What is 5/6 of 45?

How to calculate 5/6 of 45?

1. Multiply the whole number by the numerator of the fraction: 45 × 5 = 225
2. Divide this result by denominator of the fraction: 225/6 = 37.5
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 225/3 = 75
   • 6/3 = 2
4. Which gives: 75/2

Since 75/2 is an improper fraction, the result could also be expressed as a mixed number: 37 1/2

How does it work?

The principle behind finding a fraction of a number, such as 5/6 of 45, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{6}=\frac{x}{45}$ (where x represents 5/6 of 45)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 45=6x$
2. Which gives: $225=6x$
3. Divide both sides by 6 to isolate x: $\frac{225}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{225}{6}=x$ (or $\frac{75}{2}=x$)

Thus, 5/6 of 45 is equal to 75/2 (or 37.5 in its decimal form).