What is 5/6 of 64?

How to calculate 5/6 of 64?

1. Multiply the whole number by the numerator of the fraction: 64 × 5 = 320
2. Divide this result by denominator of the fraction: 320/6 = 53.333333333333
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 320/2 = 160
   • 6/2 = 3
4. Which gives: 160/3

Since 160/3 is an improper fraction, the result could also be expressed as a mixed number: 53 1/3

How does it work?

The principle behind finding a fraction of a number, such as 5/6 of 64, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{6}=\frac{x}{64}$ (where x represents 5/6 of 64)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 64=6x$
2. Which gives: $320=6x$
3. Divide both sides by 6 to isolate x: $\frac{320}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{320}{6}=x$ (or $\frac{160}{3}=x$)

Thus, 5/6 of 64 is equal to 160/3 (or 53.333333333333 in its decimal form).