Printable math worksheet titled "Are They Equivalent? (A)" designed for students to practice identifying equivalent fractions by checking equations.

We are given a list of fraction equations and asked to check which ones show equivalent fractions. Two fractions are equivalent if they represent the same value, i.e., when simplified or cross-multiplied, they are equal.

To check whether two fractions $ \frac{a}{b} = \frac{c}{d} $ are equivalent, we can use cross-multiplication:

$$
a \cdot d = b \cdot c
$$

If this is true, then the fractions are equivalent.

Let’s go through each equation one by one and determine whether it's true.

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1. $ \frac{7}{8} = \frac{91}{88} $

Cross-multiply:
$ 7 \cdot 88 = 616 $,
$ 8 \cdot 91 = 728 $ → Not equal ✘

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2. $ \frac{6}{6} = \frac{84}{84} $

Simplify both:
$ \frac{6}{6} = 1 $, $ \frac{84}{84} = 1 $ → Equal ✔

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3. $ \frac{4}{10} = \frac{60}{150} $

Simplify:
$ \frac{4}{10} = \frac{2}{5} $,
$ \frac{60}{150} = \frac{2}{5} $ → Equal ✔

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4. $ \frac{1}{3} = \frac{7}{21} $

Simplify $ \frac{7}{21} = \frac{1}{3} $ → Equal ✔

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5. $ \frac{4}{4} = \frac{48}{40} $

$ \frac{4}{4} = 1 $, $ \frac{48}{40} = 1.2 $ → Not equal ✘

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6. $ \frac{2}{8} = \frac{16}{64} $

Simplify:
$ \frac{2}{8} = \frac{1}{4} $,
$ \frac{16}{64} = \frac{1}{4} $ → Equal ✔

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7. $ \frac{4}{9} = \frac{48}{72} $

Simplify:
$ \frac{48}{72} = \frac{2}{3} $, $ \frac{4}{9} \neq \frac{2}{3} $ → Not equal ✘

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8. $ \frac{6}{12} = \frac{66}{132} $

Simplify:
$ \frac{6}{12} = \frac{1}{2} $,
$ \frac{66}{132} = \frac{1}{2} $ → Equal ✔

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9. $ \frac{1}{4} = \frac{12}{48} $

$ \frac{12}{48} = \frac{1}{4} $ → Equal ✔

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10. $ \frac{3}{3} = \frac{45}{45} $

Both are $ 1 $ → Equal ✔

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11. $ \frac{5}{11} = \frac{70}{154} $

Cross-multiply:
$ 5 \cdot 154 = 770 $,
$ 11 \cdot 70 = 770 $ → Equal ✔

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12. $ \frac{9}{9} = \frac{54}{81} $

$ \frac{9}{9} = 1 $, $ \frac{54}{81} = \frac{2}{3} $ → Not equal ✘

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13. $ \frac{3}{4} = \frac{21}{28} $

$ \frac{21}{28} = \frac{3}{4} $ → Equal ✔

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14. $ \frac{7}{7} = \frac{84}{84} $

Both equal $ 1 $ → Equal ✔

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15. $ \frac{2}{3} = \frac{20}{27} $

Cross-multiply:
$ 2 \cdot 27 = 54 $,
$ 3 \cdot 20 = 60 $ → Not equal ✘

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16. $ \frac{1}{9} = \frac{7}{126} $

Simplify $ \frac{7}{126} = \frac{1}{18} $, $ \frac{1}{9} \neq \frac{1}{18} $ → Not equal ✘

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17. $ \frac{8}{11} = \frac{48}{99} $

Cross-multiply:
$ 8 \cdot 99 = 792 $,
$ 11 \cdot 48 = 528 $ → Not equal ✘

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18. $ \frac{1}{3} = \frac{12}{33} $

$ \frac{12}{33} = \frac{4}{11} $, $ \frac{1}{3} \approx 0.333 $, $ \frac{4}{11} \approx 0.363 $ → Not equal ✘

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19. $ \frac{4}{7} = \frac{44}{35} $

$ \frac{4}{7} \approx 0.571 $, $ \frac{44}{35} \approx 1.257 $ → Not equal ✘

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20. $ \frac{10}{11} = \frac{140}{154} $

Simplify $ \frac{140}{154} = \frac{10}{11} $ (divide numerator and denominator by 14) → Equal ✔

