# How do you determine which fraction is greater 3/7 or 4/9?

Jan 13, 2016

Divide one into the other. The resulting value will indicate which is the greater: $\textcolor{w h i t e}{\ldots .} \frac{4}{9} > \frac{3}{7}$

#### Explanation:

Consider $\frac{4}{9} \div \frac{3}{7}$ giving:

$\frac{4}{9} \times \frac{7}{3} = \frac{28}{27}$ which is greater than 1 so

$\frac{4}{9} > \frac{3}{7}$

Sep 19, 2016

$\frac{3}{7} < \frac{4}{9}$

#### Explanation:

A quick method is to cross multiply the fractions.

However, this only works if you multiply in the same direction every time. $\textcolor{red}{\text{Red x Red}}$ first as shown below:

$\frac{\textcolor{red}{3}}{\textcolor{b l u e}{7}} \mathmr{and} \frac{\textcolor{b l u e}{4}}{\textcolor{red}{9}}$

$\textcolor{red}{3 \times 9} \mathmr{and} \textcolor{b l u e}{7 \times 4}$

$\textcolor{red}{27} < \textcolor{red}{28}$

$\textcolor{red}{\frac{3}{7}} < \textcolor{b l u e}{\frac{4}{9}}$

An alternative method is to get rid of the denominators

$\times L C D \text{ }$ which in this case is 63

${\cancel{63}}^{9} / 1 \times \frac{3}{\cancel{7}} \mathmr{and} {\cancel{63}}^{7} / 1 \times \frac{4}{\cancel{9}}$

$27 < 28$

$\frac{3}{7} < \frac{4}{9}$

Worst method - use a calculator!

Use a calculator to change them into decimals, then compare.

$\frac{3}{7} = 0.42857 \ldots . \text{ } \leftarrow$ smaller

$\frac{4}{9} = 0.44444 \ldots \text{ } \leftarrow$ larger

You can also use a calculator to subtract the two fractions.
If you get a positive answer, then the first fraction was bigger.
If you get a negative answer then the first fraction was smaller.