What is 10/4 of 85?

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 85? We'll show you a straightforward method to achieve that.

How to calculate 10/4 of 85?

  1. Multiply the whole number by the numerator of the fraction: 85 × 10 = 850
  2. Divide this result by denominator of the fraction: 850/4 = 212.5
  3. Simplify by dividing both the numerator and denominator by their GCD (2):
    • 850/2 = 425
    • 4/2 = 2
  4. Which gives: 425/2

Since 425/2 is an improper fraction, the result could also be expressed as a mixed number: 212 1/2

How does it work?

The principle behind finding a fraction of a number, such as 10/4 of 85, is rooted in the method of cross-multiplication.

Consider the following proportion: 10 4 = x 85 (where x represents 10/4 of 85)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 10 × 85 = 4 x
  2. Which gives: 850 = 4 x
  3. Divide both sides by 4 to isolate x: 850 4 = 4 x 4
  4. Which gives the result: 850 4 = x (or 425 2 = x )

Thus, 10/4 of 85 is equal to 425/2 (or 212.5 in its decimal form).