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Evaluate.

(2)/(5)÷(8)/(5)=

Evaluate. $\newline$ $\frac{2}{5} \div \frac{8}{5}=$

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Add, subtract, multiply, and divide integers

Full solution

Q. Evaluate.

\newline

\frac{2}{5} \div \frac{8}{5}=

Understanding division between fractions: Understand the operation of division between two fractions. $\newline$ To divide one fraction by another, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
Finding the reciprocal of the second fraction: Find the reciprocal of the second fraction. $\newline$ The second fraction is $(\frac{8}{5})$ . Its reciprocal is $(\frac{5}{8})$ .
Multiplying the first fraction by the reciprocal: Multiply the first fraction by the reciprocal of the second fraction. $\newline$ Now we multiply $(\frac{2}{5})$ by $(\frac{5}{8})$ . $\newline$ $(\frac{2}{5}) \times (\frac{5}{8}) = \frac{2 \times 5}{5 \times 8}$
Performing the multiplication: Perform the multiplication. $\newline$ Now we multiply the numerators together and the denominators together. $\newline$ $(2 \times 5)/(5 \times 8) = 10/40$
Simplifying the fraction: Simplify the fraction. $\newline$ The fraction $\frac{10}{40}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $10$ . $\newline$ $\frac{10}{40} = \frac{10/10}{40/10} = \frac{1}{4}$

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