Subtracting fractions

Brahmagupta's method works for subtraction too. What is 6/7 − 4/7? Draw a strip cut into 7 equal parts and shade 6 of them. Now remove 4 of the shaded parts. 2 shaded parts are left, so 6/7 − 4/7 = 2/7. Both fractions have the same fractional unit, 1/7, so we just subtract the numerators and keep the denominator.

When the denominators are different, first write equivalent fractions with the same fractional unit. For 3/4 − 2/3, use 12: 3/4 = (3 × 3)/(4 × 3) = 9/12 and 2/3 = (2 × 4)/(3 × 4) = 8/12. So 3/4 − 2/3 = 9/12 − 8/12 = 1/12.

Brahmagupta's method for subtracting two fractions:

• 1: change them into equivalent fractions with the same denominator;
• 2: subtract the numerators and keep the same denominator;
• 3: simplify the result into lowest terms if needed.

For example, 10/27 − 1/27 = 9/27, which in lowest terms is 1/3.

Read the question carefully: 'subtract 4 5/9 from 7 1/6' means 7 1/6 − 4 5/9, the bigger one first. Change both to fractions (43/6 and 41/9), use 18 as the common denominator, and get 129/18 − 82/18 = 47/18.

Jaya's school is 7/10 km from her home. She takes an auto for 1/2 km and walks the rest. 1/2 = 5/10, so she walks 7/10 − 5/10 = 2/10 km, which in lowest terms is 1/5 km.