Grade 6 Equivalent Fractions Worksheet with problems to find missing values in fraction equations.

Let's solve each problem in the "Equivalent Fractions" worksheet step by step. The goal is to find the missing number in each equivalent fraction equation.

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1. $ \frac{4}{5} = \frac{28}{?} $

We need to find the denominator that makes this true.

- Multiply both numerator and denominator of $ \frac{4}{5} $ by 7:
$ 4 \times 7 = 28 $, so $ 5 \times 7 = 35 $
- So, $ \frac{4}{5} = \frac{28}{35} $

✔ Answer: 35

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2. $ \frac{?}{4} = \frac{3}{8} $

We want to find the numerator such that the fractions are equal.

- Multiply both numerator and denominator of $ \frac{3}{8} $ by 2:
$ 3 \times 2 = 6 $, $ 8 \times 2 = 16 $ → but we need denominator 4.
- Wait: Let's reverse it. We want denominator 4, but $ \frac{3}{8} $ has denominator 8.

So, divide both numerator and denominator by 2:
$ \frac{3}{8} = \frac{3 \div 2}{8 \div 2} = \frac{1.5}{4} $ — not a whole number.

But we can scale up or down.

Let’s set up proportion:

$$
\frac{x}{4} = \frac{3}{8}
\Rightarrow x = \frac{3 \times 4}{8} = \frac{12}{8} = 1.5
$$

Wait! That gives a decimal. But maybe the question allows fractions?

Alternatively, perhaps we should look for an equivalent fraction with denominator 4.

But $ \frac{3}{8} $ is not equivalent to any fraction with denominator 4 unless we allow decimals.

Wait — let’s double-check: Is there a mistake?

Actually, $ \frac{3}{8} $ cannot be simplified to have denominator 4 because 8 doesn't divide evenly into 4 unless we go backwards.

But here, we're solving $ \frac{x}{4} = \frac{3}{8} $

Cross-multiply:
$$
x \cdot 8 = 3 \cdot 4 \Rightarrow 8x = 12 \Rightarrow x = \frac{12}{8} = \frac{3}{2} = 1.5
$$

So $ x = \frac{3}{2} $

But if we must write as a fraction, then $ \frac{3}{2} $

But let’s check: $ \frac{3/2}{4} = \frac{3}{2} \div 4 = \frac{3}{8} $ ✔

So yes, $ x = \frac{3}{2} $

But maybe they expect a whole number? Let's see the other problems.

Wait — maybe I misread. Let's recheck.

Wait — could it be $ \frac{?}{4} = \frac{3}{8} $, so what number over 4 equals 3/8?

Yes, answer is $ \frac{3}{2} $, or $ 1.5 $

But perhaps the question expects a fraction.

✔ Answer: $ \frac{3}{2} $ or $ 1.5 $

But let's keep going — maybe it's intended to be a whole number.

Wait — perhaps the question meant $ \frac{?}{4} = \frac{3}{8} $, so we need to scale $ \frac{3}{8} $ to denominator 4.

But 8 → 4 means divide by 2, so numerator also divided by 2: $ 3 ÷ 2 = 1.5 $

So again, $ x = 1.5 $

✔ Answer: $ \boxed{\frac{3}{2}} $ or $ \boxed{1.5} $

But let’s assume they want a fraction.

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3. $ \frac{?}{3} = \frac{8}{27} $

Let $ x $ be the missing numerator.

$$
\frac{x}{3} = \frac{8}{27}
\Rightarrow x = \frac{8 \times 3}{27} = \frac{24}{27} = \frac{8}{9}
$$

Wait — no:

Cross-multiply:
$$
x \cdot 27 = 8 \cdot 3 = 24 \Rightarrow x = \frac{24}{27} = \frac{8}{9}
$$

But that would make $ \frac{8/9}{3} = \frac{8}{27} $? Let's test:

$ \frac{8/9}{3} = \frac{8}{9} \div 3 = \frac{8}{27} $ ✔

So $ x = \frac{8}{9} $

But that seems odd. Maybe we need to think differently.

Wait — is it possible that $ \frac{x}{3} = \frac{8}{27} $, so $ x = \frac{8}{27} \times 3 = \frac{24}{27} = \frac{8}{9} $

So $ x = \frac{8}{9} $

But the left side is $ \frac{x}{3} $, so $ x $ is the numerator.

So $ \frac{8/9}{3} = \frac{8}{27} $ — correct.

But maybe the problem wants a whole number? It doesn’t seem so.

✔ Answer: $ \boxed{\frac{8}{9}} $

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Wait — let’s try to think of scaling.

Is $ \frac{8}{27} $ equivalent to some $ \frac{x}{3} $? Let's simplify $ \frac{8}{27} $ — already simplified.

To get from 27 to 3, divide by 9.

