What is 9/4 of 75?

Often, in mathematics or everyday life, we need to find a fraction of a given number. For instance, how would you quickly calculate 9/4 of 75? We'll show you a straightforward method to achieve that.

How to calculate 9/4 of 75?

  1. Multiply the whole number by the numerator of the fraction: 75 × 9 = 675
  2. Divide this result by denominator of the fraction: 675/4 = 168.75

Since 675/4 is an improper fraction, the result could also be expressed as a mixed number: 168 3/4

How does it work?

The principle behind finding a fraction of a number, such as 9/4 of 75, is rooted in the method of cross-multiplication.

Consider the following proportion: 9 4 = x 75 (where x represents 9/4 of 75)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 9 × 75 = 4 x
  2. Which gives: 675 = 4 x
  3. Divide both sides by 4 to isolate x: 675 4 = 4 x 4
  4. Which gives the result: 675 4 = x

Thus, 9/4 of 75 is equal to 675/4 (or 168.75 in its decimal form).