What is 42/56 in simplest form?

Mar 11, 2018

$\frac{3}{4}$

Explanation:

$\frac{42}{56} \implies \frac{2 \times 3 \times 7}{2 \times 2 \times 2 \times 7}$

$\implies \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 3 \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{7}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 2 \times 2 \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{7}}}}$

$\implies \frac{3}{4}$

Mar 11, 2018

Divide by common factors until you get the simplest form.
$\frac{3}{4}$

Explanation:

Divide the numerator and denominator by a common factor.
It is preferable to use the HCF, but sometimes the HCF is not obvious.

Divide both by $7$

$\frac{42 \div 7}{56 \div 7}$

$= \frac{6}{8} \text{ } \leftarrow$ they can both be divided by $2$

$= \frac{3}{4}$

The highest common factor is actually $14$. If you had seen that:

$\frac{42 \div 14}{56 \div 14} = \frac{3}{4}$