91Ó°ÊÓ

Before diving into the exercise, let's understand the process of fraction multiplication. When multiplying fractions, you multiply the numerators together and the denominators together. This means if you have two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \), the product is \( \frac{a \times c}{b \times d} \). It's as simple as that!

• Numerator: The top part of a fraction.
• Denominator: The bottom part of a fraction.

For example, the exercise asks us to find \( \frac{2}{3} \) of \( \frac{7}{8} \). We calculate this by multiplying the numerators \( 2 \times 7 = 14 \) and the denominators \( 3 \times 8 = 24 \). So, the result is \( \frac{14}{24} \).
It's important to simplify fractions whenever possible. To simplify \( \frac{14}{24} \), you divide both the numerator and denominator by their greatest common divisor, which is 2 in this case, giving you \( \frac{7}{12} \).

Subtracting fractions can be tricky if they have different denominators. To subtract fractions, they must share the same denominator, known as a common denominator.
In our exercise, after finding \( \frac{2}{3} \) of \( \frac{7}{8} \) as \( \frac{7}{12} \), we need to subtract \( \frac{7}{12} \) from \( \frac{7}{8} \).

• First, ensure both fractions have the same denominator.
• Then, subtract the numerators and keep the denominator the same.

In this case, we converted both fractions to have a denominator of 24: \( \frac{21}{24} - \frac{14}{24} \). Subtracting the numerators gives us \( \frac{21 - 14}{24} = \frac{7}{24} \). That's the result of our subtraction.

Finding the least common denominator (LCD) is essential when you add or subtract fractions with different denominators. The LCD is the smallest number that both denominators can divide into evenly.
For our example, we needed to subtract \( \frac{7}{12} \) from \( \frac{7}{8} \). The denominators here are 8 and 12. We find the LCD so these fractions can be easily combined.

• Identify the least common multiple (LCM) of 8 and 12.
• Use the LCM as the common denominator.

For 8 and 12, the LCM is 24. Therefore, \( \frac{7}{8} \) is expressed as \( \frac{21}{24} \) and \( \frac{7}{12} \) as \( \frac{14}{24} \). Now, with both fractions over the same denominator, subtraction becomes straightforward. And that’s how the concept of the least common denominator helps in fraction operations!