To convert the fractions \( \frac{3}{4}, \frac{5}{6}, \frac{7}{8} \) into equivalent like fractions, we will follow these steps:
### Step 1: Identify the denominators
The denominators of the given fractions are:
- For \( \frac{3}{4} \), the denominator is 4.
- For \( \frac{5}{6} \), the denominator is 6.
- For \( \frac{7}{8} \), the denominator is 8.
### Step 2: Find the Least Common Multiple (LCM) of the denominators
To convert these fractions into like fractions, we need to find the LCM of the denominators (4, 6, and 8).
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
- The multiples of 6 are: 6, 12, 18, 24, ...
- The multiples of 8 are: 8, 16, 24, ...
The smallest common multiple is 24. Therefore, the LCM of 4, 6, and 8 is **24**.
### Step 3: Convert each fraction to have the common denominator of 24
Now we will convert each fraction to have the denominator of 24.
1. **Convert \( \frac{3}{4} \)**:
- To convert \( \frac{3}{4} \) to a denominator of 24, we multiply both the numerator and the denominator by 6:
\[
\frac{3}{4} \times \frac{6}{6} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}
\]
2. **Convert \( \frac{5}{6} \)**:
- To convert \( \frac{5}{6} \) to a denominator of 24, we multiply both the numerator and the denominator by 4:
\[
\frac{5}{6} \times \frac{4}{4} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}
\]
3. **Convert \( \frac{7}{8} \)**:
- To convert \( \frac{7}{8} \) to a denominator of 24, we multiply both the numerator and the denominator by 3:
\[
\frac{7}{8} \times \frac{3}{3} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}
\]
### Step 4: Write the equivalent like fractions
Now we can write the equivalent like fractions:
- \( \frac{3}{4} = \frac{18}{24} \)
- \( \frac{5}{6} = \frac{20}{24} \)
- \( \frac{7}{8} = \frac{21}{24} \)
Thus, the equivalent like fractions are:
\[
\frac{18}{24}, \frac{20}{24}, \frac{21}{24}
\]
### Final Answer
The equivalent like fractions are \( \frac{18}{24}, \frac{20}{24}, \frac{21}{24} \).
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