What is 10/6 of 82?

How to calculate 10/6 of 82?

1. Multiply the whole number by the numerator of the fraction: 82 × 10 = 820
2. Divide this result by denominator of the fraction: 820/6 = 136.66666666667
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 820/2 = 410
   • 6/2 = 3
4. Which gives: 410/3

Since 410/3 is an improper fraction, the result could also be expressed as a mixed number: 136 2/3

How does it work?

The principle behind finding a fraction of a number, such as 10/6 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{6}=\frac{x}{82}$ (where x represents 10/6 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 82=6x$
2. Which gives: $820=6x$
3. Divide both sides by 6 to isolate x: $\frac{820}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{820}{6}=x$ (or $\frac{410}{3}=x$)

Thus, 10/6 of 82 is equal to 410/3 (or 136.66666666667 in its decimal form).