To solve this, we first consider the multiplication of the two fractions \( \frac{12}{30} \) and \( \frac{6}{6} \).
Step 1: Multiply the fractions
\[ \frac{12}{30} \times \frac{6}{6} = \frac{12 \times 6}{30 \times 6} = \frac{72}{180} \]
Step 2: Simplify the fraction \( \frac{72}{180} \)
To simplify \( \frac{72}{180} \), we need to find the greatest common divisor (GCD) of 72 and 180. The GCD is 36.
Now divide both the numerator and the denominator by 36: \[ \frac{72 \div 36}{180 \div 36} = \frac{2}{5} \]
Thus, in fraction form, the answer is: \[ \frac{2}{5} \]
Step 3: Convert to decimal form
To convert \( \frac{2}{5} \) to decimal form, we perform the division: \[ 2 \div 5 = 0.4 \]
Final Results:
- In fraction form: \( \frac{2}{5} \)
- In decimal form: \( 0.4 \)