To simplify the expression [tex]\(\frac{25 a}{8} \times \frac{2 a}{5}\)[/tex], follow these steps:
1. Multiply the numerators and the denominators:
- Numerators: [tex]\(25a \times 2a = 50a^2\)[/tex]
- Denominators: [tex]\(8 \times 5 = 40\)[/tex]
Therefore, the expression now becomes:
[tex]\[
\frac{50a^2}{40}
\][/tex]
2. Simplify the fraction:
To simplify [tex]\(\frac{50a^2}{40}\)[/tex], find the greatest common divisor (GCD) of 50 and 40. The GCD of 50 and 40 is 10.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{50a^2 \div 10}{40 \div 10} = \frac{5a^2}{4}
\][/tex]
Hence, the simplified form of [tex]\(\frac{25 a}{8} \times \frac{2 a}{5}\)[/tex] is:
[tex]\[
\frac{5a^2}{4}
\][/tex]