So $ \frac{8}{27} = \frac{8 \div 9}{27 \div 9} = \frac{8/9}{3} $

So yes, numerator is $ \frac{8}{9} $

✔ Answer: $ \frac{8}{9} $

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4. $ \frac{4}{6} = \frac{16}{?} $

Simplify $ \frac{4}{6} = \frac{2}{3} $

Now, $ \frac{16}{x} = \frac{2}{3} $

Cross-multiply: $ 16 \times 3 = 2x \Rightarrow 48 = 2x \Rightarrow x = 24 $

Check: $ \frac{16}{24} = \frac{2}{3} $, and $ \frac{4}{6} = \frac{2}{3} $ ✔

✔ Answer: 24

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5. $ \frac{?}{1} = \frac{1}{64} $

This means $ x = \frac{1}{64} $

Because $ \frac{x}{1} = x $, so $ x = \frac{1}{64} $

✔ Answer: $ \frac{1}{64} $

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6. $ \frac{?}{4} = \frac{2}{16} $

Simplify $ \frac{2}{16} = \frac{1}{8} $

So $ \frac{x}{4} = \frac{1}{8} $

Then $ x = \frac{1}{8} \times 4 = \frac{4}{8} = \frac{1}{2} $

Or cross-multiply: $ x \cdot 16 = 2 \cdot 4 = 8 \Rightarrow x = \frac{8}{16} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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7. $ \frac{?}{1} = \frac{10}{50} $

Simplify $ \frac{10}{50} = \frac{1}{5} $

So $ x = \frac{1}{5} $

✔ Answer: $ \frac{1}{5} $

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8. $ \frac{?}{2} = \frac{4}{12} $

Simplify $ \frac{4}{12} = \frac{1}{3} $

So $ \frac{x}{2} = \frac{1}{3} \Rightarrow x = \frac{2}{3} $

Cross-multiply: $ x \cdot 12 = 4 \cdot 2 = 8 \Rightarrow x = \frac{8}{12} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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9. $ \frac{7}{12} = \frac{?}{24} $

We want to scale $ \frac{7}{12} $ to denominator 24.

Since $ 12 \times 2 = 24 $, multiply numerator by 2: $ 7 \times 2 = 14 $

So $ \frac{7}{12} = \frac{14}{24} $

✔ Answer: 14

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10. $ \frac{3}{?} = \frac{6}{10} $

Simplify $ \frac{6}{10} = \frac{3}{5} $

So $ \frac{3}{x} = \frac{3}{5} \Rightarrow x = 5 $

✔ Answer: 5

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11. $ \frac{2}{10} = \frac{?}{40} $

Simplify $ \frac{2}{10} = \frac{1}{5} $

Now, $ \frac{x}{40} = \frac{1}{5} \Rightarrow x = \frac{40}{5} = 8 $

Or scale: $ 10 \to 40 $, multiply by 4 → $ 2 \times 4 = 8 $

✔ Answer: 8

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12. $ \frac{?}{4} = \frac{18}{24} $

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

So $ \frac{x}{4} = \frac{3}{4} \Rightarrow x = 3 $

✔ Answer: 3

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13. $ \frac{7}{8} = \frac{?}{72} $

Scale $ \frac{7}{8} $ to denominator 72.

$ 8 \times 9 = 72 $, so $ 7 \times 9 = 63 $

So $ \frac{7}{8} = \frac{63}{72} $

✔ Answer: 63

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14. $ \frac{1}{?} = \frac{9}{18} $

Simplify $ \frac{9}{18} = \frac{1}{2} $

So $ \frac{1}{x} = \frac{1}{2} \Rightarrow x = 2 $

✔ Answer: 2

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 35 |
| 2 | $ \frac{3}{2} $ or 1.5 |
| 3 | $ \frac{8}{9} $ |
| 4 | 24 |
| 5 | $ \frac{1}{64} $ |
| 6 | $ \frac{1}{2} $ |
| 7 | $ \frac{1}{5} $ |
| 8 | $ \frac{2}{3} $ |
| 9 | 14 |
| 10 | 5 |
| 11 | 8 |
| 12 | 3 |
| 13 | 63 |
| 14 | 2 |

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📝 Explanation Summary:

To solve equivalent fractions:
- Use cross-multiplication: $ \frac{a}{b} = \frac{c}{d} \Rightarrow a \cdot d = b \cdot c $
- Or scale up/down: Multiply numerator and denominator by the same number.
- Simplify fractions first when possible.

For example:
- In #1: $ \frac{4}{5} = \frac{28}{x} $ → $ 4x = 140 $ → $ x = 35 $
- In #9: $ \frac{7}{12} = \frac{x}{24} $ → since 12 × 2 = 24, so 7 × 2 = 14

All answers are now solved using these methods.

Let me know if you'd like a printable version or explanation in simpler terms!