Fill in the missing numerators in equivalent fractions.

Let's solve each problem in the "Missing Numerators" worksheet step by step. The goal is to find the missing numerators so that all fractions in each row are equivalent.

We'll go through each row and use cross-multiplication or simplification to find the missing values.

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Row 1:

1. $ \frac{9}{15} = \frac{\square}{10} = \frac{\square}{30} $

- Simplify $ \frac{9}{15} = \frac{3}{5} $
- $ \frac{3}{5} = \frac{x}{10} \Rightarrow x = \frac{3 \times 10}{5} = 6 $
- $ \frac{3}{5} = \frac{y}{30} \Rightarrow y = \frac{3 \times 30}{5} = 18 $

✔ So: $ \frac{9}{15} = \frac{6}{10} = \frac{18}{30} $

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2. $ \frac{4}{7} = \frac{\square}{35} = \frac{\square}{21} $

- $ \frac{4}{7} = \frac{x}{35} \Rightarrow x = \frac{4 \times 35}{7} = 20 $
- $ \frac{4}{7} = \frac{y}{21} \Rightarrow y = \frac{4 \times 21}{7} = 12 $

✔ So: $ \frac{4}{7} = \frac{20}{35} = \frac{12}{21} $

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Row 2:

3. $ \frac{\square}{12} = \frac{55}{60} = \frac{\square}{36} $

- Simplify $ \frac{55}{60} = \frac{11}{12} $
- $ \frac{11}{12} = \frac{x}{12} \Rightarrow x = 11 $
- $ \frac{11}{12} = \frac{y}{36} \Rightarrow y = \frac{11 \times 36}{12} = 33 $

✔ So: $ \frac{11}{12} = \frac{55}{60} = \frac{33}{36} $

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4. $ \frac{\square}{18} = \frac{\square}{45} = \frac{32}{36} $

- Simplify $ \frac{32}{36} = \frac{8}{9} $
- $ \frac{8}{9} = \frac{x}{18} \Rightarrow x = \frac{8 \times 18}{9} = 16 $
- $ \frac{8}{9} = \frac{y}{45} \Rightarrow y = \frac{8 \times 45}{9} = 40 $

✔ So: $ \frac{16}{18} = \frac{40}{45} = \frac{32}{36} $

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5. $ \frac{25}{30} = \frac{\square}{18} = \frac{\square}{24} $

- Simplify $ \frac{25}{30} = \frac{5}{6} $
- $ \frac{5}{6} = \frac{x}{18} \Rightarrow x = \frac{5 \times 18}{6} = 15 $
- $ \frac{5}{6} = \frac{y}{24} \Rightarrow y = \frac{5 \times 24}{6} = 20 $

✔ So: $ \frac{25}{30} = \frac{15}{18} = \frac{20}{24} $

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Row 3:

6. $ \frac{\square}{90} = \frac{28}{40} = \frac{\square}{30} $

- Simplify $ \frac{28}{40} = \frac{7}{10} $
- $ \frac{7}{10} = \frac{x}{90} \Rightarrow x = \frac{7 \times 90}{10} = 63 $
- $ \frac{7}{10} = \frac{y}{30} \Rightarrow y = \frac{7 \times 30}{10} = 21 $

✔ So: $ \frac{63}{90} = \frac{28}{40} = \frac{21}{30} $

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7. $ \frac{\square}{33} = \frac{\square}{18} = \frac{32}{48} $

- Simplify $ \frac{32}{48} = \frac{2}{3} $
- $ \frac{2}{3} = \frac{x}{33} \Rightarrow x = \frac{2 \times 33}{3} = 22 $
- $ \frac{2}{3} = \frac{y}{18} \Rightarrow y = \frac{2 \times 18}{3} = 12 $

✔ So: $ \frac{22}{33} = \frac{12}{18} = \frac{32}{48} $

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8. $ \frac{\square}{44} = \frac{10}{22} = \frac{\square}{66} $

- Simplify $ \frac{10}{22} = \frac{5}{11} $
- $ \frac{5}{11} = \frac{x}{44} \Rightarrow x = \frac{5 \times 44}{11} = 20 $
- $ \frac{5}{11} = \frac{y}{66} \Rightarrow y = \frac{5 \times 66}{11} = 30 $

✔ So: $ \frac{20}{44} = \frac{10}{22} = \frac{30}{66} $

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Row 4:

9. $ \frac{17}{85} = \frac{\square}{55} = \frac{\square}{40} $

- Simplify $ \frac{17}{85} = \frac{1}{5} $
- $ \frac{1}{5} = \frac{x}{55} \Rightarrow x = \frac{1 \times 55}{5} = 11 $
- $ \frac{1}{5} = \frac{y}{40} \Rightarrow y = \frac{1 \times 40}{5} = 8 $

