Practice Fractions: meaning and representation
A fraction describes equal parts of a whole: the denominator gives the number of parts and the numerator counts selected parts.
Fractions help you compare shares and measurements.
Exercises with solutions
A fraction describes equal parts of a whole. The denominator at the bottom says how many parts the whole is divided into, the numerator at the top how many of those parts you take. The fraction bar means divide: 3/4 is the same as 3 ÷ 4.
Exercise 1
A rectangle is divided into 8 equal parts, 3 of them are shaded. Which fraction is shaded?
Show solution and working
3/8
The denominator is the total number of parts, so 8. The numerator is the number of shaded parts, so 3.
Exercise 2
Which is more: 1/3 or 1/5 of a cake?
Show solution and working
1/3
With the same numerator, the fraction with the smaller denominator is larger, because the individual pieces are bigger.
Exercise 3
Write 3/4 as a division.
Show solution and working
3 ÷ 4
The fraction bar means divide. 3/4 = 3 ÷ 4 = 0.75.
Exercise 4
Which fraction is larger: 2/5 or 3/5?
Show solution and working
3/5
With the same denominator, the fraction with the larger numerator is larger, because you take more equal parts.
Common mistake
Thinking a larger denominator means a larger fraction when the numerators match. 1/8 is smaller than 1/3 because eighths are smaller pieces. Remember: the more parts, the smaller each piece.
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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