What is 1/4 × 2/3 in simplest form?
The Correct Answer and Explanation is:
To solve ( \frac{1}{4} \times \frac{2}{3} ), we need to follow the standard procedure for multiplying fractions.
Step 1: Multiply the Numerators
The numerators are the top numbers of each fraction. In this case:
[
1 \times 2 = 2
]
Step 2: Multiply the Denominators
The denominators are the bottom numbers of each fraction. Here:
[
4 \times 3 = 12
]
So, when we multiply ( \frac{1}{4} \times \frac{2}{3} ), we get:
[
\frac{1 \times 2}{4 \times 3} = \frac{2}{12}
]
Step 3: Simplify the Resulting Fraction
The fraction ( \frac{2}{12} ) can be simplified. To do this, we find the greatest common divisor (GCD) of 2 and 12. The GCD of 2 and 12 is 2.
Now, divide both the numerator and the denominator by their GCD:
[
\frac{2 \div 2}{12 \div 2} = \frac{1}{6}
]
Thus, ( \frac{1}{4} \times \frac{2}{3} = \frac{1}{6} ).
Explanation
When multiplying fractions, we always multiply the numerators together and the denominators together. This gives us a new fraction that may need to be simplified. Simplifying involves finding a common factor that divides evenly into both the numerator and the denominator. In this problem, after calculating ( \frac{2}{12} ), we simplified it to ( \frac{1}{6} ) by dividing by the GCD.
It’s essential to simplify fractions to their lowest terms, as this gives the most reduced and accurate answer. This process shows how we can handle any fraction multiplication by breaking down the steps and ensuring we reduce the answer if possible. The final answer, in its simplest form, is:
[
\frac{1}{6}
]