91Ó°ÊÓ

The concept of the **reciprocal of a fraction** is key in fraction division. A reciprocal simply means flipping a fraction. This means you swap the numerator (top number) and the denominator (bottom number). For instance, the reciprocal of \( \frac{a}{b} \) is \( \frac{b}{a} \).
You use the reciprocal when dividing fractions because division can be turned into multiplication. When you see a division problem like \( \frac{1}{150} \div \frac{1}{50} \), you change the division sign to multiplication by taking the reciprocal of the divisor (the second fraction).
So this division problem becomes \( \frac{1}{150} \times \frac{50}{1} \). Now, you're ready for the next step: multiplication!

**Multiplying fractions** is quite straightforward. You multiply the numerators together and multiply the denominators together. It's as simple as that!
Let’s look at our updated expression \( \frac{1}{150} \times \frac{50}{1} \). Here, you multiply:

• Numerators: \(1 \times 50 = 50\)
• Denominators: \(150 \times 1 = 150\)

This gives us \( \frac{50}{150} \). Multiplication of fractions is a clean process that lays the foundation for the next step: simplifying.

To **simplify fractions**, you reduce them to their simplest or lowest terms. This requires finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both terms without any remainder.
In our example, the fraction \( \frac{50}{150} \) can be simplified. First, find the GCD of 50 and 150, which is 50. Next, divide both the numerator and the denominator by the GCD:

• \(50 \div 50 = 1\)
• \(150 \div 50 = 3\)

So, \( \frac{50}{150} \) reduces to \( \frac{1}{3} \). By simplifying fractions, you make them easier to understand and work with.