What is 3/8 of 82?

How to calculate 3/8 of 82?

1. Multiply the whole number by the numerator of the fraction: 82 × 3 = 246
2. Divide this result by denominator of the fraction: 246/8 = 30.75
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 246/2 = 123
   • 8/2 = 4
4. Which gives: 123/4

Since 123/4 is an improper fraction, the result could also be expressed as a mixed number: 30 3/4

How does it work?

The principle behind finding a fraction of a number, such as 3/8 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{3}{8}=\frac{x}{82}$ (where x represents 3/8 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $3\times 82=8x$
2. Which gives: $246=8x$
3. Divide both sides by 8 to isolate x: $\frac{246}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{246}{8}=x$ (or $\frac{123}{4}=x$)

Thus, 3/8 of 82 is equal to 123/4 (or 30.75 in its decimal form).