Fraction / FREE Printable Worksheets - Free Printable

Let's solve the Equivalent Fractions worksheet step by step. The goal is to fill in the missing numerators or denominators so that the fractions on both sides of the equation are equivalent.

---

🔍 Understanding Equivalent Fractions

Two fractions are equivalent if they represent the same part of a whole. You can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same number.

For example:
- $ \frac{1}{2} = \frac{2}{4} $ because $ 1 \times 2 = 2 $ and $ 2 \times 2 = 4 $
- $ \frac{2}{6} = \frac{1}{3} $ because $ 2 \div 2 = 1 $ and $ 6 \div 2 = 3 $

We’ll use this rule for each problem.

---

✔ Solving Each Problem

#### Row 1:
1. $ \frac{1}{2} = \frac{?}{4} $
Multiply numerator and denominator by 2:
$ \frac{1 \times 2}{2 \times 2} = \frac{2}{4} $ → Answer: 2

2. $ \frac{1}{3} = \frac{?}{6} $
Multiply by 2: $ \frac{1 \times 2}{3 \times 2} = \frac{2}{6} $ → Answer: 2

3. $ \frac{2}{6} = \frac{?}{12} $
Multiply by 2: $ \frac{2 \times 2}{6 \times 2} = \frac{4}{12} $ → Answer: 4

---

#### Row 2:
4. $ \frac{1}{2} = \frac{?}{8} $
Multiply by 4: $ \frac{1 \times 4}{2 \times 4} = \frac{4}{8} $ → Answer: 4

5. $ \frac{1}{3} = \frac{?}{12} $
Multiply by 4: $ \frac{1 \times 4}{3 \times 4} = \frac{4}{12} $ → Answer: 4

6. $ \frac{2}{6} = \frac{?}{3} $
Simplify: $ \frac{2 \div 2}{6 \div 2} = \frac{1}{3} $ → So, $ \frac{2}{6} = \frac{1}{3} $ → Answer: 1

---

#### Row 3:
7. $ \frac{2}{4} = \frac{?}{8} $
Multiply by 2: $ \frac{2 \times 2}{4 \times 2} = \frac{4}{8} $ → Answer: 4

8. $ \frac{4}{8} = \frac{?}{2} $
Simplify: $ \frac{4 \div 4}{8 \div 4} = \frac{1}{2} $ → So, $ \frac{4}{8} = \frac{1}{2} $ → Answer: 1

9. $ \frac{4}{12} = \frac{?}{3} $
Simplify: $ \frac{4 \div 4}{12 \div 4} = \frac{1}{3} $ → So, $ \frac{4}{12} = \frac{1}{3} $ → Answer: 1

---

#### Row 4:
10. $ \frac{2}{4} = \frac{?}{2} $
Simplify: $ \frac{2 \div 2}{4 \div 2} = \frac{1}{2} $ → So, $ \frac{2}{4} = \frac{1}{2} $ → Answer: 1

11. $ \frac{4}{8} = \frac{?}{4} $
Simplify: $ \frac{4 \div 2}{8 \div 2} = \frac{2}{4} $ → But we want denominator 4 → $ \frac{4}{8} = \frac{2}{4} $ → Answer: 2

Alternatively: $ \frac{4}{8} = \frac{?}{4} $ → Multiply both sides by 4: $ ? = \frac{4}{8} \times 4 = 2 $

12. $ \frac{4}{12} = \frac{?}{6} $
Simplify: $ \frac{4 \div 2}{12 \div 2} = \frac{2}{6} $ → So, $ \frac{4}{12} = \frac{2}{6} $ → Answer: 2

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| $ \frac{1}{2} = \frac{?}{4} $ | 2 |
| $ \frac{1}{3} = \frac{?}{6} $ | 2 |
| $ \frac{2}{6} = \frac{?}{12} $ | 4 |
| $ \frac{1}{2} = \frac{?}{8} $ | 4 |
| $ \frac{1}{3} = \frac{?}{12} $ | 4 |
| $ \frac{2}{6} = \frac{?}{3} $ | 1 |
| $ \frac{2}{4} = \frac{?}{8} $ | 4 |
| $ \frac{4}{8} = \frac{?}{2} $ | 1 |
| $ \frac{4}{12} = \frac{?}{3} $ | 1 |
| $ \frac{2}{4} = \frac{?}{2} $ | 1 |
| $ \frac{4}{8} = \frac{?}{4} $ | 2 |
| $ \frac{4}{12} = \frac{?}{6} $ | 2 |

---

🧩 Summary Table (Completed Worksheet):

```
1/2 = 2/4 1/3 = 2/6 2/6 = 4/12
1/2 = 4/8 1/3 = 4/12 2/6 = 1/3
2/4 = 4/8 4/8 = 1/2 4/12 = 1/3
2/4 = 1/2 4/8 = 2/4 4/12 = 2/6
```

✔ All fractions are now correctly matched!

Let me know if you'd like a printable version or visual explanation!