What is 10/4 of 45?

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

How to calculate 10/4 of 45?

  1. Multiply the whole number by the numerator of the fraction: 45 × 10 = 450
  2. Divide this result by denominator of the fraction: 450/4 = 112.5
  3. Simplify by dividing both the numerator and denominator by their GCD (2):
    • 450/2 = 225
    • 4/2 = 2
  4. Which gives: 225/2

Since 225/2 is an improper fraction, the result could also be expressed as a mixed number: 112 1/2

How does it work?

The principle behind finding a fraction of a number, such as 10/4 of 45, is rooted in the method of cross-multiplication.

Consider the following proportion: 10 4 = x 45 (where x represents 10/4 of 45)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 10 × 45 = 4 x
  2. Which gives: 450 = 4 x
  3. Divide both sides by 4 to isolate x: 450 4 = 4 x 4
  4. Which gives the result: 450 4 = x (or 225 2 = x )

Thus, 10/4 of 45 is equal to 225/2 (or 112.5 in its decimal form).