To simplify the expression [tex]\(\frac{\frac{5}{12}}{\frac{3}{8}}\)[/tex], follow these steps:
1. Identify the given fractions:
- The numerator is [tex]\(\frac{5}{12}\)[/tex].
- The denominator is [tex]\(\frac{3}{8}\)[/tex].
2. Understand that dividing by a fraction is equivalent to multiplying by its reciprocal:
To divide by [tex]\(\frac{3}{8}\)[/tex], we will multiply by its reciprocal, which is [tex]\(\frac{8}{3}\)[/tex].
3. Rewrite the expression using multiplication by the reciprocal:
[tex]\[
\frac{\frac{5}{12}}{\frac{3}{8}} = \frac{5}{12} \times \frac{8}{3}
\][/tex]
4. Multiply the fractions:
When multiplying fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{5}{12} \times \frac{8}{3} = \frac{5 \times 8}{12 \times 3}
\][/tex]
5. Calculate the new numerator and denominator:
[tex]\[
5 \times 8 = 40
\][/tex]
[tex]\[
12 \times 3 = 36
\][/tex]
6. Write the resulting fraction:
[tex]\[
\frac{40}{36}
\][/tex]
7. Simplify the fraction if possible:
The greatest common divisor (GCD) of 40 and 36 is 4. To simplify, divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{40 \div 4}{36 \div 4} = \frac{10}{9}
\][/tex]
Therefore, the simplified form of [tex]\(\frac{\frac{5}{12}}{\frac{3}{8}}\)[/tex] is [tex]\(\frac{10}{9}\)[/tex].
To verify this calculation numerically:
- [tex]\(\frac{5}{12} \approx 0.4166666666666667\)[/tex]
- [tex]\(\frac{3}{8} = 0.375\)[/tex]
- [tex]\(\frac{0.4166666666666667}{0.375} \approx 1.1111111111111112\)[/tex]
Since [tex]\( \frac{10}{9} \approx 1.1111111111111112 \)[/tex],
Thus, the simplified fraction [tex]\(\frac{10}{9}\)[/tex] is indeed correct.
