Problem 30 - Basic College Mathematics

Question

Multiply. $$ \frac{12}{13} \cdot \frac{12}{13} $$

Step-by-Step Solution

Answer

The product is \(\frac{144}{169}\).

Step 1: Understand the Problem

The task is to multiply two fractions: \(\frac{12}{13} \times \frac{12}{13}\).

Step 2: Multiply the Numerators

Multiply the numerators of the fractions. \(12 \times 12 = 144\).

Step 3: Multiply the Denominators

Multiply the denominators of the fractions. \(13 \times 13 = 169\).

Step 4: Write the Result as a Fraction

Combine the results from Steps 2 and 3 to form the new fraction: \(\frac{144}{169}\).

Key Concepts

Numerators

The numerator is the top number in a fraction. It tells you how many parts of the whole you have. For example, in the fraction \( \frac{12}{13} \), the numerator is 12. When you multiply fractions, you first need to multiply the numerators.
In our exercise, we multiply the numerators like this: \( 12 \times 12 = 144 \).
This new number, 144, will now be the numerator of the resulting fraction.

Denominators

The denominator is the bottom number in a fraction. It tells you into how many parts the whole is divided. For example, in the fraction \( \frac{12}{13} \), the denominator is 13. When performing fractions multiplication, you separately multiply the denominators just as you did for the numerators.
In our exercise, we multiply the denominators like this: \( 13 \times 13 = 169 \).
This number, 169, becomes the denominator of the new fraction.

Multiplying Fractions

To multiply fractions, follow these simple steps:

• Multiply the numerators to get the new numerator.
• Multiply the denominators to get the new denominator.
• Simplify the resulting fraction if possible (though in our example, the fraction is already in its simplest form).

Here's a summary using our given problem:

\( \frac{12}{13} \times \frac{12}{13} = \frac{12 \times 12}{13 \times 13} = \frac{144}{169} \)
Multiplying fractions isn't difficult when you break it down into these steps. Just remember to handle the numerators and denominators separately, and you'll get the right answer!