Operations with fractions, decimals and percentages
Practise fractions from scratch: numerator and denominator, equivalent fractions, simplification using the GCD, adding fractions with different denominators using the LCM, multiplication and division (Keep-Change-Flip), conversion to decimals and percentages. Every question shows the full procedure.
A fraction represents a part of a whole: the numerator shows how many parts we take and the denominator how many the total is divided into. Fractions are the gateway to rational numbers and appear everywhere: recipes, percentages, probabilities and proportions.
The key concepts are equivalent fractions, simplifying with the greatest common divisor (GCD), and the operations: adding and subtracting by finding a common denominator with the lowest common multiple (LCM), multiplying straight across and dividing with the ‘Keep-Change-Flip’ rule. Knowing how to convert a fraction to a decimal and a percentage is also essential.
Practise the whole fractions and decimals block with the exam below, with the full procedure in every question so you can see each step.
Mathematics · Primary, Secondary
Primary covers simple fractions, basic decimals and easy percentages. Secondary adds powers of fractions, recurring decimals and mixed operations.
After each answer the full step-by-step calculation appears: from finding the LCM to applying Keep-Change-Flip when dividing fractions.
All questions are designed to be solved by hand, reinforcing mental arithmetic with fractions that will reappear in algebra and functions.
"A Year 5 student who confused numerator and denominator learns the rule "the bottom is the total" in the first question and never makes the mistake again."
Tricks and techniques to master this topic faster:
Equivalent fractions: multiply or divide both numerator and denominator by the same number. ½ = 2/4 = 3/6.
To add fractions with different denominators: find the LCM, convert each fraction, then add the numerators.
To divide fractions: Keep the first, Change to multiplication, Flip the second. ¾ ÷ ½ = ¾ × 2/1 = 6/4.
Percentage: "X% of Y" = Y × (X/100). "What % is A of B?" = (A/B) × 100.
If you are studying Fractions and Decimals — Maths Exam, these curriculum topics complement each other:
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