What is 5/6 of 86?

How to calculate 5/6 of 86?

1. Multiply the whole number by the numerator of the fraction: 86 × 5 = 430
2. Divide this result by denominator of the fraction: 430/6 = 71.666666666667
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 430/2 = 215
   • 6/2 = 3
4. Which gives: 215/3

Since 215/3 is an improper fraction, the result could also be expressed as a mixed number: 71 2/3

How does it work?

The principle behind finding a fraction of a number, such as 5/6 of 86, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{6}=\frac{x}{86}$ (where x represents 5/6 of 86)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 86=6x$
2. Which gives: $430=6x$
3. Divide both sides by 6 to isolate x: $\frac{430}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{430}{6}=x$ (or $\frac{215}{3}=x$)

Thus, 5/6 of 86 is equal to 215/3 (or 71.666666666667 in its decimal form).