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21. $ \frac{6}{11} = \frac{30}{55} $

$ \frac{30}{55} = \frac{6}{11} $ → Equal ✔

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22. $ \frac{11}{11} = \frac{77}{143} $

$ \frac{11}{11} = 1 $, $ \frac{77}{143} = \frac{7}{13} \approx 0.538 $ → Not equal ✘

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23. $ \frac{1}{10} = \frac{8}{80} $

$ \frac{8}{80} = \frac{1}{10} $ → Equal ✔

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24. $ \frac{4}{12} = \frac{48}{108} $

Simplify:
$ \frac{4}{12} = \frac{1}{3} $,
$ \frac{48}{108} = \frac{4}{9} $ → Not equal ✘

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25. $ \frac{6}{7} = \frac{90}{70} $

$ \frac{90}{70} = \frac{9}{7} \approx 1.285 $, $ \frac{6}{7} \approx 0.857 $ → Not equal ✘

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26. $ \frac{1}{2} = \frac{12}{18} $

$ \frac{12}{18} = \frac{2}{3} $, $ \frac{1}{2} \neq \frac{2}{3} $ → Not equal ✘

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27. $ \frac{2}{10} = \frac{16}{80} $

Simplify:
$ \frac{2}{10} = \frac{1}{5} $,
$ \frac{16}{80} = \frac{1}{5} $ → Equal ✔

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28. $ \frac{7}{9} = \frac{105}{135} $

Simplify $ \frac{105}{135} = \frac{7}{9} $ (divide by 15) → Equal ✔

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29. $ \frac{8}{8} = \frac{56}{40} $

$ \frac{8}{8} = 1 $, $ \frac{56}{40} = 1.4 $ → Not equal ✘

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30. $ \frac{7}{8} = \frac{42}{48} $

Simplify $ \frac{42}{48} = \frac{7}{8} $ → Equal ✔

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31. $ \frac{4}{8} = \frac{56}{120} $

Simplify:
$ \frac{4}{8} = \frac{1}{2} $,
$ \frac{56}{120} = \frac{7}{15} \approx 0.466 $ → Not equal ✘

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32. $ \frac{7}{8} = \frac{91}{120} $

$ \frac{7}{8} = 0.875 $, $ \frac{91}{120} \approx 0.758 $ → Not equal ✘

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33. $ \frac{3}{3} = \frac{21}{27} $

$ \frac{3}{3} = 1 $, $ \frac{21}{27} = \frac{7}{9} \approx 0.777 $ → Not equal ✘

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34. $ \frac{11}{12} = \frac{165}{120} $

$ \frac{165}{120} = \frac{11}{8} = 1.375 $, $ \frac{11}{12} \approx 0.916 $ → Not equal ✘

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35. $ \frac{7}{7} = \frac{98}{98} $

Both equal $ 1 $ → Equal ✔

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36. $ \frac{4}{10} = \frac{24}{90} $

Simplify:
$ \frac{4}{10} = \frac{2}{5} $,
$ \frac{24}{90} = \frac{4}{15} $ → Not equal ✘

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## ✔ Final Answer: Check the following equations (they are equivalent):

1. $ \frac{6}{6} = \frac{84}{84} $ ✔
2. $ \frac{4}{10} = \frac{60}{150} $ ✔
3. $ \frac{1}{3} = \frac{7}{21} $ ✔
4. $ \frac{2}{8} = \frac{16}{64} $ ✔
5. $ \frac{6}{12} = \frac{66}{132} $ ✔
6. $ \frac{1}{4} = \frac{12}{48} $ ✔
7. $ \frac{3}{3} = \frac{45}{45} $ ✔
8. $ \frac{5}{11} = \frac{70}{154} $ ✔
9. $ \frac{3}{4} = \frac{21}{28} $ ✔
10. $ \frac{7}{7} = \frac{84}{84} $ ✔
11. $ \frac{10}{11} = \frac{140}{154} $ ✔
12. $ \frac{6}{11} = \frac{30}{55} $ ✔
13. $ \frac{1}{10} = \frac{8}{80} $ ✔
14. $ \frac{7}{9} = \frac{105}{135} $ ✔
15. $ \frac{7}{8} = \frac{42}{48} $ ✔
16. $ \frac{7}{7} = \frac{98}{98} $ ✔

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✔ Total of 16 equivalent fractions.

Let me know if you'd like them listed in a table or marked on the original image!