IGCSE Mathematics: Fractions, Decimals and Percentages Practice Questions
Fractions, decimals and percentages are three ways of writing the same value. Converting between them and handling mixed numbers correctly is what most marks in this topic depend on.
Topic 1.4 of Cambridge IGCSE Mathematics 0580 dominates the non-calculator paper. Nearly every lost mark comes from adding fractions without a common denominator, or from mishandling a mixed number. The questions below cover both, plus converting a recurring decimal.
What you need to know for Fractions, Decimals and Percentages
- Adding and subtracting fractionsConvert to a common denominator first, then add or subtract the numerators only. Change mixed numbers to improper fractions before starting.
- Multiplying fractionsMultiply the numerators and multiply the denominators. Cancel common factors before multiplying to keep the numbers small.
- Dividing fractionsMultiply by the reciprocal of the second fraction. Turn the second fraction upside down and change the sign to multiplication.
- Converting a fraction to a decimalDivide the numerator by the denominator. A denominator whose only prime factors are 2 and 5 gives a terminating decimal. Any other denominator gives a recurring decimal.
- Recurring decimal to fractionFor a two digit repeating block, place the block over 99. For a one digit block, place it over 9. Then cancel to lowest terms.
- Percentage of an amountTo find one quantity as a percentage of another, divide the first by the second and multiply by 100.
IGCSE Mathematics Fractions, Decimals and Percentages questions and answers
4 exam-style questions written to the 0580 syllabus. Try each one on paper first, then open the worked answer to check your method against the marks.
Work out 2 and 3 quarters plus 1 and 5 sixths, giving your answer as a mixed number in its simplest form.
Show the worked answer
- Convert both to improper fractions: 2 and 3 quarters = 11 quarters, and 1 and 5 sixths = 11 sixths.
- The lowest common denominator of 4 and 6 is 12. Convert: 11 quarters = 33 twelfths, and 11 sixths = 22 twelfths.
- Add the numerators: 33 + 22 = 55, giving 55 twelfths.
- Convert back to a mixed number: 12 goes into 55 four times with 7 remaining, so the answer is 4 and 7 twelfths.
Convert the recurring decimal 0.363636 recurring into a fraction in its simplest form.
Show the worked answer
- The repeating block is 36, which is two digits long.
- A two digit repeating block is placed over 99, giving 36 over 99.
- Find the highest common factor of 36 and 99. Both divide by 9: 36 divided by 9 = 4 and 99 divided by 9 = 11.
- The fraction in its simplest form is 4 elevenths. Check by dividing: 4 divided by 11 = 0.363636 recurring.
Work out 4 fifths divided by 2 thirds, giving your answer as a mixed number.
Show the worked answer
- To divide by a fraction, multiply by its reciprocal. The reciprocal of 2 thirds is 3 halves.
- So 4 fifths divided by 2 thirds becomes 4 fifths multiplied by 3 halves.
- Multiply across: numerators 4 x 3 = 12, denominators 5 x 2 = 10, giving 12 tenths.
- Simplify by dividing both by 2 to get 6 fifths, which as a mixed number is 1 and 1 fifth.
Find 3 eighths of 240, then express that answer as a percentage of 240.
Show the worked answer
- Divide 240 by the denominator: 240 divided by 8 = 30.
- Multiply by the numerator: 30 x 3 = 90.
- To express 90 as a percentage of 240, divide 90 by 240 = 0.375.
- Multiply by 100 to get 37.5 per cent. As a check, 3 eighths as a decimal is 0.375, which is the same value.
Common mistakes in this topic
- Adding denominators when adding fractions.
- Leaving an answer as an improper fraction when a mixed number is asked for.
- Inverting the wrong fraction when dividing.
- Using the wrong number of nines when converting a recurring decimal.
- Forgetting to simplify the final fraction.
Exam tips
- Convert every mixed number to an improper fraction before doing anything else.
- Cancel common factors before multiplying, not after. The numbers stay much smaller.
- Show the common denominator line explicitly. It is usually worth a method mark.
- Check a fraction answer by converting it to a decimal on your calculator when one is allowed.
- Learn the common fraction to decimal conversions: a half, quarters, eighths, fifths and tenths.
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Fractions, Decimals and Percentages FAQs
How do I add mixed numbers?
Convert each mixed number to an improper fraction, find a common denominator, add the numerators only, then convert the result back to a mixed number and simplify. Trying to add the whole numbers and fractions separately works but causes errors when the fractional parts add to more than one.
How do I divide by a fraction?
Multiply by the reciprocal of the fraction you are dividing by. Turn that second fraction upside down and change the division sign to a multiplication sign, then multiply the numerators and the denominators. Only the second fraction is inverted.
How do I convert a recurring decimal to a fraction?
Count the digits in the repeating block and place the block over that many nines. A one digit block goes over 9, a two digit block over 99, a three digit block over 999. Then cancel the fraction to its lowest terms.
How do I write one number as a percentage of another?
Divide the first number by the second, then multiply by 100. To express 90 as a percentage of 240, calculate 90 divided by 240, which is 0.375, then multiply by 100 to get 37.5 per cent.
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Written to the published Cambridge IGCSE Mathematics (0580) syllabus. Check your school entry code and syllabus year, because Core and Extended candidates are assessed on different content. Last reviewed 2026-08-12.