From beginner to expert, IDNLearn.com has answers for everyone. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.

Solve the following:

[tex]\[
\frac{3}{4} \div \frac{5}{2} =
\][/tex]


Sagot :

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].