Comparing and Ordering Fractions

If Fractions have similar Denominators

•  The fraction with the smaller numerator is smaller.
•  The fraction with the larger numerator is larger.

If Fractions have similar Numerators

•   The fraction with the smaller denominator is larger.
•  The fraction with the larger denominator is smaller.

Note:

There are instances that the fractions to be compared have different denominators.The conditions above cannot be applied. Below are the steps to be considered:

If Fractions have unlike Denominators

•  Find the least common denominator (LCD).
•   Convert the fractions into equivalent fractions with the LCD.
•  Since the fractions have similar denominators, compare the numerators.

Which is smaller: 11/15 or 13/15

Explanation:

Since the fractions have similar denominators, compare the numerators.
Since 11 is smaller than 13, therefore 11/15 is smaller.

Which is larger: 7/8 or 7/12

Explanation:

Since the fractions have similar numerators, compare the denominators.
Since 8 is smaller than 12, therefore 7/8 is larger.

Fill in the blank with the correct inequality symbol: 5/9 ___ 6/11

Explanation:

Since the fractions have unlike denominators, get the least common denominator (LCD).

 9 = 3 × 3 11 = 3 × 3 × 11 LCD = 3 × 3 × 11

Converting the fractions into equivalent fractions with 99 as the denominator:
5/9 × 11/11 = 55/99
6/11 × 9/9 = 54/99
Since the fractions have similar denominators, compare the numerators.
Since 55 is greater than 54, therefore 55/99 > 54/99 or 5/9 > 6/11.

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