# Equivalent fractions

Two fractions are** equivalent** when they express the same part of a unit or when they have the same value.

For example:

We can test if two fractions are equivalent by cross-multiplying their numerators and denominators. This is also called taking the cross-product:

If you multiply or divide the numerator and the denominator of a fraction by the same number, except zero, you obtain one equivalent fraction.

HOW DO YOU GET EQUIVALENT FRACTIONS? As we said, there are two methods:

- **Amplifying**: Multiply numerator and denominator by the same number

- **Simplifying**: Divide numerator and denominator by the same number.

Simplifying (or reducing) fractions means to make the fraction as simple as possible. Why say four-eighths (4/8) when you really mean one half (1/2) ?

You make this by dividing the numerator and the denominator by the same number (except zero).

One fraction that you can’t simplify is called **irreducible fraction**. Then, the numerator and the denominator are **coprimes**.

**To simplify**:

- Decompose the numerator and the denominator

- Cross out the numbers that are repeated in the numerator and in the denominator

- If there’s no number in the numerator, put 1

- At the end, you obtain the irreducible fraction equivalent to the first fraction

**Exercises:**

1.- Decide if the following pairs of fractions are equivalent or not:

a) 2/5 and 3/7

b) 3/7 and 21/49

2.- Find two equivalent fractions to these ones:

a) -1/5

b) 3/7

3.- Simplify these fractions:

a) 210/300

b) 3000/2700

Solutions: 1.- a) not equivalent; b) equivalent; 2.- a) -2/10 and -3/15; b) 6/14 and 30/70; 3.- a) 7/10; b) 10/9

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