Lowest terms

2 rotis among 3 children, 4 rotis among 6 and 6 rotis among 9 all give the same share, so 2/3 = 4/6 = 6/9. Of these, 2/3 uses the smallest numbers: it is called the simplest form of 4/6 and of 6/9.

A fraction is in lowest terms (its simplest form) when its numerator and denominator have no common factor except 1. To put a fraction in lowest terms, divide the numerator and the denominator by a common factor, and keep going until only 1 is common. Dividing both by the same number is the opposite of multiplying both by it, so the value does not change.

Is 16/20 in lowest terms? No: 4 is a common factor of 16 and 20. Dividing both by 4 gives 16/20 = 4/5, and 4 and 5 have no common factor other than 1. So 16/20 in lowest terms is 4/5. Dividing by the highest common factor gets there in one step.

We can also go in steps. For 36/60:

• Both numbers are even, so divide by 2: 18/30.
• Both are even again: 9/15.
• Now 9 and 15 are both multiples of 3: 3/5.

Or notice at once that 36 = 3 × 12 and 60 = 5 × 12, and divide both by 12. Either way, 36/60 = 3/5.