Question

Find each product or quotient.

$\frac{1}{9}\cdot \frac{3}{4}$

Short answer

The product is $\frac{1}{12}$.

Step-by-step solution

Step 1. Concept of the 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 the opposite sign is always negative.

Step 2. Concept of the product of fractions.

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

Step 3. Evaluate the product.

To multiply the give fractions, multiply numerators and denominators of both fractions together and cancel out any common factors to simplify further as shown below:

$$\begin{gathered} \frac{1}{9}\cdot \frac{3}{4}=\frac{1\cdot 3}{9\cdot 4} \\ =\frac{3}{36} \\ =\frac{1}{12} \end{gathered}$$

Thus, the product is $\frac{1}{12}$.