# Ordering Fractions With The Same Numerator

Ordering is arranging either in increasing or decreasing order. We are dealing with fractions with the same numerators here. To order these fractions, we consider their denominators and order them, either from least to the greatest or from the greatest to the least. The order of fractions will be reverse of the order of the denominators. (As greater the denominator, smaller is the fraction)

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

• To arrange the fractions d/a, d/b, d/c in increasing order, we find that the fractions have same numerator. We arrange the denominators in increasing order as a < b < c. The order of fractions will be reverse of the order of the denominators. Hence, the fractions in increasing order would be d/c < d/b < d/a.

• To arrange the fractions d/a, d/b, d/c in decreasing order, we find the fractions have same numerator. We arrange the denominators in decreasing order as c > b > a.
The order of fractions will be reverse of the order of the denominators.
Hence, the fractions in decreasing order would be d/a > d/b > d/c

Order the following fractions from the least to greatest

$\frac{3}{11}$, $\frac{3}{6}$, $\frac{3}{8}$

### Solution

Step 1:

The numerator of each fraction is the same 3. So we look at the denominators. Here is the order of the denominators from least to the greatest.

6 < 8 < 11

Step 2:

The order of the fractions from least to greatest is the reverse

$\frac{3}{11}$ < $\frac{3}{8}$ < $\frac{3}{6}$

Order the following fractions from the least to greatest.

$\frac{5}{9}$, $\frac{5}{12}$, $\frac{5}{8}$

### Solution

Step 1:

The numerator of each fraction is the same 5. So we look at the denominators. Here is the order of the denominators from least to the greatest.

8 < 9 < 12

Step 2:

The order of the fractions from least to greatest is the reverse

$\frac{5}{12}$ < $\frac{5}{9}$ < $\frac{5}{8}$

Order the following fractions from the least to greatest.

$\frac{3}{8}$, $\frac{3}{7}$, $\frac{3}{5}$

### Solution

Step 1:

The numerator of each fraction is the same 3. So we look at the denominators. Here is the order of the denominators from least to the greatest.

5 < 7 < 8

Step 2:

The order of the fractions from least to greatest is the reverse

$\frac{3}{8}$ < $\frac{3}{7}$ < $\frac{3}{5}$