Practice Fractions: multiplication and division
Multiply fractions by multiplying their numerators and their denominators; common factors can be cancelled first.
This helps you calculate a fraction of a quantity.
Exercises with solutions
Multiply the numerators and multiply the denominators. Cancel common factors first when possible. Write whole numbers with denominator 1 and convert mixed numbers to improper fractions.
Exercise 1
Calculate 2/3 × 3/5.
Show solution and working
2/5
Cancel the common factor 3. This leaves 2 × 1 / (1 × 5) = 2/5.
Exercise 2
Calculate 4 × 3/8.
Show solution and working
3/2 = 1 1/2
Write 4 as 4/1. The product is 12/8 = 3/2.
Exercise 3
Calculate 1 1/2 × 2/3.
Show solution and working
1
1 1/2 = 3/2. Then 3/2 × 2/3 = 6/6 = 1.
Exercise 4
A cake needs 3/4 l of milk. How much is needed for half the recipe?
Show solution and working
3/8 l
Half the amount is 1/2 × 3/4 l = 3/8 l.
Common mistake
A common denominator is unnecessary for multiplication. You may cancel factors across a product, but never across an addition or subtraction.
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
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