# Grade 4 Module 5: Fractions (Topic B + Topic C) Practice

Use scratch paper to show work. For any problem that mentions a model, use a rectangle area model, tape diagram, or a number line.

## Topic B: Equivalent Fractions (Multiply/Divide)

### 1) Prove These Are True (write a multiplication number sentence)
1. \(\frac{3}{5} = \frac{6}{10}\)
2. \(\frac{4}{8} = \frac{8}{16}\)

### 2) Make Equivalent Fractions Using Multiplication
Fill in the blanks so the fractions stay equivalent.

3. \(\frac{3}{4} = \frac{3 \times \_\_}{4 \times \_\_} = \frac{\_\_}{\_\_}\)
4. \(\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{\_\_}{\_\_}\)
5. \(\frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{\_\_}{\_\_}\)
6. \(\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{\_\_}{\_\_}\)

### 3) Explain With a Model (one or two sentences)
7. Explain how a model can show \(\frac{2}{6}\) is equivalent to \(\frac{1}{3}\).

### 4) Make Equivalent Fractions Using Division (Simplify)
Fill in the blanks so the fractions stay equivalent.

8. \(\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{\_\_}{\_\_}\)
9. \(\frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{\_\_}{\_\_}\)

### 5) Rename Each Fraction Using Division (simplify as much as you can)
10. \(\frac{16}{20} = \_\_\)
11. \(\frac{18}{20} = \_\_\)
12. \(\frac{8}{12} = \_\_\)

## Topic C: Comparing Fractions (<, >, =)

For each problem, compare the fractions and write `<`, `>`, or `=`. Show work by rewriting both fractions with a common denominator (or by using a number line/tape diagram).

13. \(\frac{2}{3} \ \_\_ \ \frac{3}{5}\)
14. \(\frac{1}{4} \ \_\_ \ \frac{2}{8}\)
15. \(\frac{3}{7} \ \_\_ \ \frac{4}{9}\)
16. \(\frac{5}{6} \ \_\_ \ \frac{7}{9}\)
17. \(\frac{2}{5} \ \_\_ \ \frac{3}{10}\)
18. \(\frac{3}{8} \ \_\_ \ \frac{1}{2}\)
19. \(\frac{4}{5} \ \_\_ \ \frac{6}{10}\)
20. \(\frac{7}{12} \ \_\_ \ \frac{2}{3}\)

### Word Problems (compare, then write a sentence)
21. Ed rode \(\frac{2}{5}\) of a mile. Matt rode \(\frac{1}{2}\) of a mile. Who rode farther? Explain with a comparison.
22. There is \(\frac{3}{8}\) of a cheese pizza left and \(\frac{5}{12}\) of a pepperoni pizza left. Which pizza has more left? Explain with a comparison.

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# Answer Key (for grown-ups)

1. Multiply by 2: \(\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}\)
2. Multiply by 2: \(\frac{4}{8} = \frac{4 \times 2}{8 \times 2} = \frac{8}{16}\)
3. Any same multiplier works (example): \(\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}\)
4. \(\frac{2}{12}\)
5. \(\frac{6}{21}\)
6. \(\frac{8}{20}\)
7. Example explanation: A model can show the same shaded amount. If you split each third into 2 equal parts, you get 6 equal parts. Shading 1 out of 3 becomes shading 2 out of 6, so \(\frac{1}{3}=\frac{2}{6}\).
8. \(\frac{3}{5}\)
9. \(\frac{1}{3}\)
10. \(\frac{4}{5}\)
11. \(\frac{9}{10}\)
12. \(\frac{2}{3}\)
13. \(>\) (common denominator 15: \(\frac{10}{15} > \frac{9}{15}\))
14. \(=\) (both \(\frac{2}{8}\))
15. \(<\) (common denominator 63: \(\frac{27}{63} < \frac{28}{63}\))
16. \(>\) (common denominator 18: \(\frac{15}{18} > \frac{14}{18}\))
17. \(>\) (common denominator 10: \(\frac{4}{10} > \frac{3}{10}\))
18. \(<\) (common denominator 8: \(\frac{3}{8} < \frac{4}{8}\))
19. \(>\) (common denominator 10: \(\frac{8}{10} > \frac{6}{10}\))
20. \(<\) (common denominator 12: \(\frac{7}{12} < \frac{8}{12}\))
21. Matt rode farther: \(\frac{1}{2} > \frac{2}{5}\) (common denominator 10: \(\frac{5}{10} > \frac{4}{10}\)).
22. Pepperoni has more left: \(\frac{5}{12} > \frac{3}{8}\) (common denominator 24: \(\frac{10}{24} > \frac{9}{24}\)).