What is 10/9 of 75?

How to calculate 10/9 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: 750/9 = 83.333333333333
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 750/3 = 250
   • 9/3 = 3
4. Which gives: 250/3

Since 250/3 is an improper fraction, the result could also be expressed as a mixed number: 83 1/3

How does it work?

The principle behind finding a fraction of a number, such as 10/9 of 75, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{9}=\frac{x}{75}$ (where x represents 10/9 of 75)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 75=9x$
2. Which gives: $750=9x$
3. Divide both sides by 9 to isolate x: $\frac{750}{9}=\frac{9x}{9}$
4. Which gives the result: $\frac{750}{9}=x$ (or $\frac{250}{3}=x$)

Thus, 10/9 of 75 is equal to 250/3 (or 83.333333333333 in its decimal form).