What is 10/8 of 75?

How to calculate 10/8 of 75?

1. Multiply the whole number by the numerator of the fraction: 75 × 10 = 750
2. Divide this result by denominator of the fraction: 750/8 = 93.75
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 750/2 = 375
   • 8/2 = 4
4. Which gives: 375/4

Since 375/4 is an improper fraction, the result could also be expressed as a mixed number: 93 3/4

How does it work?

The principle behind finding a fraction of a number, such as 10/8 of 75, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{8}=\frac{x}{75}$ (where x represents 10/8 of 75)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 75=8x$
2. Which gives: $750=8x$
3. Divide both sides by 8 to isolate x: $\frac{750}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{750}{8}=x$ (or $\frac{375}{4}=x$)

Thus, 10/8 of 75 is equal to 375/4 (or 93.75 in its decimal form).