What is 6/7 of 82?

How to calculate 6/7 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: 492/7 = 70.285714285714

Since 492/7 is an improper fraction, the result could also be expressed as a mixed number: 70 2/7

How does it work?

The principle behind finding a fraction of a number, such as 6/7 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{7}=\frac{x}{82}$ (where x represents 6/7 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 82=7x$
2. Which gives: $492=7x$
3. Divide both sides by 7 to isolate x: $\frac{492}{7}=\frac{7x}{7}$
4. Which gives the result: $\frac{492}{7}=x$

Thus, 6/7 of 82 is equal to 492/7 (or 70.285714285714 in its decimal form).