What is 5/6 of 32?

How to calculate 5/6 of 32?

1. Multiply the whole number by the numerator of the fraction: 32 × 5 = 160
2. Divide this result by denominator of the fraction: 160/6 = 26.666666666667
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 160/2 = 80
   • 6/2 = 3
4. Which gives: 80/3

Since 80/3 is an improper fraction, the result could also be expressed as a mixed number: 26 2/3

How does it work?

The principle behind finding a fraction of a number, such as 5/6 of 32, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{6}=\frac{x}{32}$ (where x represents 5/6 of 32)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 32=6x$
2. Which gives: $160=6x$
3. Divide both sides by 6 to isolate x: $\frac{160}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{160}{6}=x$ (or $\frac{80}{3}=x$)

Thus, 5/6 of 32 is equal to 80/3 (or 26.666666666667 in its decimal form).