Equivalent Fractions worksheet for practicing identifying and creating equivalent fractions, suitable for elementary math education.

Let's solve this Equivalent Fractions (C) worksheet step by step, explaining each part clearly.

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🔷 Section A: Write the missing number for these equivalent fractions.

We find missing numbers by using cross-multiplication or scaling up/down (multiplying/dividing numerator and denominator by the same number).

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#### 1.
$$
\frac{2}{9} = \frac{?}{27} = \frac{14}{?} = \frac{?}{99}
$$

- $ \frac{2}{9} = \frac{?}{27} $:
$ 9 \times 3 = 27 $ → $ 2 \times 3 = 6 $ → $ \boxed{6} $

- $ \frac{2}{9} = \frac{14}{?} $:
$ 2 \times 7 = 14 $ → $ 9 \times 7 = 63 $ → $ \boxed{63} $

- $ \frac{2}{9} = \frac{?}{99} $:
$ 9 \times 11 = 99 $ → $ 2 \times 11 = 22 $ → $ \boxed{22} $

✔ So:
$$
\frac{2}{9} = \frac{6}{27} = \frac{14}{63} = \frac{22}{99}
$$

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#### 2.
$$
\frac{3}{4} = \frac{?}{24} = \frac{9}{?} = \frac{21}{?}
$$

- $ \frac{3}{4} = \frac{?}{24} $:
$ 4 \times 6 = 24 $ → $ 3 \times 6 = 18 $ → $ \boxed{18} $

- $ \frac{3}{4} = \frac{9}{?} $:
$ 3 \times 3 = 9 $ → $ 4 \times 3 = 12 $ → $ \boxed{12} $

- $ \frac{3}{4} = \frac{21}{?} $:
$ 3 \times 7 = 21 $ → $ 4 \times 7 = 28 $ → $ \boxed{28} $

✔ So:
$$
\frac{3}{4} = \frac{18}{24} = \frac{9}{12} = \frac{21}{28}
$$

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#### 3.
$$
\frac{7}{10} = \frac{?}{80} = \frac{28}{?} = \frac{?}{110}
$$

- $ \frac{7}{10} = \frac{?}{80} $:
$ 10 \times 8 = 80 $ → $ 7 \times 8 = 56 $ → $ \boxed{56} $

- $ \frac{7}{10} = \frac{28}{?} $:
$ 7 \times 4 = 28 $ → $ 10 \times 4 = 40 $ → $ \boxed{40} $

- $ \frac{7}{10} = \frac{?}{110} $:
$ 10 \times 11 = 110 $ → $ 7 \times 11 = 77 $ → $ \boxed{77} $

✔ So:
$$
\frac{7}{10} = \frac{56}{80} = \frac{28}{40} = \frac{77}{110}
$$

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#### 4.
$$
\frac{5}{12} = \frac{?}{96} = \frac{35}{?} = \frac{60}{?}
$$

- $ \frac{5}{12} = \frac{?}{96} $:
$ 12 \times 8 = 96 $ → $ 5 \times 8 = 40 $ → $ \boxed{40} $

- $ \frac{5}{12} = \frac{35}{?} $:
$ 5 \times 7 = 35 $ → $ 12 \times 7 = 84 $ → $ \boxed{84} $

- $ \frac{5}{12} = \frac{60}{?} $:
$ 5 \times 12 = 60 $ → $ 12 \times 12 = 144 $ → $ \boxed{144} $

✔ So:
$$
\frac{5}{12} = \frac{40}{96} = \frac{35}{84} = \frac{60}{144}
$$

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✔ Section A Answers:

| Row | Missing Numbers |
|-----|------------------|
| 1 | 6, 63, 22 |
| 2 | 18, 12, 28 |
| 3 | 56, 40, 77 |
| 4 | 40, 84, 144 |

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🔷 Section B: Fill in the missing numbers

We simplify or scale to match.

