Arrange the following in ascending order :- 7 9 , 5 12 , 11 18 , 17 36
The correct answer and explanation is:
Correct Answer (Ascending Order):
5/12, 17/36, 11/18, 7/9
Explanation:
To arrange the fractions 7/9, 5/12, 11/18, and 17/36 in ascending order, the best approach is to express all of them with a common denominator. This allows a direct comparison of their numerators. First, determine the least common denominator (LCD) of all the denominators: 9, 12, 18, and 36.
The least common multiple (LCM) of 9, 12, 18, and 36 is 72. Now convert each fraction to an equivalent fraction with a denominator of 72:
- 7/9
Multiply numerator and denominator by 8:
(7 × 8)/(9 × 8) = 56/72 - 5/12
Multiply numerator and denominator by 6:
(5 × 6)/(12 × 6) = 30/72 - 11/18
Multiply numerator and denominator by 4:
(11 × 4)/(18 × 4) = 44/72 - 17/36
Multiply numerator and denominator by 2:
(17 × 2)/(36 × 2) = 34/72
Now, compare the numerators:
- 30/72 (from 5/12)
- 34/72 (from 17/36)
- 44/72 (from 11/18)
- 56/72 (from 7/9)
Clearly, 30 < 34 < 44 < 56.
Therefore, the fractions in ascending order are:
5/12, 17/36, 11/18, 7/9
This method ensures accuracy without guessing or estimating decimal values. Using a common denominator transforms all fractions into comparable terms. It avoids errors that may occur when relying on mental approximations or calculators. The ascending arrangement shows the fractions from smallest to largest in a clear and mathematically sound manner.