Convert `(1)/(4),(5)/(8),(7)/(12) and (13)/(24)` into like fractions.

Answer

To convert the fractions \( \frac{1}{4}, \frac{5}{8}, \frac{7}{12}, \frac{13}{24} \) into like fractions, we need to find a common denominator. Here’s a step-by-step solution:

### Step 1: Identify the denominators
The denominators of the given fractions are 4, 8, 12, and 24.

### Step 2: Find the Least Common Multiple (LCM)
To convert the fractions into like fractions, we need to find the LCM of the denominators (4, 8, 12, and 24).

- The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, ...
- The multiples of 8 are: 8, 16, 24, 32, ...
- The multiples of 12 are: 12, 24, 36, ...
- The multiples of 24 are: 24, 48, ...

The smallest common multiple among these is **24**. Therefore, the LCM is 24.

### Step 3: Convert each fraction to have the common denominator
Now we will convert each fraction to have a denominator of 24.

1. **Convert \( \frac{1}{4} \)**:
- To convert \( \frac{1}{4} \) to a denominator of 24, we find what we need to multiply 4 by to get 24.
- \( 4 \times 6 = 24 \)
- Therefore, we multiply the numerator by 6 as well:
\[ \frac{1 \times 6}{4 \times 6} = \frac{6}{24} \]

2. **Convert \( \frac{5}{8} \)**:
- To convert \( \frac{5}{8} \) to a denominator of 24, we find what we need to multiply 8 by to get 24.
- \( 8 \times 3 = 24 \)
- Therefore, we multiply the numerator by 3 as well:
\[ \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \]

3. **Convert \( \frac{7}{12} \)**:
- To convert \( \frac{7}{12} \) to a denominator of 24, we find what we need to multiply 12 by to get 24.
- \( 12 \times 2 = 24 \)
- Therefore, we multiply the numerator by 2 as well:
\[ \frac{7 \times 2}{12 \times 2} = \frac{14}{24} \]

4. **Convert \( \frac{13}{24} \)**:
- The denominator is already 24, so we do not need to change this fraction:
\[ \frac{13}{24} = \frac{13}{24} \]

### Step 4: Write the final answer
Now we have converted all fractions into like fractions:
\[ \frac{1}{4} = \frac{6}{24}, \quad \frac{5}{8} = \frac{15}{24}, \quad \frac{7}{12} = \frac{14}{24}, \quad \frac{13}{24} = \frac{13}{24} \]

Thus, the like fractions are:
\[ \frac{6}{24}, \frac{15}{24}, \frac{14}{24}, \frac{13}{24} \]