Practice Simplifying and expanding fractions
Simplifying or expanding a fraction divides or multiplies its numerator and denominator by the same nonzero number.
The value stays the same, which helps you compare and add fractions.
Exercises with solutions
To simplify a fraction, divide its numerator and denominator by the same number. To expand it, multiply both by the same number. Its value stays unchanged.
Exercise 1
Simplify 18/24 fully.
Show solution and working
3/4
The greatest common divisor is 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. 3 and 4 have no common divisor greater than 1.
Exercise 2
Write 3/5 with denominator 20.
Show solution and working
12/20
5 × 4 = 20, so multiply the numerator by 4 as well: 3 × 4 = 12.
Exercise 3
Simplify 42/56 fully.
Show solution and working
3/4
Divide both numbers by 14: 42 ÷ 14 = 3 and 56 ÷ 14 = 4.
Exercise 4
Find the missing number: 5/8 = ?/40.
Show solution and working
25
The denominator is multiplied by 5. Multiply the numerator by 5 too: 5 × 5 = 25.
Common mistake
Changing only the numerator or only the denominator changes the value. Apply the same factor to both.
Free maths worksheets with worked solutions
Fractions: free German worksheet with solutions (PDF)
Grades 5/6: questions 1–5 cover foundations; 6–10 practise fraction calculations.
PDF and questions in German
Maths by grade
Keep learning with MatheJump
Create a free account and explore math practice. Choose from the available exercises to suit your learning needs.