What is 8/6 of 77?

How to calculate 8/6 of 77?

1. Multiply the whole number by the numerator of the fraction: 77 × 8 = 616
2. Divide this result by denominator of the fraction: 616/6 = 102.66666666667
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 616/2 = 308
   • 6/2 = 3
4. Which gives: 308/3

Since 308/3 is an improper fraction, the result could also be expressed as a mixed number: 102 2/3

How does it work?

The principle behind finding a fraction of a number, such as 8/6 of 77, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{8}{6}=\frac{x}{77}$ (where x represents 8/6 of 77)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $8\times 77=6x$
2. Which gives: $616=6x$
3. Divide both sides by 6 to isolate x: $\frac{616}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{616}{6}=x$ (or $\frac{308}{3}=x$)

Thus, 8/6 of 77 is equal to 308/3 (or 102.66666666667 in its decimal form).