What is 10/4 of 31?

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

How to calculate 10/4 of 31?

  1. Multiply the whole number by the numerator of the fraction: 31 × 10 = 310
  2. Divide this result by denominator of the fraction: 310/4 = 77.5
  3. Simplify by dividing both the numerator and denominator by their GCD (2):
    • 310/2 = 155
    • 4/2 = 2
  4. Which gives: 155/2

Since 155/2 is an improper fraction, the result could also be expressed as a mixed number: 77 1/2

How does it work?

The principle behind finding a fraction of a number, such as 10/4 of 31, is rooted in the method of cross-multiplication.

Consider the following proportion: 10 4 = x 31 (where x represents 10/4 of 31)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 10 × 31 = 4 x
  2. Which gives: 310 = 4 x
  3. Divide both sides by 4 to isolate x: 310 4 = 4 x 4
  4. Which gives the result: 310 4 = x (or 155 2 = x )

Thus, 10/4 of 31 is equal to 155/2 (or 77.5 in its decimal form).