A fraction equivalent to `8/(12)` is

Options

A. `(8+4)/(12+4)`
B. `(8-:4)/(12-:4)`
C. `(8-4)/(12-4)`
D. None of these

Answer

To find a fraction equivalent to \( \frac{8}{12} \), we can follow these steps:

### Step 1: Simplify the Fraction
To simplify \( \frac{8}{12} \), we need to find the greatest common divisor (GCD) of the numerator (8) and the denominator (12).

- The factors of 8 are: 1, 2, 4, 8
- The factors of 12 are: 1, 2, 3, 4, 6, 12
- The common factors are: 1, 2, 4
- The greatest common factor is 4.

Now, we divide both the numerator and the denominator by their GCD.

\[ \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \]

### Step 2: Identify Equivalent Fractions
Now that we have simplified \( \frac{8}{12} \) to \( \frac{2}{3} \), we can find equivalent fractions by multiplying both the numerator and the denominator by the same number.

Let’s multiply both by 2:

\[ \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]

Let’s multiply both by 3:

\[ \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \]

Let’s multiply both by 4:

\[ \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \quad \text{(which is the original fraction)} \]

### Step 3: Conclusion
Thus, the fractions \( \frac{4}{6} \) and \( \frac{6}{9} \) are equivalent to \( \frac{8}{12} \).