12; 12 − 12 = 0
- Divide 6 by 6. Bring down the 6 to make 6.1 × 6 = 6; 6 − 6 = 0
- Write the answer. The last remainder is what is left over, and it must be smaller than the divisor.721
Check. 721 × 6 + 0 = 4,326. ✓
Watch out. The remainder must be smaller than the number you divide by. If it is not, you can take one more group.
Key words. In division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer, and the remainder is what is left over.
Method. Share the number into groups of the divisor, one digit at a time, and keep the remainder smaller than the divisor.
- Divide 35 by 4. Use the first digits that make a number at least as big as 4.8 × 4 = 32; 35 − 32 = 3
- Divide 34 by 4. Bring down the 4 to make 34.8 × 4 = 32; 34 − 32 = 2
- Divide 22 by 4. Bring down the 2 to make 22.5 × 4 = 20; 22 − 20 = 2
- Write the answer. The last remainder is what is left over, and it must be smaller than the divisor.885 remainder 2
Check. 885 × 4 + 2 = 3,542. ✓
Watch out. The remainder must be smaller than the number you divide by. If it is not, you can take one more group.
Method. Use the column method, one digit at a time, and check with an estimate.
- Multiply by the ones digit. Write 3 under the ones, and multiply the whole number by it.
1,247 × 53 -------- 3,741 + 62,350 -------- 66,0911247 × 3 = 3741 - Multiply by the tens digit, using a 0 place holder. The tens digit is worth ten times more, so write a 0 first.1247 × 5 = 6235, then 6235 × 10 = 62350
- Add the two rows. Add the partial products to find the total.3741 + 62350 = 66,091
- Write the answer. This is the product.66,091
Check. Estimate: 1,000 × 50 = 50,000. The exact answer 66,091 is bigger than the estimate, because we rounded both numbers down. ✓
Watch out. Keep each column lined up. Multiply the tens row by 10 by writing a 0 first.
Key words. In division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer, and the remainder is what is left over.
Method. Share the number into groups of the divisor, one digit at a time, and keep the remainder smaller than the divisor.
- Divide 48 by 23. Use the first digits that make a number at least as big as 23.
209 23 ) 4816 46 -- 2 0 - 21 207 --- 92 × 23 = 46; 48 − 46 = 2 - Divide 21 by 23. Bring down the 1 to make 21.0 × 23 = 0; 21 − 0 = 21
- Divide 216 by 23. Bring down the 6 to make 216.9 × 23 = 207; 216 − 207 = 9
- Write the answer. The last remainder is what is left over, and it must be smaller than the divisor.209 remainder 9
Check. 209 × 23 + 9 = 4,816. ✓
Watch out. The remainder must be smaller than the number you divide by. If it is not, you can take one more group.
Key words. In division, the dividend is the number being divided, the divisor is the number we divide by, the quotient is the answer, and the remainder is what is left over.
Method. Share the number into groups of the divisor, one digit at a time, and keep the remainder smaller than the divisor.
- Divide 62 by 35. Use the first digits that make a number at least as big as 35.
177 35 ) 6205 35 -- 27 245 --- 25 245 --- 101 × 35 = 35; 62 − 35 = 27 - Divide 270 by 35. Bring down the 0 to make 270.7 × 35 = 245; 270 − 245 = 25
- Divide 255 by 35. Bring down the 5 to make 255.7 × 35 = 245; 255 − 245 = 10
- Write the answer. The last remainder is what is left over, and it must be smaller than the divisor.177 remainder 10
Check. 177 × 35 + 10 = 6,205. ✓
Watch out. The remainder must be smaller than the number you divide by. If it is not, you can take one more group.
Key words. The order of operations says what to work out first: brackets, then multiplication and division from left to right, then addition and subtraction from left to right.
Method. Work out the multiplication and division first, then the addition and subtraction.
- Work out the multiplication and the division first. Multiplication and division come before addition and subtraction.4 × 5 = 20 and 6 ÷ 2 = 3
- Then add and subtract from left to right. Start at the left and work across.3 + 20 − 3 = 20
- Write the answer. 20
Check. Working strictly from left to right gives 3 + 4 = 7, 7 × 5 = 35, 35 - 6 = 29, and 29 ÷ 2 = 14.5, which is wrong. ✓
Watch out. Multiply and divide before you add and subtract.
Method. Use the column method, one digit at a time, and check with an estimate.
- Multiply by the ones digit. Write 5 under the ones, and multiply the whole number by it.
1,248 × 25 -------- 6,240 + 24,960 -------- 31,2001248 × 5 = 6240 - Multiply by the tens digit, using a 0 place holder. The tens digit is worth ten times more, so write a 0 first.1248 × 2 = 2496, then 2496 × 10 = 24960
- Add the two rows. Add the partial products to find the total.6240 + 24960 = 31,200
- Write the answer. This is the product.31,200
Check. Estimate: 1,000 × 20 = 20,000. The exact answer 31,200 is bigger than the estimate, because we rounded both numbers down. ✓
Watch out. Keep each column lined up. Multiply the tens row by 10 by writing a 0 first.
Key words. The order of operations says what to work out first: brackets, then multiplication and division from left to right, then addition and subtraction from left to right.
Method. Work out the brackets first, then the multiplication and the division from left to right.
- Work out the brackets first. Brackets come before every other operation.12 + 8 = 20 and 15 − 9 = 6
- Multiply and divide from left to right. Here the multiplication comes first, then the division.20 × 6 = 120, then 120 ÷ 5 = 24
- Write the answer. 24
Check. Without the brackets the answer would be different: 12 + 8 × 15 - 9 ÷ 5 = 12 + 120 - 1.8, which is not 24. ✓
Watch out. Brackets change the order. Work them out first, even when the bracket is on the left.