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Division

FoundationChallengeAQAEdexcelOCR

This free Foundation GCSE Maths worksheet on division helps you revise short and long division. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Check a division by multiplying your answer back by the divisor.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

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Topic overview

Division shares an amount into equal parts or finds how many times one number fits into another. Short division suits dividing by a single digit, and long division handles larger divisors.

The method works from the left, which is the opposite of addition and subtraction. You divide each digit in turn, carrying any remainder into the next digit as a ten.

When dividing decimals, the key trick is that dividing by a decimal is awkward, so you scale both numbers by a power of ten until the divisor is a whole number. Since both numbers grow by the same factor, the answer is unchanged.

Revision notes

Short division

Divide each digit from the left, writing the answer above and carrying any remainder to the next digit.

For \(852 \div 4\): \(8 \div 4 = 2\); \(5 \div 4 = 1\) remainder \(1\), so carry the \(1\) to make \(12\); \(12 \div 4 = 3\). The answer is \(213\).

Remainders

A remainder can be left as a whole number, converted to a fraction, or continued as a decimal by adding a decimal point and zeros.

So \(43 \div 5\) is \(8\) remainder \(3\), or \(8\frac{3}{5}\), or \(8.6\). Read the question to see which form is wanted, especially in context questions about buses or boxes.

Dividing by a decimal

Multiply both numbers by a power of ten until the divisor is whole.

For \(4.8 \div 0.2\), multiply both by \(10\) to get \(48 \div 2 = 24\). The answer is unchanged because both numbers were scaled equally.

Key points

  • Short division works from left to right.
  • Carry remainders into the next digit as tens.
  • A remainder can be a whole number, a fraction or a decimal.
  • Scale both numbers so the divisor is a whole number.
  • Scaling both numbers equally leaves the answer unchanged.
  • Read the context to decide how to treat a remainder.

Worked examples

Example 1

Work out \(756 \div 6\).

Working

\[7 \div 6 = 1 \text{ r } 1\]divide the first digit and carry the remainder
\[15 \div 6 = 2 \text{ r } 3\]the carried 1 makes 15
\[36 \div 6 = 6 \text{, giving } 126\]the carried 3 makes 36

Example 2

Work out \(4.8 \div 0.2\).

Working

\[48 \div 2\]multiply both numbers by 10 so the divisor is whole
\[= 24\]carry out the division

Example 3

\(53\) students travel in minibuses holding \(8\) each. How many minibuses are needed?

Working

\[53 \div 8 = 6 \text{ r } 5\]divide to find how many full minibuses
\[7 \text{ minibuses}\]the remaining 5 students still need a bus, so round up

Common mistakes

  • Working from right to left.

    Division starts from the left, unlike addition and subtraction.

  • Ignoring the remainder in a context question.

    If 5 students are left over they still need transport, so the answer rounds up.

  • Scaling only one number when dividing by a decimal.

    Both must be multiplied by the same power of ten or the answer changes.

  • Dropping a zero in the answer.

    If a digit divides exactly zero times, write the 0 in the answer rather than skipping it.

Exam tips

  • Decide early whether the context needs rounding up or down.
  • Check by multiplying your answer back by the divisor.
  • Scale decimals before dividing rather than during.
  • Write remainders clearly so the method is visible.

Key terms

Divisor
The number you are dividing by.
Dividend
The number being divided.
Quotient
The result of a division.
Remainder
What is left over when a division is not exact.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.