What is 5/6 of 82?

How to calculate 5/6 of 82?

1. Multiply the whole number by the numerator of the fraction: 82 × 5 = 410
2. Divide this result by denominator of the fraction: 410/6 = 68.333333333333
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 410/2 = 205
   • 6/2 = 3
4. Which gives: 205/3

Since 205/3 is an improper fraction, the result could also be expressed as a mixed number: 68 1/3

How does it work?

The principle behind finding a fraction of a number, such as 5/6 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{6}=\frac{x}{82}$ (where x represents 5/6 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 82=6x$
2. Which gives: $410=6x$
3. Divide both sides by 6 to isolate x: $\frac{410}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{410}{6}=x$ (or $\frac{205}{3}=x$)

Thus, 5/6 of 82 is equal to 205/3 (or 68.333333333333 in its decimal form).