Corbett Maths Multiply Fractions: Explained

Corbett Maths provides free online tutorials and practice questions for multiplying fractions, a key topic in the UK maths curriculum. This guide explains the method, shows worked examples, and addresses common questions so you can multiply fractions with confidence.

Formula

To multiply two fractions, multiply the numerators together and multiply the denominators together. The formula is:

\[ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \]

Where a and c are the numerators (top numbers) and b and d are the denominators (bottom numbers). The result is a new fraction. You can simplify it if the numerator and denominator share a common factor.

Worked Example

Using the default values from the calculator: multiply \( \frac{2}{3} \times \frac{4}{5} \).

1. Multiply the numerators: 2 × 4 = 8.
2. Multiply the denominators: 3 × 5 = 15.
3. The product is \( \frac{8}{15} \).

The calculator shows 8/15 as the product (rounded to 2 decimal places as 0.53) and the simplified form is also 8/15 because 8 and 15 have no common factors other than 1.

When to Use Multiplying Fractions

Multiplying fractions appears in many real-life situations:

• Scaling a recipe – if you want half of a recipe that calls for \( \frac{3}{4} \) cup of sugar, you compute \( \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \) cup.
• Finding a fraction of a quantity – e.g., \( \frac{2}{5} \) of 20 is \( \frac{2}{5} \times 20 = 8 \).
• Area problems – the area of a rectangle with fractional side lengths is found by multiplying the fractions.

This operation is also the basis for more advanced topics like multiplying mixed numbers and algebraic fractions.

How to Read the Result

The product of two fractions is always a fraction (or a whole number if the denominator divides the numerator). For example, \( \frac{2}{3} \times \frac{3}{2} = 1 \), because the numerators and denominators cancel. In general, the result can be larger or smaller than the original fractions; unlike addition, multiplication does not require a common denominator.

If you get an improper fraction (numerator larger than denominator), you can convert it to a mixed number. For instance, \( \frac{9}{4} \) is \( 2 \frac{1}{4} \). The calculator gives the improper fraction, but you can convert it mentally or with a separate step.

Common Mistakes and Misconceptions

Students often make these errors:

• Finding a common denominator – you do NOT need a common denominator for multiplication, only for addition and subtraction.
• Cross-cancelling incorrectly – you can simplify before multiplying, but only if you divide a numerator and a denominator by the same number. For example, \( \frac{2}{3} \times \frac{3}{4} \) can be simplified to \( \frac{1}{1} \times \frac{1}{2} = \frac{1}{2} \).
• Forgetting to simplify – always check if the final fraction can be reduced. For instance, \( \frac{2}{4} \) should be written as \( \frac{1}{2} \).
• Mixing up numerator and denominator – the numerator is on top, denominator on bottom.

Corbett Maths Resources

Corbett Maths offers a dedicated video tutorial on multiplying fractions, typically under the “Fractions” section of their website. The video explains the process step by step, and there are accompanying practice questions with answers. The site also provides textbook exercises and revision cards. These resources are free and widely used by students preparing for GCSE maths.

To get the most out of them:

• Watch the video once without pausing to get an overview.
• Then watch again, pausing to try the examples yourself.
• Complete the practice questions and check your answers.

Alternatives and Related Operations

If you need to divide fractions, you multiply by the reciprocal. For example, \( \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6} \).

Adding and subtracting fractions require a common denominator, which is a different process. Mixed numbers should be converted to improper fractions before multiplying. For instance, \( 1 \frac{1}{2} \times 2 \frac{1}{3} \) becomes \( \frac{3}{2} \times \frac{7}{3} = \frac{21}{6} = 3 \frac{1}{2} \).

You can also use a calculator like the one above to check your manual work, but understanding the method is essential for exams and real-world problem solving.

Frequently Asked Questions

Do I need a common denominator to multiply fractions?

No. Unlike addition or subtraction, multiplication does not require a common denominator. You simply multiply the numerators together and the denominators together.

How do I multiply mixed numbers?

Convert each mixed number to an improper fraction first. For example, \( 2 \frac{1}{3} = \frac{7}{3} \). Then multiply the improper fractions as usual, and simplify the result.

What does cross-cancelling mean?

Cross-cancelling is simplifying before multiplying by dividing a numerator and a denominator by a common factor. For instance, in \( \frac{4}{9} \times \frac{3}{8} \), you can divide 4 and 8 by 4, and 9 and 3 by 3, giving \( \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \).

Why is my answer different from the calculator?

Check that you entered the correct numbers and that you are not simplifying incorrectly. The calculator uses the standard formula and gives both the unsimplified and simplified forms. If you are converting to a decimal, remember that \( \frac{1}{3} \) is 0.333…, which rounds to 0.33.

Can I multiply more than two fractions?

Yes, multiply all numerators together and all denominators together. For example, \( \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} = \frac{6}{24} = \frac{1}{4} \).

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in a | First fraction numerator | - | 2 | 0
in b | First fraction denominator | - | 3 | 0
in c | Second fraction numerator | - | 4 | 0
in d | Second fraction denominator | - | 5 | 0
out result | Product (as fraction) | - | (a*c) / (b*d) | 2
out simplified | Simplified numerator | - | (a*c) / gcd(a*c, b*d) | 0
out simplified_den | Simplified denominator | - | (b*d) / gcd(a*c, b*d) | 0