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.

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

Exercise.- Simplify the following fractions: