What is 6/9 of 82?

How to calculate 6/9 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: 492/9 = 54.666666666667
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 492/3 = 164
   • 9/3 = 3
4. Which gives: 164/3

Since 164/3 is an improper fraction, the result could also be expressed as a mixed number: 54 2/3

How does it work?

The principle behind finding a fraction of a number, such as 6/9 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{9}=\frac{x}{82}$ (where x represents 6/9 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 82=9x$
2. Which gives: $492=9x$
3. Divide both sides by 9 to isolate x: $\frac{492}{9}=\frac{9x}{9}$
4. Which gives the result: $\frac{492}{9}=x$ (or $\frac{164}{3}=x$)

Thus, 6/9 of 82 is equal to 164/3 (or 54.666666666667 in its decimal form).