Compare Unlike Fractions by Finding the Common Denominator - II

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 two 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

×6 ×7
↓ ↓
24 35
--- ○ ---
42 42
```

- First blank (left): 6
- Second blank (right): 7
- Middle circle (comparison): <
- Bottom left fraction: 24/42
- Bottom right fraction: 35/42
- Bottom comparison: <

---

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

#### Step 1: Find the LCD of 3 and 8
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
- Multiples of 8: 8, 16, 24, 32, ...
- LCM = 24

Common denominator = 24

#### Step 2: Convert both fractions

- $\frac{1}{3} \to \frac{1 \times 8}{3 \times 8} = \frac{8}{24}$
- $\frac{1}{8} \to \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$

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

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

---

✔ Fill in the blanks for Problem 2:

```
1 1
--- ○ ---
3 8

×8 ×3
↓ ↓
8 3
--- ○ ---
24 24
```

- First blank (left): 8
- Second blank (right): 3
- Middle circle: >
- Bottom left: 8/24
- Bottom right: 3/24
- Bottom comparison: >

---

✔ Final Answer Summary:

#### Problem 1:
- Left multiplier: 6
- Right multiplier: 7
- Comparison: <
- Converted: $\frac{24}{42} < \frac{35}{42}$

#### Problem 2:
- Left multiplier: 8
- Right multiplier: 3
- Comparison: >
- Converted: $\frac{8}{24} > \frac{3}{24}$

✔ This method helps compare fractions by converting them to have the same denominator, making it easy to compare numerators.