Multiplying Fractions
Multiplying fractions means multiplying the numerators, then the denominators. Then simplify if you can. Cross-cancelling divides a top and bottom by a common factor first to keep numbers smaller.
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How Do We Multiply Fractions?
- Multiply the numerators together and multiply the denominators together.
- Then simplify the fraction, if possible.
What Is Cross-Cancelling When Multiplying Fractions?
- You can simplify first by cross-cancelling a numerator with a denominator.
- Cross-cancelling makes the numbers smaller and easier to multiply.
How Do We Multiply a Fraction by a Whole Number?
- Write the whole number as a fraction over 1.
- Then multiply as you would with two fractions.
How Do We Multiply Mixed Numbers?
- Convert mixed numbers into improper fractions first.
- Then multiply and simplify the final answer.
Practice Questions
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What is ?
Correct! 🎉 +10 pointsNot quite right
Multiply the numerators: . Then, multiply the denominators: . The result is , which cannot be simplified further.
What is of 15?
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Multiply by rewriting 15 as . Cross-cancel 5 and 15 to get 1 and 3. Multiply 7 by 3 to get 21.
What is ?
Correct! 🎉 +20 pointsNot quite right
Simplify to and to . Multiply the numerators: . Multiply the denominators: . The result is .
What is ?
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Simplify: 16 and 24 divide by 8, becoming 2 and 3, and 18 and 27 divide by 9, becoming 2 and 3. Multiply: and , giving .
What is using the cross-cancelling method?
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Simplify: 25 and 50 divide by 25, becoming 1 and 2, and 40 and 32 divide by 8, becoming 5 and 4. Multiply: and , giving , which simplifies to .
What is using the cross-cancelling method?
Correct! 🎉 +30 pointsNot quite right
Convert into an improper fraction: . Cross-cancel: 9 and 3 divide by 3, becoming 3 and 1. Multiply: and , giving .
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Write the whole number over a denominator of 1, then multiply the numerators together and the denominators together. You can cross-cancel first if a top number and a bottom number share a factor, which keeps the working small. The method is the same as multiplying any two fractions.
Always change each mixed number into an improper fraction before you multiply. A mixed number means a whole number plus a fraction, not multiplied. Multiplying the parts separately gives a wrong answer. Once converted, multiply the numerators and the denominators as usual.
Cross-cancelling keeps the numbers small. If you multiply first and simplify later, the numerators and denominators grow quickly. That makes the final fraction harder to simplify. Cancelling a common factor before multiplying means you work with smaller numbers and often reach the simplest form straight away.
Often yes. After multiplying straight across, the answer may still share common factors that you need to cancel. However, if you cross-cancel before multiplying, the answer is frequently already in its simplest form. Always check the final fraction for any common factors.
The highest common factor (HCF) is the largest number that divides a chosen top number and bottom number exactly. You divide each by it to cancel them in a single step before multiplying. Using the highest common factor keeps the numbers as small as possible.