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#### 1.
$$
\frac{10}{15} = \frac{?}{3} = \frac{30}{?} = \frac{?}{60}
$$

First, simplify $ \frac{10}{15} = \frac{2}{3} $

- $ \frac{2}{3} = \frac{?}{3} $ → $ \boxed{2} $
- $ \frac{2}{3} = \frac{30}{?} $:
$ 2 \times 15 = 30 $ → $ 3 \times 15 = 45 $ → $ \boxed{45} $
- $ \frac{2}{3} = \frac{?}{60} $:
$ 3 \times 20 = 60 $ → $ 2 \times 20 = 40 $ → $ \boxed{40} $

✔ So:
$$
\frac{10}{15} = \frac{2}{3} = \frac{30}{45} = \frac{40}{60}
$$

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#### 2.
$$
\frac{18}{24} = \frac{?}{72} = \frac{3}{?} = \frac{9}{?}
$$

Simplify $ \frac{18}{24} = \frac{3}{4} $

- $ \frac{3}{4} = \frac{?}{72} $:
$ 4 \times 18 = 72 $ → $ 3 \times 18 = 54 $ → $ \boxed{54} $
- $ \frac{3}{4} = \frac{3}{?} $ → $ \boxed{4} $
- $ \frac{3}{4} = \frac{9}{?} $:
$ 3 \times 3 = 9 $ → $ 4 \times 3 = 12 $ → $ \boxed{12} $

✔ So:
$$
\frac{18}{24} = \frac{54}{72} = \frac{3}{4} = \frac{9}{12}
$$

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#### 3.
$$
\frac{12}{32} = \frac{?}{16} = \frac{48}{?} = \frac{?}{8}
$$

Simplify $ \frac{12}{32} = \frac{3}{8} $

- $ \frac{3}{8} = \frac{?}{16} $:
$ 8 \times 2 = 16 $ → $ 3 \times 2 = 6 $ → $ \boxed{6} $
- $ \frac{3}{8} = \frac{48}{?} $:
$ 3 \times 16 = 48 $ → $ 8 \times 16 = 128 $ → $ \boxed{128} $
- $ \frac{3}{8} = \frac{?}{8} $ → $ \boxed{3} $

✔ So:
$$
\frac{12}{32} = \frac{6}{16} = \frac{48}{128} = \frac{3}{8}
$$

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#### 4.
$$
\frac{50}{125} = \frac{?}{25} = \frac{100}{?} = \frac{2}{?}
$$

Simplify $ \frac{50}{125} = \frac{2}{5} $

- $ \frac{2}{5} = \frac{?}{25} $:
$ 5 \times 5 = 25 $ → $ 2 \times 5 = 10 $ → $ \boxed{10} $
- $ \frac{2}{5} = \frac{100}{?} $:
$ 2 \times 50 = 100 $ → $ 5 \times 50 = 250 $ → $ \boxed{250} $
- $ \frac{2}{5} = \frac{2}{?} $ → $ \boxed{5} $

✔ So:
$$
\frac{50}{125} = \frac{10}{25} = \frac{100}{250} = \frac{2}{5}
$$

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✔ Section B Answers:

| Row | Missing Numbers |
|-----|------------------|
| 1 | 2, 45, 40 |
| 2 | 54, 4, 12 |
| 3 | 6, 128, 3 |
| 4 | 10, 250, 5 |

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🔷 Section C: Create 8 equivalent fractions for each

We multiply numerator and denominator by different integers.

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#### 1. $ \frac{3}{4} $

Multiply by 2 to 9:

- $ \frac{3 \times 2}{4 \times 2} = \frac{6}{8} $
- $ \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $
- $ \frac{3 \times 4}{4 \times 4} = \frac{12}{16} $
- $ \frac{3 \times 5}{4 \times 5} = \frac{15}{20} $
- $ \frac{3 \times 6}{4 \times 6} = \frac{18}{24} $
- $ \frac{3 \times 7}{4 \times 7} = \frac{21}{28} $
- $ \frac{3 \times 8}{4 \times 8} = \frac{24}{32} $
- $ \frac{3 \times 9}{4 \times 9} = \frac{27}{36} $

✔ So:
$ \frac{6}{8}, \frac{9}{12}, \frac{12}{16}, \frac{15}{20}, \frac{18}{24}, \frac{21}{28}, \frac{24}{32}, \frac{27}{36} $

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#### 2. $ \frac{2}{7} $

Multiply by 2 to 9:

- $ \frac{4}{14} $
- $ \frac{6}{21} $
- $ \frac{8}{28} $
- $ \frac{10}{35} $
- $ \frac{12}{42} $
- $ \frac{14}{49} $
- $ \frac{16}{56} $
- $ \frac{18}{63} $

✔ So:
$ \frac{4}{14}, \frac{6}{21}, \frac{8}{28}, \frac{10}{35}, \frac{12}{42}, \frac{14}{49}, \frac{16}{56}, \frac{18}{63} $

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#### 3. $ \frac{4}{9} $

Multiply by 2 to 9:

- $ \frac{8}{18} $
- $ \frac{12}{27} $
- $ \frac{16}{36} $
- $ \frac{20}{45} $
- $ \frac{24}{54} $
- $ \frac{28}{63} $
- $ \frac{32}{72} $
- $ \frac{36}{81} $

