Comparing and Ordering Fractions

 Scenarios to be considered

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.

Fraction Comparision Example

Example 1:
 `11/15`

Explanation:

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

Example 2:
 `7/8`

Explanation:

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

Example 3:
 `>`

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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