Maths · Fractions, Decimals & Percentages
Fractions (four ops)
Add, subtract, multiply, and divide fractions.
Practice & Master are locked until you try:
Adding and Subtracting Fractions
To add or subtract fractions, first find a common denominator (bottom number). Convert both fractions so they share this denominator. Then add or subtract the numerators (top numbers) and keep the denominator the same. Always simplify your answer by dividing top and bottom by their greatest common factor.
Multiplying Fractions
Multiplying fractions is simpler than adding them! Multiply the numerators together to get the new numerator. Multiply the denominators together to get the new denominator. You can simplify before or after multiplying. Look for common factors to cancel across numerators and denominators.
Dividing Fractions
To divide by a fraction, flip the second fraction upside down (this is called the reciprocal). Then multiply instead of dividing. Remember: dividing by a fraction is the same as multiplying by its reciprocal. So ½ ÷ ¼ becomes ½ × 4.
Simplifying Your Answers
Always write fractions in their simplest form. This means the numerator and denominator have no common factors except 1. Divide both by their highest common factor. For example, 6/8 simplifies to 3/4 by dividing both by 2.
Worked examples
1. Calculate 2/5 + 1/3
- Find a common denominator: 5 × 3 = 15
- Convert: 2/5 = 6/15 and 1/3 = 5/15
- Add numerators: 6/15 + 5/15 = 11/15
- 11/15 is already in simplest form
2. Calculate 3/4 × 2/9
- Multiply numerators: 3 × 2 = 6
- Multiply denominators: 4 × 9 = 36
- Result: 6/36
- Simplify by dividing both by 6: 6/36 = 1/6
3. Calculate 2/3 ÷ 4/5
- Flip the second fraction to get its reciprocal: 4/5 becomes 5/4
- Change division to multiplication: 2/3 × 5/4
- Multiply: (2 × 5)/(3 × 4) = 10/12
- Simplify by dividing both by 2: 10/12 = 5/6
Try it yourself
Calculate 3/8 + 1/4
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