What is 10/6 of 80?

How to calculate 10/6 of 80?

1. Multiply the whole number by the numerator of the fraction: 80 × 10 = 800
2. Divide this result by denominator of the fraction: 800/6 = 133.33333333333
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 800/2 = 400
   • 6/2 = 3
4. Which gives: 400/3

Since 400/3 is an improper fraction, the result could also be expressed as a mixed number: 133 1/3

How does it work?

The principle behind finding a fraction of a number, such as 10/6 of 80, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{6}=\frac{x}{80}$ (where x represents 10/6 of 80)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 80=6x$
2. Which gives: $800=6x$
3. Divide both sides by 6 to isolate x: $\frac{800}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{800}{6}=x$ (or $\frac{400}{3}=x$)

Thus, 10/6 of 80 is equal to 400/3 (or 133.33333333333 in its decimal form).