# Ordering Fractions With The Same Denominator

Ordering is arranging either in increasing or decreasing order. We are ordering fractions with same denominators here. To order these fractions, we consider their numerators and order them, either from least to the greatest or from the greatest to the least. The same order applies to the fractions as well.

If a, b, c and d are any four real numbers and a < b < c then

• To arrange the fractions a/d, b/d, c/d in increasing order, we find that the fractions have same denominator. We arrange the numerator in increasing order as a < b < c. Here the fractions in increasing order would be a/d < b/d < c/d.

• To arrange the fractions a/d, b/d, c/d in decreasing order, we find the fractions have same denominator. We arrange the numerators in decreasing order as c > b > a. Here the fractions in decreasing order would be c/d > b/d > a/d

Order the following fractions from least to greatest

$\frac{5}{7}$, $\frac{6}{7}$, $\frac{4}{7}$

### Solution

Step 1:

The denominator of each fraction is the same 7. So to order the fraction, we must simply order the numerators. Here are the numerators in order from least to greatest.

4 < 5 < 6

Step 2:

So, the fractions, ordered from least to greatest are

$\frac{4}{7}$ < $\frac{5}{7}$ < $\frac{6}{7}$

Order the following fractions from greatest to least

$\frac{8}{11}$, $\frac{6}{11}$, $\frac{9}{11}$

### Solution

Step 1:

The denominator of each fraction is the same 11. So to order the fraction, we must simply order the numerators. Here are the numerators in order from greatest to least.

9 > 8 > 6

Step 2:

So, the fractions, ordered from greatest to least are

$\frac{9}{11}$ > $\frac{8}{11}$ > $\frac{6}{11}$

Order the following fractions from least to greatest

$\frac{8}{9}$, $\frac{7}{9}$, $\frac{5}{9}$

### Solution

Step 1:

The denominator of each fraction is the same 9. So to order the fraction, we must simply order the numerators. Here are the numerators in order from least to greatest.

5 < 7 < 8

Step 2:

So, the fractions, ordered from least to greatest are

$\frac{5}{9}$ < $\frac{7}{9}$ < $\frac{8}{9}$