What is 6/9 of 86?

How to calculate 6/9 of 86?

1. Multiply the whole number by the numerator of the fraction: 86 × 6 = 516
2. Divide this result by denominator of the fraction: 516/9 = 57.333333333333
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 516/3 = 172
   • 9/3 = 3
4. Which gives: 172/3

Since 172/3 is an improper fraction, the result could also be expressed as a mixed number: 57 1/3

How does it work?

The principle behind finding a fraction of a number, such as 6/9 of 86, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{9}=\frac{x}{86}$ (where x represents 6/9 of 86)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 86=9x$
2. Which gives: $516=9x$
3. Divide both sides by 9 to isolate x: $\frac{516}{9}=\frac{9x}{9}$
4. Which gives the result: $\frac{516}{9}=x$ (or $\frac{172}{3}=x$)

Thus, 6/9 of 86 is equal to 172/3 (or 57.333333333333 in its decimal form).