Are These Fractions Equivalent? (Multiplier Range 2 to 5) (A) - Free Printable

Let's solve the problem step by step.

Task:

Determine which of the given equations show equivalent fractions.
We need to check each equation and mark (✓) those where the two fractions are equivalent.

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How to Check if Two Fractions Are Equivalent

Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent if:

$$
\frac{a}{b} = \frac{c}{d} \quad \text{if and only if} \quad a \cdot d = b \cdot c
$$

Alternatively, simplify both fractions and see if they reduce to the same value.

We'll go through each pair one by one.

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1. $\frac{5}{11} = \frac{25}{55}$

- Simplify $\frac{25}{55}$: divide numerator and denominator by 5 → $\frac{5}{11}$
✔ Equivalent

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2. $\frac{5}{5} = \frac{10}{10}$

- $\frac{5}{5} = 1$, $\frac{10}{10} = 1$
✔ Equivalent

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3. $\frac{6}{9} = \frac{30}{45}$

- $\frac{6}{9} = \frac{2}{3}$, $\frac{30}{45} = \frac{2}{3}$
✔ Equivalent

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4. $\frac{8}{12} = \frac{32}{48}$

- $\frac{8}{12} = \frac{2}{3}$, $\frac{32}{48} = \frac{2}{3}$
✔ Equivalent

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5. $\frac{6}{11} = \frac{18}{33}$

- $\frac{18}{33} = \frac{6}{11}$ (divide by 3)
✔ Equivalent

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6. $\frac{3}{4} = \frac{9}{12}$

- $\frac{9}{12} = \frac{3}{4}$
✔ Equivalent

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7. $\frac{5}{9} = \frac{10}{18}$

- $\frac{10}{18} = \frac{5}{9}$
✔ Equivalent

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8. $\frac{6}{6} = \frac{30}{30}$

- Both equal 1
✔ Equivalent

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9. $\frac{5}{10} = \frac{15}{30}$

- $\frac{5}{10} = \frac{1}{2}$, $\frac{15}{30} = \frac{1}{2}$
✔ Equivalent

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10. $\frac{10}{10} = \frac{30}{30}$

- Both equal 1
✔ Equivalent

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11. $\frac{4}{6} = \frac{20}{18}$

- $\frac{4}{6} = \frac{2}{3}$, $\frac{20}{18} = \frac{10}{9}$ → Not equal
✘ Not equivalent

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12. $\frac{1}{3} = \frac{2}{6}$

- $\frac{2}{6} = \frac{1}{3}$
✔ Equivalent

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13. $\frac{7}{8} = \frac{35}{40}$

- $\frac{35}{40} = \frac{7}{8}$
✔ Equivalent

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14. $\frac{3}{9} = \frac{9}{36}$

- $\frac{3}{9} = \frac{1}{3}$, $\frac{9}{36} = \frac{1}{4}$ → Not equal
✘ Not equivalent

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15. $\frac{2}{8} = \frac{10}{40}$

- $\frac{2}{8} = \frac{1}{4}$, $\frac{10}{40} = \frac{1}{4}$
✔ Equivalent

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16. $\frac{4}{5} = \frac{12}{15}$

- $\frac{12}{15} = \frac{4}{5}$
✔ Equivalent

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17. $\frac{2}{7} = \frac{10}{14}$

- $\frac{10}{14} = \frac{5}{7}$ ≠ $\frac{2}{7}$
✘ Not equivalent

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18. $\frac{4}{8} = \frac{12}{32}$

- $\frac{4}{8} = \frac{1}{2}$, $\frac{12}{32} = \frac{3}{8}$ → Not equal
✘ Not equivalent

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19. $\frac{1}{2} = \frac{2}{10}$

- $\frac{2}{10} = \frac{1}{5}$ ≠ $\frac{1}{2}$
✘ Not equivalent

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20. $\frac{5}{11} = \frac{15}{33}$

- $\frac{15}{33} = \frac{5}{11}$ (divide by 3)
✔ Equivalent

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21. $\frac{3}{10} = \frac{12}{40}$

- $\frac{12}{40} = \frac{3}{10}$
✔ Equivalent

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22. $\frac{3}{7} = \frac{6}{14}$

