What is 6/4 of 75?

How to calculate 6/4 of 75?

1. Multiply the whole number by the numerator of the fraction: 75 × 6 = 450
2. Divide this result by denominator of the fraction: 450/4 = 112.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 450/2 = 225
   • 4/2 = 2
4. Which gives: 225/2

Since 225/2 is an improper fraction, the result could also be expressed as a mixed number: 112 1/2

How does it work?

The principle behind finding a fraction of a number, such as 6/4 of 75, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{4}=\frac{x}{75}$ (where x represents 6/4 of 75)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 75=4x$
2. Which gives: $450=4x$
3. Divide both sides by 4 to isolate x: $\frac{450}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{450}{4}=x$ (or $\frac{225}{2}=x$)

Thus, 6/4 of 75 is equal to 225/2 (or 112.5 in its decimal form).