What is 3/4 of 82?

How to calculate 3/4 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: 246/4 = 61.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 246/2 = 123
   • 4/2 = 2
4. Which gives: 123/2

Since 123/2 is an improper fraction, the result could also be expressed as a mixed number: 61 1/2

How does it work?

The principle behind finding a fraction of a number, such as 3/4 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{3}{4}=\frac{x}{82}$ (where x represents 3/4 of 82)

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

Thus, 3/4 of 82 is equal to 123/2 (or 61.5 in its decimal form).