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Simplify [tex]\(\frac{25a}{8} \times \frac{2a}{5}\)[/tex].

Give your answer as a single fraction in its simplest form.

Sagot :

GinnyAnswer
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]
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