Challenging Fraction Puzzles

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Part 1: Fraction Clues

Solve each puzzle. Show your thinking using multiplication or division.

1. I am an equivalent fraction to 3/4. My denominator is 20. What fraction am I?

2. A fraction is equivalent to 5/8. Its numerator is 35. What is its denominator?

3. Which fraction is greater: 7/12 or 5/8? Prove your answer by finding a common denominator.

4. A number is between 1/2 and 3/4. It has a denominator of 12. What could the fraction be? Find all possible answers.

Part 2: Show It in Pictures

Draw and label your diagrams carefully. Shade shapes to represent the fractions.

5. Draw a rectangle divided into equal parts. Shade 5/8, then show an equivalent fraction with a denominator of 16.

6. Draw a number line from 0 to 1. Mark and label 1/4, 1/2, 3/4 and 7/8.

7. Use a shaded shape or number line to explain why 2/3 is equivalent to 8/12.

8. A cake has 12 equal pieces. Mia eats 5 pieces and Arlo eats 1/4 of the cake. What fraction of the cake is left? Explain with a diagram and a calculation.

Part 3: Create a Partner Puzzle

Design one challenging fraction puzzle for a partner. Include an equivalent-fraction clue, a number-line clue, or a shaded-shape clue. Do not write the answer yet.

9. My partner’s fraction puzzle:

10. Solve your partner’s puzzle. Explain your answer using a diagram, multiplication or division.