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Multiplication

FoundationChallengeAQAEdexcelOCR

Get to grips with multiplication using these Foundation GCSE Maths practice questions. The worksheet focuses on short and long multiplication, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Estimate first so you can spot if a long-multiplication answer is the wrong size.

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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

Long multiplication breaks a difficult multiplication into easier parts. The grid method and the column method both do this, and either is acceptable in an exam provided the working is clear.

The grid method splits each number by place value, multiplies every pair, and adds the results. It is slower but very hard to get wrong, because each step is a simple multiplication.

The column method multiplies by each digit in turn, remembering that a digit in the tens column is worth ten times its face value. That is why the second row is shifted one place left, or written with a zero placeholder.

Revision notes

The grid method

Split both numbers by place value along the edges of a grid, multiply each pair, then add all the products.

For \(23 \times 14\), the grid gives \(20 \times 10 = 200\), \(20 \times 4 = 80\), \(3 \times 10 = 30\) and \(3 \times 4 = 12\). Adding these gives \(322\).

The column method

Multiply the top number by the units digit, then by the tens digit, writing a zero in the units column of the second row because you are really multiplying by a multiple of ten.

For \(23 \times 14\): \(23 \times 4 = 92\), then \(23 \times 10 = 230\), and \(92 + 230 = 322\).

Multiplying decimals

Ignore the decimal points, multiply as whole numbers, then count the total decimal places in the question and put that many in the answer.

For \(0.3 \times 0.4\), work out \(3 \times 4 = 12\). There are two decimal places in total, so the answer is \(0.12\).

Key points

  • Break the multiplication into place-value parts.
  • The grid method multiplies every pair and adds the results.
  • The column method needs a zero placeholder in the second row.
  • Estimate first by rounding to check the answer.
  • For decimals, multiply as whole numbers first.
  • Count the total decimal places to place the point.

Worked examples

Example 1

Work out \(34 \times 26\) using the grid method.

Working

\[30 \times 20 = 600 \text{, } 30 \times 6 = 180\]multiply the tens of the first number by each part
\[4 \times 20 = 80 \text{, } 4 \times 6 = 24\]multiply the units by each part
\[600 + 180 + 80 + 24 = 884\]add all four products

Example 2

Work out \(126 \times 3\).

Working

\[6 \times 3 = 18\]multiply the units, write 8 and carry 1
\[2 \times 3 + 1 = 7\]multiply the tens and add the carry
\[1 \times 3 = 3 \text{, giving } 378\]multiply the hundreds

Example 3

Work out \(0.6 \times 0.07\).

Working

\[6 \times 7 = 42\]ignore the decimal points and multiply as whole numbers
\[\text{3 decimal places in total}\]count the decimal places in 0.6 and 0.07
\[= 0.042\]place the decimal point three places from the right

Common mistakes

  • Forgetting the zero placeholder in the column method.

    The second row multiplies by tens, so it must be shifted left or padded with a zero.

  • Miscounting decimal places.

    0.6 × 0.07 has three decimal places in total, giving 0.042, not 0.42.

  • Adding instead of multiplying within the grid.

    Each cell is a product; only the final combination is an addition.

  • Not estimating first.

    Rounding 34 × 26 to 30 × 30 gives roughly 900, which flags a wildly wrong answer instantly.

Exam tips

  • Use whichever method you find most reliable — both earn full marks.
  • Estimate by rounding before you start.
  • Set work out neatly in columns so digits stay aligned.
  • For decimals, count the decimal places in the question, not the answer.

Key terms

Product
The result of a multiplication.
Grid method
Splitting numbers by place value into a multiplication grid.
Placeholder
A zero used to keep digits in the correct column.
Partial product
One of the individual multiplications that are added together.

Related topics

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