LESSON: Equivalent Fractions: READ: Write Given Fractions in Simplest Form

LESSON: Equivalent Fractions

Equivalent Fractions

READ: Write Given Fractions in Simplest Form

Write Given Fractions in Simplest Form

One of the trickiest things to think about with equivalent fractions is being able to determine whether or not they are equivalent. Look at this example.

Example

Are $\frac{3}{6}$ and $\frac{4}{8}$ equivalent?

This is tricky because we can’t tell if the numerator and denominator were multiplied by the same number. These fractions look like they might be equal, but how can we tell for sure? This is where simplifying fractions is important.

How do we simplify fractions?

You can think of simplifying fractions as the opposite of creating equal fractions. When we created equal fractions we multiplied. When we simplify fractions, we divide.

What do we divide?

To simplify a fraction, we divide the top and the bottom number by the Greatest Common Factor.

Let’s simplify $\frac{3}{6}$ . To do this, we need to divide the numerator and denominator by the GCF.

The GCF of 3 and 6 is 3.

$\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$

Let’s simplify $\frac{4}{8}$ . To do this, we need to divide the numerator and the denominator by the GCF.

The GCF of 4 and 8 is 4.

$\frac{4 \div 4}{8 \div 4} = \frac{1}{2}$

We can see that $\frac{3}{6}$ and $\frac{4}{8} = \frac{1}{2}$ . They are equivalent fractions.

We can use simplifying to determine if two fractions are equivalent, or we can just simplify a fraction to be sure that it is the simplest it can be. Sometimes you will also hear simplifying called reducing a fraction.