3
Standard division and tricky stories
Discover Mathematics P4: Term 1, Unit 7, Lessons 11–16
GoalDivide 3-digit numbers by 1-digit numbers with the standard algorithm, and check by multiplying.
New words
long division · the written method that divides one place at a time from the leftbring down · write the next digit beside what is leftcheck · multiply the quotient by the divisor and add the remainder
Explanation
The standard algorithm divides place by place, starting from the left. For 756 ÷ 4: 7 hundreds ÷ 4 = 1 hundred, and 3 hundreds are left (7 − 4 = 3). Bring down the 5 tens to make 35 tens. 35 ÷ 4 = 8 tens, because 4 × 8 = 32, and 3 tens are left. Bring down the 6 ones to make 36. 36 ÷ 4 = 9. The quotient is 189. Check: 189 × 4 = 756. If a place cannot be divided we write 0 in the quotient: in 485 ÷ 6, 48 ÷ 6 = 8 and then 5 ÷ 6 = 0 with 5 left, so 485 ÷ 6 = 80 R 5. Check: 80 × 6 + 5 = 485. In each step: divide, multiply, subtract, bring down.
756 ÷ 4 = 189
| Place | Divide | Multiply | Subtract | Bring down |
|---|---|---|---|---|
| hundreds | 7 ÷ 4 = 1 | 4 × 1 = 4 | 7 − 4 = 3 | 5 |
| tens | 35 ÷ 4 = 8 | 4 × 8 = 32 | 35 − 32 = 3 | 6 |
| ones | 36 ÷ 4 = 9 | 4 × 9 = 36 | 36 − 36 = 0 | — |
Worked examples
Find 756 ÷ 4 = 189 (shown above). Check: 189 × 4 = 756, because 4 × 9 = 36, 4 × 80 = 320 and 4 × 100 = 400, and 36 + 320 + 400 = 756.
485 ÷ 6 = 80 R 5
| Place | Divide | Left |
|---|---|---|
| hundreds and tens | 48 ÷ 6 = 8 | 0 |
| ones | 5 ÷ 6 = 0 | 5 |
A shop has 905 kg of rice in bags of 7 kg. 9 ÷ 7 = 1 R 2. Bring down 0: 20 ÷ 7 = 2 R 6. Bring down 5: 65 ÷ 7 = 9 R 2. The quotient is 129, the remainder is 2. There are 129 full bags and 2 kg of rice left. Check: 129 × 7 + 2 = 905.
Class activity
Check it backwards. A grown-up gives a 3-digit number and a 1-digit divisor. The child divides, then multiplies the quotient by the divisor and adds the remainder to see if the first number comes back.
Practice
1
Find 672 ÷ 3 and check.
6 ÷ 3 = 2; 7 ÷ 3 = 2, 1 left; 12 ÷ 3 = 4. The quotient is 224. Check: 224 × 3 = 672.
2
Find 845 ÷ 5.
8 ÷ 5 = 1, 3 left; 34 ÷ 5 = 6, 4 left; 45 ÷ 5 = 9. The quotient is 169. Check: 169 × 5 = 845.
3
Find 534 ÷ 8 and write the remainder.
53 ÷ 8 = 6, 5 left; 54 ÷ 8 = 6, 6 left. The answer is 66 R 6. Check: 8 × 66 + 6 = 534.
4
365 kg of dates are packed in bags of 4 kg. How many full bags? How many kg are left over?
365 ÷ 4 = 91 R 1. 91 full bags and 1 kg left over.
5
Ahmed finds 624 ÷ 6 = 14. How can he see that this is wrong? What is the right answer?
14 × 6 = 84, not 624. He forgot the zero: 6 ÷ 6 = 1, 2 ÷ 6 = 0, 24 ÷ 6 = 4. The answer is 104. Check: 104 × 6 = 624.