To divide the fractions [tex]\(\frac{3}{4} \div \frac{5}{2}\)[/tex], follow these steps:
1. Understand Fraction Division:
- Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\(\frac{5}{2}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex].
2. Rewrite the Division as Multiplication:
[tex]\[
\frac{3}{4} \div \frac{5}{2} = \frac{3}{4} \times \frac{2}{5}
\][/tex]
3. Multiply the Numerators:
- Multiply the numerators (the top parts) of the fractions together:
[tex]\[
3 \times 2 = 6
\][/tex]
So, the resulting numerator is 6.
4. Multiply the Denominators:
- Multiply the denominators (the bottom parts) of the fractions together:
[tex]\[
4 \times 5 = 20
\][/tex]
So, the resulting denominator is 20.
5. Put It All Together:
- The fraction obtained from the multiplication is:
[tex]\[
\frac{6}{20}
\][/tex]
6. Simplify the Fraction (if possible):
- To simplify [tex]\(\frac{6}{20}\)[/tex], find the greatest common divisor (GCD) of 6 and 20. The GCD of 6 and 20 is 2.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{6 \div 2}{20 \div 2} = \frac{3}{10}
\][/tex]
Therefore, the simplified fraction after dividing [tex]\(\frac{3}{4}\)[/tex] by [tex]\(\frac{5}{2}\)[/tex] is:
[tex]\[
\frac{3}{10}
\][/tex]
In summary:
- The result of the multiplication before simplifying is [tex]\(\frac{6}{20}\)[/tex].
- The simplified result is [tex]\(\frac{3}{10}\)[/tex].
