Short division (the bus stop method) is used when dividing by a single digit. Work left to right through each digit of the dividend, carrying any remainder into the next digit.
Example 1 — Calculate \(987 \div 7\)
Step 1
How many 7s in 9? 1 remainder 2. Write 1, carry the 2.
Step 2
Bring down: 28. How many 7s in 28? 4 remainder 0. Write 4.
How many 18s in 18? 1 exactly. Subtract: \(18 - 18 = 0\). Write 1.
Step 2
Bring down 9 → 09. How many 18s in 9? 0. Write 0, bring down 0 → 90.
Step 3
How many 18s in 90? \(18 \times 5 = 90\). Write 5. Subtract: 0. Answer: \(\mathbf{105}\).
Tip for estimating quotient digits: If you're not sure how many times the divisor goes in, try multiples: \(24 \times 8 = 192\), \(24 \times 9 = 216\), \(24 \times 10 = 240\). Since 223 is between 216 and 240, the answer is 9.
✓ Quick Check 2 — Long Division
Question 1 of 10
Remainders in Real-Life Contexts
In real-life problems, remainders must be interpreted carefully. Sometimes you round up (e.g. you need one more vehicle), sometimes you round down (e.g. you can only make whole portions), and sometimes the remainder is given as a fraction or decimal.
Example 5 — Buses needed (round up)
Step 1
47 people need transport. Each bus holds 9 passengers. \(47 \div 9 = 5\) remainder \(2\).
Step 2
5 full buses carry \(5 \times 9 = 45\) people. 2 people are still without a bus.
Step 3
Round up: \(\mathbf{6}\) buses are needed.
Example 6 — Complete boxes (round down)
Step 1
130 oranges are packed into boxes of 12. \(130 \div 12 = 10\) remainder \(10\).
Step 2
Only 10 complete boxes can be filled. The leftover 10 oranges do not fill a box.
Step 3
Answer: \(\mathbf{10}\) complete boxes.
Example 7 — Sharing money (express remainder as a decimal)
Step 1
Three friends share £47 equally. Calculate \(47 \div 3\).
Step 2
\(3 \times 15 = 45\), remainder \(2\). Write this as \(47 \div 3 = 15\) remainder \(2\).
Step 3
Convert the remainder to a decimal: place a decimal point and continue dividing. \(20 \div 3 = 6\) remainder \(2\); \(20 \div 3 = 6\) remainder \(2\)…
Step 4
Round to the nearest penny (2 d.p.): \(47 \div 3 \approx \mathbf{£15.67}\).
£47 shared equally among 3 people = £15.67 each (to the nearest penny)
Try it: Party Tables
83 guests are seated at tables of 8. How many tables are needed? How many seats are empty?
\(83 \div 8 = 10\) remainder \(3\). You need \(\mathbf{11}\) tables. The last table has \(8 - 3 = \mathbf{5}\) empty seats.
✓ Quick Check 3 — Remainders in Context
Question 1 of 10
Practice: Dividing Whole Numbers
Enter your answers as numbers.
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Question
Answer
Result
1
936 ÷ 8
2
1,248 ÷ 12
3
£675 is shared equally among 15 people. How much does each person get?
4
2,208 ÷ 24
5
A minibus carries 18 passengers. How many minibuses are needed for 250 passengers?
6
864 ÷ 6
7
1,890 ÷ 15
8
£960 is shared equally among 12 people. How much does each person get?
9
3,168 ÷ 33
10
A coach carries 52 passengers. How many coaches are needed for 300 passengers?
⚠ Things to Watch Out For
Remainder goes in the wrong place: In short division (bus stop), the remainder is carried to the NEXT digit on the right, not written at the end until the very last step.
Misinterpreting remainders: "47 people need buses of 9" → 47÷9 = 5 remainder 2. You need 6 buses (round UP because the remaining 2 people still need transport). Always interpret remainders in context.
Long division — bringing down wrong digit: After each subtraction in long division, bring down the NEXT digit from the dividend. Bringing down two digits or skipping one is the most common error.
Division by zero: Division by zero is undefined — it has no answer. If you get a zero divisor in a problem, re-read the question.
Confusing dividend and divisor: In 48 ÷ 6, the dividend is 48 (what you're dividing) and the divisor is 6 (what you're dividing by). Swapping them gives a completely different answer.