# How do you write the fraction 20/35 in simplest form?

Mar 9, 2018

$\frac{4}{7}$

#### Explanation:

When writing a fraction in it's simplest form, this means simplifying it. You do this by finding a common number that goes into both the numerator and the denominator (top and bottom number) and divide the numerator and denominator by that number. You can find this number by finding the factors of the numerator and denominator.

Factors of 20:

$20 \to 20 \times 1 , 10 \times 2 \mathmr{and} 5 \times 4$

Factors of 35:

$35 \to 35 \times 1 \mathmr{and} 7 \times 5$

As you can see the highest common factor in both $20$ and $35$ is $5$, therefore we divide the numerator and denominator by $5$ respectively.

$\frac{20}{5} = 4$ therefore the numerator changes from $20 \to 4$

$\frac{35}{5} = 7$ therefore the denominator changes from $35 \to 7$

$\therefore$ $\frac{20}{35} \to \frac{4}{7}$

Mar 9, 2018

Remove common factors.

#### Explanation:

$\frac{20}{35} = \frac{5 \cdot 4}{5 \cdot 7} = \frac{\cancel{5} \cdot 4}{\cancel{5} \cdot 7} = \frac{4}{7}$

You can also think of it this way:

$\frac{20}{35} = \frac{\textcolor{red}{5} \cdot 4}{\textcolor{red}{5} \cdot 7} = \textcolor{red}{\frac{5}{5}} \cdot \frac{4}{7} = \textcolor{red}{1} \cdot \frac{4}{7} = \frac{4}{7}$