More or less than 1

In your book, Maths Mela (Chapter 2), we learn a quick way to tell whether a fraction is more or less than 1 whole. Compare the top number (the numerator) with the bottom number (the denominator).

The denominator tells how many pieces make 1 whole. If the numerator is the SAME as the denominator, you have exactly 1 whole: 4/4 = 1 and 8/8 = 1. If the numerator is SMALLER, you do not have enough pieces for a whole, so the fraction is less than 1: 7/9 is less than 1, because 9 ninths make a whole and you have only 7. If the numerator is BIGGER, you have more than a whole, so the fraction is more than 1: 9/4, 13/11 and 12/5 are all more than 1.

We can use 1 to compare two fractions. Sevi and Shami ate paratha one evening: one of them ate 7/8 paratha and the other ate 8/6 paratha. Who ate less? 7/8 is less than 1, because 8 eighths make a whole and there are only 7. 8/6 is more than 1, because 6 sixths make a whole and there are 8. Something less than 1 is always smaller than something more than 1. So 7/8 < 8/6, and the one who ate 7/8 ate less.

This trick works when one fraction is below 1 and the other is above 1 (or exactly 1). 8/7 > 9/15, because 8/7 is more than 1 and 9/15 is less than 1. 6/6 < 19/12, because 6/6 is exactly 1 and 19/12 is more than 1.