Dividing Whole Numbers (up to 1000 ÷ 2-digit)

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Division means sharing equally or grouping. It is the inverse (opposite) of multiplication: if 142 × 6 = 852, then 852 ÷ 6 = 142. On this page you will learn to estimate, to use short division ("bus stop"), chunking and long division, and to decide what to do with a remainder in a real problem.

Key words

Remember: dividend ÷ divisor = quotient remainder, and the check is quotient × divisor + remainder = dividend.

1. Estimate first: use friendly numbers

For division do not just round to the nearest hundred. Change the dividend to a nearby number that divides easily because you know a multiplication fact. These are called compatible numbers.

You can also find which two tens the answer lies between: for 768 ÷ 24, 24 × 30 = 720 and 24 × 40 = 960, so the answer is between 30 and 40 (and close to 30).

2. Short division (÷ a 1-digit number)

1. Write the dividend inside the "bus stop" and the divisor outside on the left.
2. Start at the left (the biggest place value). How many 6s in 8? 1, remainder 2. Write 1 on top.
3. Carry the remainder 2 to the next digit: it makes 25. How many 6s in 25? 4, remainder 1.
4. Carry the 1: it makes 12. How many 6s in 12? 2, remainder 0.
5. Answer 142. Check: 142 × 6 = 852 ✓ (and 142 is close to the estimate 140).

In 935 ÷ 4: 9 ÷ 4 = 2 r 1 → 13 ÷ 4 = 3 r 1 → 15 ÷ 4 = 3 r 3. Nothing is left to carry into, so the answer is 233 r 3. Check: 233 × 4 + 3 = 932 + 3 = 935 ✓

Two special cases. (1) If the first digit is smaller than the divisor, look at the first two digits: 315 ÷ 7 → 3 ÷ 7 = 0, so work out 31 ÷ 7 = 4 r 3, then 35 ÷ 7 = 5. Answer 45. (2) If a step gives 0, you must write the 0 in the answer: 624 ÷ 6 → 6 ÷ 6 = 1, 2 ÷ 6 = 0 r 2, 24 ÷ 6 = 4. Answer 104, not 14.

3. Dividing by a 2-digit number: chunking

Chunking means taking away big, easy chunks (multiples of the divisor) until nothing (or only a remainder) is left. Then add up how many lots you took. Start by writing a few easy multiples of the divisor: 1×, 2×, 5×, 10×, 20×.

• 768 − 480 (20 lots) = 288
• 288 − 240 (10 lots) = 48
• 48 − 48 (2 lots) = 0
• Total: 20 + 10 + 2 = 32, so 768 ÷ 24 = 32. Check: 32 × 24 = 768 ✓

Bigger chunks = fewer steps. Using 30 × 24 = 720 straight away: 768 − 720 = 48 = 2 × 24, so the answer is 30 + 2 = 32.

4. Long division (÷ a 2-digit number)

Long division is the written method for chunking. Each step has the same four parts: Divide, Multiply, Subtract, Bring down (remember "Does My Sister Bake?").

1. 989 ÷ 23. 23 does not go into 9, so use 98. Divide: 23 × 4 = 92 and 23 × 5 = 115 (too big), so write 4 above the 8.
2. Multiply: 4 × 23 = 92. Subtract: 98 − 92 = 6.
3. Bring down the next digit 9 to make 69.
4. Divide: 23 × 3 = 69, so write 3 above the 9. Multiply and subtract: 69 − 69 = 0.
5. No digits left. Answer 43, remainder 0. Check: 43 × 23 = 989 ✓ and 43 is close to the estimate 40.

When the division is not exact, the last subtraction leaves a remainder. The remainder must always be smaller than the divisor — if it is not, your quotient digit is too small.

Short division by a 2-digit number works too if you list multiples first. For 864 ÷ 16: list 16, 32, 48, 64, 80, 96. 86 ÷ 16 = 5 r 6 (5 × 16 = 80), then 64 ÷ 16 = 4. Answer 54.

5. Remainders in real life

In a word problem you must decide what the remainder means. Read the question again before you write the answer.