✔ So:
$ \frac{8}{18}, \frac{12}{27}, \frac{16}{36}, \frac{20}{45}, \frac{24}{54}, \frac{28}{63}, \frac{32}{72}, \frac{36}{81} $

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✔ Section C Answers:

- For $ \frac{3}{4} $: $ \frac{6}{8}, \frac{9}{12}, \frac{12}{16}, \frac{15}{20}, \frac{18}{24}, \frac{21}{28}, \frac{24}{32}, \frac{27}{36} $
- For $ \frac{2}{7} $: $ \frac{4}{14}, \frac{6}{21}, \frac{8}{28}, \frac{10}{35}, \frac{12}{42}, \frac{14}{49}, \frac{16}{56}, \frac{18}{63} $
- For $ \frac{4}{9} $: $ \frac{8}{18}, \frac{12}{27}, \frac{16}{36}, \frac{20}{45}, \frac{24}{54}, \frac{28}{63}, \frac{32}{72}, \frac{36}{81} $

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🔷 Extension: Circle the fractions in Section B that are in simplest form

Simplest form means numerator and denominator have no common factors other than 1.

Look at all the fractions from Section B:

From earlier:

- $ \frac{10}{15} $ → not simplest (divisible by 5)
- $ \frac{2}{3} $ → ✔ simplest
- $ \frac{30}{45} $ → divisible by 15 → not simplest
- $ \frac{40}{60} $ → divisible by 20 → not simplest
- $ \frac{18}{24} $ → divisible by 6 → not simplest
- $ \frac{54}{72} $ → divisible by 18 → not simplest
- $ \frac{3}{4} $ → ✔ simplest
- $ \frac{9}{12} $ → divisible by 3 → not simplest
- $ \frac{12}{32} $ → divisible by 4 → not simplest
- $ \frac{6}{16} $ → divisible by 2 → not simplest
- $ \frac{48}{128} $ → divisible by 16 → not simplest
- $ \frac{3}{8} $ → ✔ simplest
- $ \frac{50}{125} $ → divisible by 25 → not simplest
- $ \frac{10}{25} $ → divisible by 5 → not simplest
- $ \frac{100}{250} $ → divisible by 50 → not simplest
- $ \frac{2}{5} $ → ✔ simplest

✔ Fractions in simplest form:
- $ \frac{2}{3} $
- $ \frac{3}{4} $
- $ \frac{3}{8} $
- $ \frac{2}{5} $

Circle these four.

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✔ Final Summary:

#### Section A Answers:
1. $ \frac{2}{9} = \frac{6}{27} = \frac{14}{63} = \frac{22}{99} $
2. $ \frac{3}{4} = \frac{18}{24} = \frac{9}{12} = \frac{21}{28} $
3. $ \frac{7}{10} = \frac{56}{80} = \frac{28}{40} = \frac{77}{110} $
4. $ \frac{5}{12} = \frac{40}{96} = \frac{35}{84} = \frac{60}{144} $

#### Section B Answers:
1. $ \frac{10}{15} = \frac{2}{3} = \frac{30}{45} = \frac{40}{60} $
2. $ \frac{18}{24} = \frac{54}{72} = \frac{3}{4} = \frac{9}{12} $
3. $ \frac{12}{32} = \frac{6}{16} = \frac{48}{128} = \frac{3}{8} $
4. $ \frac{50}{125} = \frac{10}{25} = \frac{100}{250} = \frac{2}{5} $

#### Section C Answers (8 equivalents each):
- $ \frac{3}{4} $: $ \frac{6}{8}, \frac{9}{12}, \frac{12}{16}, \frac{15}{20}, \frac{18}{24}, \frac{21}{28}, \frac{24}{32}, \frac{27}{36} $
- $ \frac{2}{7} $: $ \frac{4}{14}, \frac{6}{21}, \frac{8}{28}, \frac{10}{35}, \frac{12}{42}, \frac{14}{49}, \frac{16}{56}, \frac{18}{63} $
- $ \frac{4}{9} $: $ \frac{8}{18}, \frac{12}{27}, \frac{16}{36}, \frac{20}{45}, \frac{24}{54}, \frac{28}{63}, \frac{32}{72}, \frac{36}{81} $

#### Extension: Circle these in Section B
- $ \frac{2}{3} $
- $ \frac{3}{4} $
- $ \frac{3}{8} $
- $ \frac{2}{5} $

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