✔ So: $ \frac{17}{85} = \frac{11}{55} = \frac{8}{40} $

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10. $ \frac{15}{60} = \frac{\square}{48} = \frac{\square}{80} $

- Simplify $ \frac{15}{60} = \frac{1}{4} $
- $ \frac{1}{4} = \frac{x}{48} \Rightarrow x = 12 $
- $ \frac{1}{4} = \frac{y}{80} \Rightarrow y = 20 $

✔ So: $ \frac{15}{60} = \frac{12}{48} = \frac{20}{80} $

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11. $ \frac{50}{80} = \frac{\square}{24} = \frac{\square}{40} $

- Simplify $ \frac{50}{80} = \frac{5}{8} $
- $ \frac{5}{8} = \frac{x}{24} \Rightarrow x = \frac{5 \times 24}{8} = 15 $
- $ \frac{5}{8} = \frac{y}{40} \Rightarrow y = \frac{5 \times 40}{8} = 25 $

✔ So: $ \frac{50}{80} = \frac{15}{24} = \frac{25}{40} $

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Row 5:

12. $ \frac{\square}{42} = \frac{24}{72} = \frac{\square}{63} $

- Simplify $ \frac{24}{72} = \frac{1}{3} $
- $ \frac{1}{3} = \frac{x}{42} \Rightarrow x = 14 $
- $ \frac{1}{3} = \frac{y}{63} \Rightarrow y = 21 $

✔ So: $ \frac{14}{42} = \frac{24}{72} = \frac{21}{63} $

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13. $ \frac{\square}{36} = \frac{16}{24} = \frac{\square}{27} $

- Simplify $ \frac{16}{24} = \frac{2}{3} $
- $ \frac{2}{3} = \frac{x}{36} \Rightarrow x = 24 $
- $ \frac{2}{3} = \frac{y}{27} \Rightarrow y = 18 $

✔ So: $ \frac{24}{36} = \frac{16}{24} = \frac{18}{27} $

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14. $ \frac{12}{60} = \frac{\square}{70} = \frac{\square}{80} $

- Simplify $ \frac{12}{60} = \frac{1}{5} $
- $ \frac{1}{5} = \frac{x}{70} \Rightarrow x = 14 $
- $ \frac{1}{5} = \frac{y}{80} \Rightarrow y = 16 $

✔ So: $ \frac{12}{60} = \frac{14}{70} = \frac{16}{80} $

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Row 6:

15. $ \frac{12}{18} = \frac{\square}{27} = \frac{\square}{51} $

- Simplify $ \frac{12}{18} = \frac{2}{3} $
- $ \frac{2}{3} = \frac{x}{27} \Rightarrow x = 18 $
- $ \frac{2}{3} = \frac{y}{51} \Rightarrow y = 34 $

✔ So: $ \frac{12}{18} = \frac{18}{27} = \frac{34}{51} $

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16. $ \frac{4}{56} = \frac{\square}{84} = \frac{\square}{42} $

- Simplify $ \frac{4}{56} = \frac{1}{14} $
- $ \frac{1}{14} = \frac{x}{84} \Rightarrow x = 6 $
- $ \frac{1}{14} = \frac{y}{42} \Rightarrow y = 3 $

✔ So: $ \frac{4}{56} = \frac{6}{84} = \frac{3}{42} $

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17. $ \frac{\square}{40} = \frac{3}{4} = \frac{\square}{68} $

- $ \frac{3}{4} = \frac{x}{40} \Rightarrow x = \frac{3 \times 40}{4} = 30 $
- $ \frac{3}{4} = \frac{y}{68} \Rightarrow y = \frac{3 \times 68}{4} = 51 $

✔ So: $ \frac{30}{40} = \frac{3}{4} = \frac{51}{68} $

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✔ Final Answer Summary:

| Problem | Missing Numerators |
|--------|---------------------|
| 1 | 6, 18 |
| 2 | 20, 12 |
| 3 | 11, 33 |
| 4 | 16, 40 |
| 5 | 15, 20 |
| 6 | 63, 21 |
| 7 | 22, 12 |
| 8 | 20, 30 |
| 9 | 11, 8 |
| 10 | 12, 20 |
| 11 | 15, 25 |
| 12 | 14, 21 |
| 13 | 24, 18 |
| 14 | 14, 16 |
| 15 | 18, 34 |
| 16 | 6, 3 |
| 17 | 30, 51 |

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📝 Explanation:

To solve each problem:
- We simplified the known fraction (or used it directly).
- Then found an equivalent fraction with the given denominator using cross-multiplication.
- Used the rule: if $ \frac{a}{b} = \frac{c}{d} $, then $ c = \frac{a \cdot d}{b} $.

This ensures all fractions in a row are equivalent.

Let me know if you'd like this as a printable answer sheet! 😊