Practice Percentages
A percentage expresses a share out of one hundred; one percent is one hundredth of the whole.
Percentages help you compare discounts, survey results and changes in quantities.
Exercises with solutions
One percent is one hundredth. Divide the whole by 100 to find 1%, then multiply by the percentage. Subtract a discount amount from the original price to find the new price.
Exercise 1
What is 25% of €80?
Show solution and working
€20
1% of €80 is €0.80. 25 × €0.80 = €20; alternatively, 25% is one quarter.
Exercise 2
A backpack costs €60 and has a 15% discount. What is its new price?
Show solution and working
€51
The discount is 0.15 × €60 = €9. Subtract it: €60 − €9 = €51.
Exercise 3
6 out of 24 children cycle to school. What percentage is that?
Show solution and working
25%
The fraction is 6/24 = 1/4, which equals 25/100 = 25%.
Exercise 4
Extension: 30% of a quantity is 18 kg. Find the whole quantity.
Show solution and working
60 kg
1% is 18 kg ÷ 30 = 0.6 kg. Multiply by 100 to find the whole: 60 kg.
Common mistake
The discount amount is not the new price. A 15% discount does not always mean €15 off: it depends on the original price.
Free maths worksheets with worked solutions
Percentages: free German worksheet with solutions (PDF)
Foundations from Grade 6: questions 1–6. Questions 7–10 extend the foundations.
PDF and questions in German
Maths by grade
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