Sure, let's solve the given problem step by step.
You are asked to multiply the following fractions:
[tex]\[
\frac{3}{5} \times \frac{10}{12} \times \frac{1}{2}
\][/tex]
Step 1: First, consider [tex]\(\frac{3}{5} \times \frac{10}{12}\)[/tex].
- Multiply the numerators: [tex]\(3 \times 10 = 30\)[/tex].
- Multiply the denominators: [tex]\(5 \times 12 = 60\)[/tex].
So,
[tex]\[
\frac{3}{5} \times \frac{10}{12} = \frac{30}{60}
\][/tex]
Step 2: Simplify [tex]\(\frac{30}{60}\)[/tex].
The greatest common divisor (GCD) of 30 and 60 is 30.
[tex]\[
\frac{30 \div 30}{60 \div 30} = \frac{1}{2}
\][/tex]
Step 3: Now, multiply the result with [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\frac{1}{2} \times \frac{1}{2}
\][/tex]
- Multiply the numerators: [tex]\(1 \times 1 = 1\)[/tex].
- Multiply the denominators: [tex]\(2 \times 2 = 4\)[/tex].
So,
[tex]\[
\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\][/tex]
Therefore, the result of multiplying [tex]\(\frac{3}{5} \times \frac{10}{12} \times \frac{1}{2}\)[/tex] is:
[tex]\[
\boxed{\frac{1}{4}}
\][/tex]
