Using a Common Denominator to Order Fraction

Ordering fractions is arranging them either in increasing or decreasing order. The fractions that are to be ordered can have pke or unpke denominators.

In case we are required to order fractions with unpke denominators, we write their equivalent fractions with pke denominators after finding their least common denominator. Then we order their numerators and the same order apppes to the original fractions.

First, rewrite $frac{9}{11}$ and $frac{5}{6}$ so that they have a common denominator. Then use <, = or > to order $frac{9}{11}$ and $frac{5}{6}$.

Solution

Step 1:

We must rewrite the fractions so that they have a common denominator.

We can use the least common denominator (LCD)

The LCD of $frac{9}{11}$ and $frac{5}{6}$ is 66.

Step 2:

Now we rewrite the fractions with this denominator.

$frac{9}{11}$ = 9×6 ÷ 11×6 = $frac{54}{66}$

$frac{5}{6}$ = 5×11 ÷ 6×11 = $frac{55}{66}$

Step 3:

Since $frac{54}{66}$ and $frac{55}{66}$ have a common denominator, we can order them using their numerators.

Because 54 < 55, we have

$frac{54}{66}$ < $frac{55}{66}$

Step 4:

Writing these fractions in original form $frac{9}{11}$ < $frac{5}{6}$

First, rewrite $frac{1}{9}$ and $frac{2}{15}$ so that they have a common denominator. Then use <, = or > to order $frac{1}{9}$ and $frac{2}{15}$.

Solution

Step 1:

We must rewrite the fractions so that they have a common denominator.

We can use the least common denominator (LCD)

The LCD of $frac{1}{9}$ and $frac{2}{15}$ is 45.

Step 2:

Now we rewrite the fractions with this denominator.

$frac{1}{9}$ = 1×5 ÷ 9×5 = $frac{5}{45}$

$frac{2}{15}$ = 2×3÷ 15×3 = $frac{6}{45}$

Step 3:

Since $frac{5}{45}$ and $frac{6}{45}$ have a common denominator, we can order them using their numerators.

Because 5 < 6, we have $frac{5}{45}$ < $frac{6}{45}$

Step 4:

Writing these fractions in original form $frac{1}{9}$ < $frac{2}{15}$