What is 10/4 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 10/4 of 75? We'll show you a straightforward method to achieve that.

How to calculate 10/4 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: 750/4 = 187.5
  3. Simplify by dividing both the numerator and denominator by their GCD (2):
    • 750/2 = 375
    • 4/2 = 2
  4. Which gives: 375/2

Since 375/2 is an improper fraction, the result could also be expressed as a mixed number: 187 1/2

How does it work?

The principle behind finding a fraction of a number, such as 10/4 of 75, is rooted in the method of cross-multiplication.

Consider the following proportion: 10 4 = x 75 (where x represents 10/4 of 75)

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

Thus, 10/4 of 75 is equal to 375/2 (or 187.5 in its decimal form).