What is 9/4 of 78?

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

How to calculate 9/4 of 78?

  1. Multiply the whole number by the numerator of the fraction: 78 × 9 = 702
  2. Divide this result by denominator of the fraction: 702/4 = 175.5
  3. Simplify by dividing both the numerator and denominator by their GCD (2):
    • 702/2 = 351
    • 4/2 = 2
  4. Which gives: 351/2

Since 351/2 is an improper fraction, the result could also be expressed as a mixed number: 175 1/2

How does it work?

The principle behind finding a fraction of a number, such as 9/4 of 78, is rooted in the method of cross-multiplication.

Consider the following proportion: 9 4 = x 78 (where x represents 9/4 of 78)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 9 × 78 = 4 x
  2. Which gives: 702 = 4 x
  3. Divide both sides by 4 to isolate x: 702 4 = 4 x 4
  4. Which gives the result: 702 4 = x (or 351 2 = x )

Thus, 9/4 of 78 is equal to 351/2 (or 175.5 in its decimal form).