Mental Maths (Comparison of Fractions) - Part 2

Model 5 : 

• For a fraction Less than 1 :

• If the difference between the numerator and the denominator is same then the fraction with the larger values of numerator and denominator will be the largest. Have a look at the following example.

• Which of the following fractions is the largest?
• (31/37), (23/29), (17/23), (35/41), (13/19) 
• The difference between the numerator and the denominator of each fraction is 6.... So the fraction with the larger numerals i.e., 35/41 is the greatest and the fraction with smaller numerals i.e., 13/19 is the smallest.

• For a fraction Greater than 1 :

• If the difference between the numerator and denominator is same, then the fraction with the smaller values will be the largest.

• Which of the following fraction is largest ?
• (31/27), (43/39), (57/53), (27/23), (29/25)
• As the difference between the numerator and the denominator is same, the fraction with the smaller values i.e., 27/23 is the largest.

Model 6 : 

• Which of the following fractions is the largest?
• (15/17), (23/29), (31/34), (11/15)
• Comparing fractions 15/17 and 23/29
• The numerator of the fraction has increased from 15 to 23. i.e. 8/15 i.e. a little more than 50%.  The denominator of the fraction has increased from 17 to 29. i.e., 12/17 i.e., well over 50%. As the percentage increase in the numerator is less than the  percentage increase in the denominator, the fraction 15/17 > 23/29.
• Now compare 15/17 with 31/34
• As the change in the numerator is more than double (15 to 31), and the change in the denominator is exactly double, the fraction 15/17 < 31/34.
• Now compare 11/15 and 31/34
• The numerator has almost tripled from 11 to 31 whereas the denominator has just over doubled from 15 to 34. Since the increase in numerator is greater than the increase in the denominator, 31 /34 > 11/15.
• So, 31/34 is the largest fraction :)

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