We want to order the fractions from least to greatest.

\frac{4}{5}, \frac{1}{2}, \frac{9}{1 0}, \frac{3}{4}

To compare fractions we follow three steps.

Let's start!

The least common denominator is the least common multiple of the denominators.

\frac{4}{5}, \frac{1}{2}, \frac{9}{1 0}, \frac{3}{4}

To find the LCM of

5,

2,

10,

and

4,

we start by writing their prime factorizations. We will color each factor differently to help us with the next step.

5 = 2 = 10 = 4 = 52 2 \times 5 2 \times 2

Next, we multiply the prime factors, being sure to include each unique prime factor only once.

5 \cdot 2 \cdot 2 = 20

We want to find fractions with a denominator of

20

that are equivalent to the given fractions. Let's start with

\frac{4}{5} .

We multiply

5

by

4

to get

20,

so we will also multiply

4

by

4

to get its equivalent fraction.

We found that

\frac{1 6}{2 0}

is equivalent to

\frac{4}{5} .

Let's consider

\frac{1}{2}

next. We multiply

2

by

10

to get

20,

so we will also multiply

1

by

10

to get our equivalent fraction.

We found that

\frac{1 0}{2 0}

is equivalent to

\frac{1}{5} .

Next, let's find an equivalent fraction for

\frac{9}{1 0} .

This time we will multiply the numerator and denominator by

2 .

Our fraction that is equivalent to

\frac{9}{1 0}

is

\frac{1 8}{2 0} .

Finally, we will rewrite

\frac{3}{4}

to have a denominator of

20 .

We multiply

4

by

5

to get

20,

so we will also multiply

3

by

5

to get our equivalent fraction.

The final equivalent fraction is

\frac{1 5}{2 0} .

Let's write all the equivalent fractions and consider their numerators.

To order the fractions with the same denominator from least to greatest, we order the numerators from least to greatest.

Exercise