- Equivalent Fraction
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# 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 like or unlike denominators.

In case we are required to order fractions with unlike denominators, we write their equivalent fractions with like denominators after finding their least common denominator. Then we order their numerators and the same order applies 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 $\frac{1}{9}$ < $\frac{2}{15}$