What is 6/8 of 82?

How to calculate 6/8 of 82?

1. Multiply the whole number by the numerator of the fraction: 82 × 6 = 492
2. Divide this result by denominator of the fraction: 492/8 = 61.5
3. Simplify by dividing both the numerator and denominator by their GCD (4):
   • 492/4 = 123
   • 8/4 = 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 6/8 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{8}=\frac{x}{82}$ (where x represents 6/8 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 82=8x$
2. Which gives: $492=8x$
3. Divide both sides by 8 to isolate x: $\frac{492}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{492}{8}=x$ (or $\frac{123}{2}=x$)

Thus, 6/8 of 82 is equal to 123/2 (or 61.5 in its decimal form).