Adding fractions

Meena's father made some chikki. Meena ate 1/2 of it and her younger brother ate 1/4 of it. Split Meena's half into two quarters: 1/2 = 1/4 + 1/4. So together they ate 1/4 + 1/4 + 1/4 = 3 × 1/4 = 3/4 of the chikki.

When two fractions have the same fractional unit, just add the number of units. 2/5 + 1/5: two fifths and one fifth make three fifths, 3/5. 4/7 + 6/7 = 10/7, and 10/7 = 1 + 3/7 = 1 3/7. The denominator stays the same; only the numerators are added. (Adding the denominators too is a common mistake: fifths plus fifths are still fifths.)

When the units are different, first make them the same. For 1/4 + 1/3 we can use 4 × 3 = 12 as the common denominator: 1/4 = 3/12 and 1/3 = 4/12, so 1/4 + 1/3 = 3/12 + 4/12 = 7/12. In the same way, 2/5 + 1/4 = 8/20 + 5/20 = 13/20. Brahmagupta first described this method in general in 628 CE.

Brahmagupta's method for adding fractions has three steps:

• 1: find equivalent fractions with a common fractional unit, using a common multiple of the denominators.
• 2: add the numerators and keep the same denominator.
• 3: give the answer in lowest terms if needed.

For 2/3 + 1/5, use 15: 10/15 + 3/15 = 13/15. For 1/6 + 1/3, use 6: 1/6 + 2/6 = 3/6, which in lowest terms is 1/2.