College

Multiply the fractions and write your answer in the lowest terms.

[tex]\[
\frac{12}{25} \cdot \frac{5}{8}
\][/tex]

Answer :

To solve the multiplication of the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{5}{8}\)[/tex], and simplify the result, follow these steps:

1. Multiply the Numerators:
Multiply the numerators of the fractions:
[tex]\[
12 \times 5 = 60
\][/tex]

2. Multiply the Denominators:
Multiply the denominators of the fractions:
[tex]\[
25 \times 8 = 200
\][/tex]

3. Form the New Fraction:
With the multiplied numerator and denominator, you have a new fraction:
[tex]\[
\frac{60}{200}
\][/tex]

4. Simplify the Fraction:
To simplify [tex]\(\frac{60}{200}\)[/tex], find the greatest common divisor (GCD) of both the numerator and the denominator. In this case, the GCD is 20.

5. Divide Both the Numerator and the Denominator by the GCD:
- Divide the numerator by 20:
[tex]\[
\frac{60}{20} = 3
\][/tex]
- Divide the denominator by 20:
[tex]\[
\frac{200}{20} = 10
\][/tex]

6. Write the Simplified Fraction:
The fraction [tex]\(\frac{60}{200}\)[/tex] simplifies to [tex]\(\frac{3}{10}\)[/tex].

So, the product of [tex]\(\frac{12}{25} \cdot \frac{5}{8}\)[/tex] in its lowest terms is [tex]\(\frac{3}{10}\)[/tex].

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