To divide the fractions [tex]\(\frac{9}{2}\)[/tex] and [tex]\(\frac{72}{7}\)[/tex], we can multiply by the reciprocal of the second fraction. Here is the step-by-step process:
1. Identify the fractions involved:
[tex]\[
\frac{9}{2} \quad \text{and} \quad \frac{72}{7}
\][/tex]
2. Rewrite the division as multiplication by the reciprocal:
[tex]\[
\frac{9}{2} \div \frac{72}{7} = \frac{9}{2} \times \frac{7}{72}
\][/tex]
3. Multiply the numerators and the denominators:
[tex]\[
\text{Numerator: } 9 \times 7 = 63
\][/tex]
[tex]\[
\text{Denominator: } 2 \times 72 = 144
\][/tex]
4. Form the new fraction:
[tex]\[
\frac{63}{144}
\][/tex]
5. Simplify the fraction:
[tex]\[
\frac{63}{144} \quad \text{can be checked if it can be simplified by finding the greatest common divisor (GCD)}
\][/tex]
In this case, [tex]\(\frac{63}{144}\)[/tex] does not simplify further without explicitly expressing it using GCD computations. As a result, the simplified fraction is:
[tex]\[
\frac{63}{144}
\][/tex]
6. Convert the simplified fraction to a decimal if needed:
[tex]\[
\frac{63}{144} = 0.4375
\][/tex]
Therefore, [tex]\(\frac{9}{2} \div \frac{72}{7} = \frac{63}{144} = 0.4375\)[/tex].
