Multiplication and division (1)
Division
In Stage 6 we divide whole numbers up to 1000 by 1-digit and 2-digit numbers. Always estimate first so you can check your answer is reasonable. The number being divided is the dividend, the number you divide by is the divisor, the answer is the quotient, and anything left over is the remainder.
Estimate first
Round the dividend and the divisor to friendly numbers to get a rough answer. Example: for 936 ÷ 16, round to 900 ÷ 15 = 60, so the answer should be about 60.
Divide by a 1-digit number
Use short division, working from the left. Sometimes the dividend does not split exactly and there is an amount left over — this is the remainder. Write it as 'remainder 2', for example.
Divide by a 2-digit number
Find how many of the divisor fit into the dividend. Take away that many (for example 24 × 20 = 480), then keep going with what is left until nothing remains.
Use factors to divide
If the divisor splits into factors, you can divide in two easier steps. To divide by 15, use 15 = 3 × 5: divide by 3, then divide that answer by 5.
Worked examples
Estimating a quotient
- You want to estimate 936 ÷ 16.
- Round the dividend 936 to 900.
- Round the divisor 16 to 15.
- Work out 900 ÷ 15.
Answer: 936 ÷ 16 is about 60.
Dividing by a 2-digit number
- Calculate 552 ÷ 24. Estimate first: 600 ÷ 25 = 24, so the answer is close to 24.
- There are twenty 24s in 552, because 24 × 20 = 480. Record 2 tens.
- Subtract: 552 − 480 = 72.
- There are three 24s in 72, because 24 × 3 = 72. Record 3 ones, and 72 − 72 = 0.
Answer: 552 ÷ 24 = 23.
Dividing with a remainder
- Calculate 765 ÷ 7.
- 7 into 7 goes 1; 7 into 6 goes 0 remainder 6; bring down the 5 to make 65.
- 7 into 65 goes 9 remainder 2.
Answer: 765 ÷ 7 = 109 remainder 2.
Using factors to divide
- Calculate 960 ÷ 15 using factors. Since 15 = 3 × 5, divide by 3 then by 5.
- 960 ÷ 3 = 320.
- 320 ÷ 5 = 64.
Answer: 960 ÷ 15 = 64.
A division word problem
- Eggs are packed into boxes that each hold 12 eggs.
- A farmer has 684 eggs, so divide 684 ÷ 12.
- 12 × 57 = 684, so the eggs fill the boxes exactly.
Answer: The farmer needs 57 boxes.
Where you see this in real life
- Packing 684 eggs into boxes of 12.
- Sharing the cost of a $297 meal equally between 11 people.
- Working out how many pies a chef can make from her apples.
Key words
- Dividend
- The number that is being divided.
- Divisor
- The number you divide by.
- Quotient
- The answer to a division.
- Remainder
- The amount left over when a number does not divide exactly.