- $\frac{6}{14} = \frac{3}{7}$
✔ Equivalent

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23. $\frac{7}{9} = \frac{21}{27}$

- $\frac{21}{27} = \frac{7}{9}$
✔ Equivalent

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24. $\frac{1}{6} = \frac{5}{30}$

- $\frac{5}{30} = \frac{1}{6}$
✔ Equivalent

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25. $\frac{9}{9} = \frac{18}{18}$

- Both equal 1
✔ Equivalent

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26. $\frac{5}{9} = \frac{10}{18}$

- $\frac{10}{18} = \frac{5}{9}$
✔ Equivalent

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27. $\frac{1}{2} = \frac{2}{10}$

- $\frac{2}{10} = \frac{1}{5}$ ≠ $\frac{1}{2}$
✘ Not equivalent

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28. $\frac{4}{7} = \frac{8}{14}$

- $\frac{8}{14} = \frac{4}{7}$
✔ Equivalent

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29. $\frac{6}{8} = \frac{18}{32}$

- $\frac{6}{8} = \frac{3}{4}$, $\frac{18}{32} = \frac{9}{16}$ → Not equal
✘ Not equivalent

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30. $\frac{5}{11} = \frac{15}{33}$

- Already checked: yes
✔ Equivalent

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31. $\frac{6}{6} = \frac{24}{30}$

- $\frac{6}{6} = 1$, $\frac{24}{30} = \frac{4}{5}$ → Not equal
✘ Not equivalent

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32. $\frac{1}{2} = \frac{4}{4}$

- $\frac{4}{4} = 1$, $\frac{1}{2} = 0.5$ → Not equal
✘ Not equivalent

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33. $\frac{1}{7} = \frac{5}{35}$

- $\frac{5}{35} = \frac{1}{7}$
✔ Equivalent

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34. $\frac{3}{5} = \frac{9}{15}$

- $\frac{9}{15} = \frac{3}{5}$
✔ Equivalent

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35. $\frac{2}{2} = \frac{8}{10}$

- $\frac{2}{2} = 1$, $\frac{8}{10} = 0.8$ → Not equal
✘ Not equivalent

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36. $\frac{3}{3} = \frac{15}{9}$

- $\frac{3}{3} = 1$, $\frac{15}{9} = \frac{5}{3} ≈ 1.67$ → Not equal
✘ Not equivalent

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✔ Final Answer: Mark the following as equivalent:

1. $\frac{5}{11} = \frac{25}{55}$
2. $\frac{5}{5} = \frac{10}{10}$
3. $\frac{6}{9} = \frac{30}{45}$
4. $\frac{8}{12} = \frac{32}{48}$
5. $\frac{6}{11} = \frac{18}{33}$
6. $\frac{3}{4} = \frac{9}{12}$
7. $\frac{5}{9} = \frac{10}{18}$
8. $\frac{6}{6} = \frac{30}{30}$
9. $\frac{5}{10} = \frac{15}{30}$
10. $\frac{10}{10} = \frac{30}{30}$
12. $\frac{1}{3} = \frac{2}{6}$
13. $\frac{7}{8} = \frac{35}{40}$
15. $\frac{2}{8} = \frac{10}{40}$
16. $\frac{4}{5} = \frac{12}{15}$
20. $\frac{5}{11} = \frac{15}{33}$
21. $\frac{3}{10} = \frac{12}{40}$
22. $\frac{3}{7} = \frac{6}{14}$
23. $\frac{7}{9} = \frac{21}{27}$
24. $\frac{1}{6} = \frac{5}{30}$
25. $\frac{9}{9} = \frac{18}{18}$
26. $\frac{5}{9} = \frac{10}{18}$
28. $\frac{4}{7} = \frac{8}{14}$
30. $\frac{5}{11} = \frac{15}{33}$
33. $\frac{1}{7} = \frac{5}{35}$
34. $\frac{3}{5} = \frac{9}{15}$

> ✘ The rest are not equivalent.

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🔍 Summary:

There are 24 equivalent fraction pairs in this list.

Let me know if you'd like this formatted as a checklist or printable answer sheet!