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Addition and Subtraction

January 15, 2025
1 min read
addition subtraction brahmagupta

Brahmagupta’s Method

Brahmagupta (628 CE) formally described the rules we use today.

Step 1: Common Fractional Unit

If denominators are different, find a common denominator (often the product of the two denominators). Example: Add 14\frac{1}{4} and 13\frac{1}{3}. Common denominator = 4×3=124 \times 3 = 12.

14=312,13=412\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12}

Step 2: Add/Subtract Numerators

Now that the units are the same (112\frac{1}{12}), we just add the number of pieces.

312+412=3+412=712\frac{3}{12} + \frac{4}{12} = \frac{3+4}{12} = \frac{7}{12}

Subtraction Example

Subtract 23\frac{2}{3} from 34\frac{3}{4}. Problem: 34−23\frac{3}{4} - \frac{2}{3}. Common Denominator: 12.

34=912\frac{3}{4} = \frac{9}{12} 23=812\frac{2}{3} = \frac{8}{12} 912−812=112\frac{9}{12} - \frac{8}{12} = \frac{1}{12}