Find Common Denominator & Compare Unlike Fractions - Math ... - Free Printable

Let's solve each problem step by step by comparing unlike fractions using the common denominator method.

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🔹 Problem 1: Compare $\frac{4}{7}$ and $\frac{5}{6}$

We need to find a common denominator for 7 and 6.

#### Step 1: Find the Least Common Denominator (LCD)
- Multiples of 7: 7, 14, 21, 28, 35, 42, ...
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...
- The least common multiple (LCM) is 42

So, the common denominator is 42.

#### Step 2: Convert both fractions to equivalent fractions with denominator 42

- For $\frac{4}{7}$:
- Multiply numerator and denominator by $ \frac{6}{6} $ (since $7 \times 6 = 42$)
- $\frac{4 \times 6}{7 \times 6} = \frac{24}{42}$

- For $\frac{5}{6}$:
- Multiply numerator and denominator by $ \frac{7}{7} $ (since $6 \times 7 = 42$)
- $\frac{5 \times 7}{6 \times 7} = \frac{35}{42}$

#### Step 3: Compare the new fractions
- $\frac{24}{42} < \frac{35}{42}$

So, $\frac{4}{7} < \frac{5}{6}$

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✔ Fill in the blanks for Problem 1:

```
4 5
--- ○ ---
7 6
↓ ↓
[24] [35]
--- ○ ---
[42] [42]
```

- Left multiplier: $ \boxed{6} $
- Right multiplier: $ \boxed{7} $
- Comparison symbol: $ \boxed{<} $

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🔹 Problem 2: Compare $\frac{1}{3}$ and $\frac{1}{8}$

Find the LCD of 3 and 8.

- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
- Multiples of 8: 8, 16, 24, ...
- LCM = 24

So, common denominator = 24

#### Step 2: Convert fractions

- $\frac{1}{3}$ → multiply numerator and denominator by 8:
- $\frac{1 \times 8}{3 \times 8} = \frac{8}{24}$

- $\frac{1}{8}$ → multiply by 3:
- $\frac{1 \times 3}{8 \times 3} = \frac{3}{24}$

#### Step 3: Compare
- $\frac{8}{24} > \frac{3}{24}$

So, $\frac{1}{3} > \frac{1}{8}$

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✔ Fill in the blanks for Problem 2:

```
1 1
--- ○ ---
3 8
↓ ↓
[8] [3]
--- ○ ---
[24] [24]
```

- Left multiplier: $ \boxed{8} $
- Right multiplier: $ \boxed{3} $
- Comparison symbol: $ \boxed{>} $

---

🟩 Final Answer Summary:

#### Problem 1:
- $ \frac{4}{7} < \frac{5}{6} $
- Equivalent fractions: $ \frac{24}{42} $ and $ \frac{35}{42} $
- Multipliers: $ \boxed{6} $ and $ \boxed{7} $
- Symbol: $ \boxed{<} $

#### Problem 2:
- $ \frac{1}{3} > \frac{1}{8} $
- Equivalent fractions: $ \frac{8}{24} $ and $ \frac{3}{24} $
- Multipliers: $ \boxed{8} $ and $ \boxed{3} $
- Symbol: $ \boxed{>} $

✔ These steps help compare unlike fractions by making their denominators the same — this makes comparing numerators straightforward!