Worked examples

Worked example 1 (1 mark) — Ring the best estimate for 618 ÷ 8. 7 60 80 700

640 is close to 618 and 64 ÷ 8 = 8, so 640 ÷ 8 = 80. Answer: 80. (Exact: 77 r 2.) Common mistake: 700 — that is the dividend rounded, not the quotient.

Worked example 2 (1 mark) — Calculate 624 ÷ 6.

6 ÷ 6 = 1. 2 ÷ 6 = 0 remainder 2 → write 0, carry 2. 24 ÷ 6 = 4. Answer: 104. Check: 104 × 6 = 624 ✓. Common mistake: writing 14. Estimate 600 ÷ 6 = 100 shows that 14 is far too small.

Worked example 3 (2 marks) — Calculate 816 ÷ 34. Show your working.

• Estimate: 800 ÷ 40 = 20 (or 816 is about 850 = 25 × 34), so the answer is between 20 and 25.
• Chunk: 20 × 34 = 680. 816 − 680 = 136.
• Multiples: 2 × 34 = 68, 4 × 34 = 136. 136 − 136 = 0.
• 20 + 4 = 24. Check: 24 × 34 = 816 ✓

Worked example 4 (1 mark) — 460 students go on a school trip. Each bus has 52 seats. How many buses are needed?

460 ÷ 52: 52 × 8 = 416, 52 × 9 = 468 (too big). 460 − 416 = 44, so 460 ÷ 52 = 8 r 44. The 44 students still need a bus, so round up. Answer: 9 buses. Common mistake: writing "8 r 44" or "8" — a remainder is never the final answer to a "how many buses/boxes are needed" question.

Worked example 5 (1 mark) — When a number is divided by 15 the answer is 42 remainder 7. What is the number?

Use the inverse: number = quotient × divisor + remainder = 42 × 15 + 7 = 630 + 7 = 637. Check: 637 ÷ 15 → 15 × 42 = 630, remainder 7 ✓

Worked example 6 (2 marks) — 932 ÷ 7. Give your answer with a remainder, then explain how to check it.

9 ÷ 7 = 1 r 2 → 23 ÷ 7 = 3 r 2 → 22 ÷ 7 = 3 r 1. Answer: 133 r 1. Check: 133 × 7 + 1 = 931 + 1 = 932 ✓

Practice

All pages in this course

Start here

• Checkpoint 6 Maths: The Test and How to Prepare

Number: integers and calculation

• Counting On and Back and Negative Numbers
• Sequences, Letters and Position-to-Term Rules
• Order of Operations, Brackets and Laws of Arithmetic
• Multiplying Whole Numbers (up to 10 000 × 2-digit)
• Dividing Whole Numbers (up to 1000 ÷ 2-digit)
• Factors, Multiples and Tests of Divisibility
• Square Numbers and Cube Numbers

Number: place value, decimals, fractions, percentages and ratio

• Place Value and Decimals to Thousandths
• Rounding Decimals
• Fractions: Division, Operators and Simplest Form
• Adding and Subtracting Fractions
• Multiplying and Dividing Fractions by Whole Numbers
• Fractions, Decimals and Percentages: Equivalence and Ordering
• Adding, Subtracting, Multiplying and Dividing Decimals
• Ratio and Direct Proportion

Geometry and measure

• Time: Decimals and Mixed Units
• Quadrilaterals: Properties and Classification
• Circles: Parts and Constructing Circles
• Angles: Measuring, Drawing and Angles in a Triangle
• Area of Rectangles and Right-angled Triangles
• 3D Shapes, Compound Shapes and Nets
• Capacity, Volume and Surface Area
• Coordinates in Four Quadrants
• Rotational Symmetry, Translation, Reflection and Rotation

Statistics and probability

• Collecting and Representing Data
• Mode, Median, Mean and Range, and Interpreting Data
• Probability

Practice tests

• Checkpoint 6 Maths — Practice Test 1
• Checkpoint 6 Maths — Practice Test 2
• Checkpoint 6 Maths — Practice Test 3