Exploring Fractions: Equivalence and Simplification

Fractions are like slices of a pie: they show parts of a whole. Sometimes, fractions look different but mean the same thing—that’s what we call equivalent fractions. Simplifying fractions makes them easier to work with and understand.

Understanding Equivalent Fractions

• Equivalent fractions are fractions that represent the same value, even though they look different.
• Imagine slicing the same-sized pie into different numbers of pieces. Whether you have half a pie or two quarters, you still have the same amount of pie.

For example, $\frac{1}{2}$, $\frac{2}{4}$, and $\frac{4}{8}$ all show the same amount—half of something—just in different forms.

 

How to Find Equivalent Fractions

To find an equivalent fraction, multiply or divide both the numerator (top number) and the denominator (bottom number) by the same number.

Example 1: Making Equivalent Fractions

Let’s find fractions equivalent to $\frac{2}{3}$

1. Multiply both the numerator and the denominator by $2$: $$\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$$
2. Multiply both the numerator and the denominator by $3$: $$\frac{2 \times 3}{3 \times 3} = \frac{6}{9}$$

So, we have: $$\frac{2}{3} = \frac{4}{6} = \frac{6}{9}$$

Finding Equivalent Fractions

To find an equivalent fraction, you multiply or divide the numerator and the denominator by the same number. Remember, whatever you do to the top, you must do to the bottom

 

 

 

Simplifying Fractions

Simplifying a fraction means making it as simple as possible by dividing both the numerator and the denominator by the greatest common divisor (GCD). This gives you the same fraction in its simplest form.

Steps to Simplify a Fraction

1. Find the GCD of the numerator and the denominator.
2. Divide both the numerator and the denominator by the GCD.

Example 2: Simplifying Fractions

Let’s simplify $\frac{8}{12}$

1. The GCD of $8$ and $12$ is $4$.
2. Divide both the numerator and the denominator by $4$: $$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$$

So, $\frac{8}{12}$ simplifies to: $$\frac{2}{3}$$