Getting a fraction question wrong does not always mean you have forgotten fractions. You may know the rules but switch between addition, multiplication and division without noticing that each operation needs a different approach.
This short practice session separates those decisions. It uses original StudyForA questions, followed by solutions you can check. The arithmetic is useful foundation work for both Core and Extended learners; it is not a complete revision list for either tier.
Check your examination year first
Cambridge's 2025–2027 Mathematics 0580 syllabus includes a dedicated non-calculator paper at each tier. Choose the syllabus for the year you sit the exam, rather than the year you started the course. You can find the current documents on the official Mathematics 0580 page.
Older questions can still help with arithmetic, but an older paper's instructions are not a reliable guide to your current calculator arrangements.
Decide what the operation requires
For addition or subtraction, the pieces must have the same size. That is why you find a common denominator. For multiplication, you multiply the numerators and denominators, simplifying factors where helpful. For division by a non-zero fraction, multiply by its reciprocal.
Write the operation in words before calculating if you tend to mix these up. “Subtract two amounts” should prompt a different first step from “divide by two-thirds”.
Worked example: subtract, then simplify
Find 5/6 − 1/4.
The least common denominator is 12. Rewrite the fractions without changing their values: 5/6 = 10/12 and 1/4 = 3/12. The difference is therefore 7/12.
Notice what did not happen: we did not subtract the denominators. The denominator still describes twelfths; the numerator counts how many twelfths remain.
A quick size check helps. Five-sixths is greater than three-quarters. Subtracting one-quarter should leave a result greater than one-half. Seven-twelfths fits that expectation. A negative result would tell you to inspect the subtraction.
Worked example: divide by a fraction
Find 3/5 ÷ 9/10.
Multiply by the reciprocal of the divisor: 3/5 × 10/9. Cancel the common factors before multiplying: 10/5 = 2 and 3/9 = 1/3. The result is 2/3.
Check division by multiplying the answer by the divisor. Two-thirds of 9/10 is 18/30, which simplifies to 3/5. That returns the original amount.
Try three questions before reading the answers
- Find 7/8 − 1/3.
- Find 4/9 ÷ 2/3.
- Find 1 1/2 × 2/5.
For each question, write one line that explains your first step. This makes it easier to distinguish a wrong method from a small arithmetic slip.
Answers and useful checks
- Use twenty-fourths: 21/24 − 8/24 = 13/24. The result is positive and smaller than 7/8.
- Multiply by 3/2: 4/9 × 3/2 = 12/18 = 2/3. Checking gives 2/3 × 2/3 = 4/9.
- Change the mixed number to 3/2, then multiply: 3/2 × 2/5 = 3/5. The answer is greater than 2/5 because you multiplied by a number greater than one.
Use the mistake to choose your next question
If your denominator was wrong, practise rewriting equivalent fractions. If you flipped the first fraction, practise division while explicitly labelling the divisor. If the method was right but the multiplication failed, slow down that arithmetic step before adding a timer.
Next time, change the numbers and solve without the worked example beside you. Being able to explain the first step matters more than recognising an answer you have already seen.
Choose another Maths 0580 lesson on StudyForA, or use the past-paper revision routine to select your next skill.