Problem 137 - Introductory Algebra for College Students

Question

Explain how to multiply fractions and give an example.

Step-by-Step Solution

Answer

The multiplication of \( \frac{3}{4} \) and \( \frac{2}{5} \) is \( \frac{6}{20} \) which simplifies to \( \frac{3}{10} \).

Step 1: Understanding the concept

Multiplication of fractions is straightforward and easier than addition and subtraction of fractions. In multiplication, no need of common denominator. Instead, just multiply the numerators (top number) of the fractions with each other and the denominators (bottom number) with each other.

Step 1: Setting up the problem

Let's say we have two fractions that we want to multiply, \( \frac{3}{4} \) and \( \frac{2}{5} \). So, our multiplication problem is \( \frac{3}{4} \) × \( \frac{2}{5} \).

Step 2: Multiply the numerators

First, multiply the numerators of the fractions, which are 3 and 2. The result is 6.

Step 3: Multiply the denominators

Next, multiply the denominators of the fractions, which are 4 and 5. The result is 20.

Step 4: Write down the answer

The multiplication of the numerators (6) becomes the numerator of the answer, and the multiplication of the denominators (20) becomes the denominator of the answer. Therefore, the solution to our problem \( \frac{3}{4} \) × \( \frac{2}{5} \) is \( \frac{6}{20} \).

Step 5: Simplify the fraction

When possible, fractions should be simplified to their lowest terms for the final answer. Both the numerator and denominator of our fraction \( \frac{6}{20} \) can be divided evenly by 2. Dividing 6 and 20 by 2 results in \( \frac{3}{10} \).