Sure, let's address each part of the question step by step.
### Part 1: Multiply the fractions
Let's multiply [tex]\(\frac{2}{5}\)[/tex] by [tex]\(\frac{6}{7}\)[/tex].
1. Multiply the numerators: [tex]\(2 \times 6 = 12\)[/tex].
2. Multiply the denominators: [tex]\(5 \times 7 = 35\)[/tex].
So,
[tex]\[
\frac{2}{5} \times \frac{6}{7} = \frac{12}{35}
\][/tex]
The fraction [tex]\(\frac{12}{35}\)[/tex] is already in its simplest form, as 12 and 35 have no common factors other than 1.
So,
[tex]\[
\frac{2}{5} \times \frac{6}{7} = \frac{12}{35}
\][/tex]
### Part 2: Divide the fractions
Let's divide [tex]\(\frac{1}{4}\)[/tex] by [tex]\(\frac{3}{8}\)[/tex].
1. Reciprocal of the divisor: The reciprocal of [tex]\(\frac{3}{8}\)[/tex] is [tex]\(\frac{8}{3}\)[/tex].
2. Multiply the dividend by the reciprocal of the divisor: Now, we multiply [tex]\(\frac{1}{4}\)[/tex] by [tex]\(\frac{8}{3}\)[/tex].
3. Multiply the numerators: [tex]\(1 \times 8 = 8\)[/tex].
4. Multiply the denominators: [tex]\(4 \times 3 = 12\)[/tex].
So,
[tex]\[
\frac{1}{4} \div \frac{3}{8} = \frac{1}{4} \times \frac{8}{3} = \frac{8}{12}
\][/tex]
5. Simplify the fraction: The greatest common divisor of 8 and 12 is 4. So, divide the numerator and the denominator by 4:
[tex]\[
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
\][/tex]
Therefore,
[tex]\[
\frac{1}{4} \div \frac{3}{8} = \frac{2}{3}
\][/tex]
### Part 3: Conversion (requires more context)
It seems that Part 3 is incomplete. If you provide more information or a specific conversion problem, I'd be glad to assist further!
