What is 7/6 of 86?

How to calculate 7/6 of 86?

1. Multiply the whole number by the numerator of the fraction: 86 × 7 = 602
2. Divide this result by denominator of the fraction: 602/6 = 100.33333333333
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 602/2 = 301
   • 6/2 = 3
4. Which gives: 301/3

Since 301/3 is an improper fraction, the result could also be expressed as a mixed number: 100 1/3

How does it work?

The principle behind finding a fraction of a number, such as 7/6 of 86, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{7}{6}=\frac{x}{86}$ (where x represents 7/6 of 86)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $7\times 86=6x$
2. Which gives: $602=6x$
3. Divide both sides by 6 to isolate x: $\frac{602}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{602}{6}=x$ (or $\frac{301}{3}=x$)

Thus, 7/6 of 86 is equal to 301/3 (or 100.33333333333 in its decimal form).