What is 5/6 of 75?

How to calculate 5/6 of 75?

1. Multiply the whole number by the numerator of the fraction: 75 × 5 = 375
2. Divide this result by denominator of the fraction: 375/6 = 62.5
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 375/3 = 125
   • 6/3 = 2
4. Which gives: 125/2

Since 125/2 is an improper fraction, the result could also be expressed as a mixed number: 62 1/2

How does it work?

The principle behind finding a fraction of a number, such as 5/6 of 75, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{6}=\frac{x}{75}$ (where x represents 5/6 of 75)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 75=6x$
2. Which gives: $375=6x$
3. Divide both sides by 6 to isolate x: $\frac{375}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{375}{6}=x$ (or $\frac{125}{2}=x$)

Thus, 5/6 of 75 is equal to 125/2 (or 62.5 in its decimal form).