   SEARCH HOME Math Central Quandaries & Queries  Question from shealla, a student: Please help me with my assignment please I'm having trouble answering this one.. Write the larger fraction in each pair.. A. 2/3, 4/7 B. 1/3, 2/5 C. 5/8, 3/5 Hi Shealla,

I am going to look at $\frac59$ and $\frac{3}{5}.$

It is easy to compare two fractions if they have the same denominator and hence I want to find equivalent fractions to $\frac59$ and $\frac35$ which have a common denominator. One common denominator that will always work is the product of the two denominators. This I am going to find fractions, equivalent to $\frac59$ and $\frac35$ that have a denominator of $9 \times 5 = 45.$

To change the denominator of $\frac59$ to $45$ I need to multiply the denominator by $5$ so I need also to multiply the numerator by $5$ and hence

$\frac59 = \frac{5 \times 5}{9 \times 5} = \frac{25}{45}.$

Likewise to change the denominator of $\frac35$ to $45$ I multiply the denominator by $9$ and hence I multiply the numerator also by $9$ to get

$\frac35 = \frac{3 \times 9}{5 \times 9} = \frac{27}{45}.$

Now I can see the relation, $\frac{27}{45}$ is larger than $\frac{25}{45}$ and hence $\frac35$ is larger that $\frac{5}{9}.$      