Question

Find each product or quotient. Write in the simplest form.

$\frac{2}{5}\cdot \frac{5}{9}$

Short answer

The product is $\frac{2}{9}$.

Step-by-step solution

Step 1. Concept of product of like and unlike sign integers.

The product of two fractions with the same sign is always positive.

The product of two fractions with opposite signs is always negative.

Step 2. Concept of the product of fractions.

Multiply the numerator of one fraction to the other one and follows the same rule for denominator and then simplify.

Step 3. Evaluate the product.

$\begin{array}{l}=\frac{2}{5}\cdot \frac{5}{9}\\ =\frac{2\times 5}{5\times 9}\end{array}$

Divide 5 by 5

$=\frac{2}{9}$

The product is $\frac{2}{9}$.