What is 10/9 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 10/9 of 78? We'll show you a straightforward method to achieve that.

How to calculate 10/9 of 78?

  1. Multiply the whole number by the numerator of the fraction: 78 × 10 = 780
  2. Divide this result by denominator of the fraction: 780/9 = 86.666666666667
  3. Simplify by dividing both the numerator and denominator by their GCD (3):
    • 780/3 = 260
    • 9/3 = 3
  4. Which gives: 260/3

Since 260/3 is an improper fraction, the result could also be expressed as a mixed number: 86 2/3

How does it work?

The principle behind finding a fraction of a number, such as 10/9 of 78, is rooted in the method of cross-multiplication.

Consider the following proportion: 10 9 = x 78 (where x represents 10/9 of 78)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 10 × 78 = 9 x
  2. Which gives: 780 = 9 x
  3. Divide both sides by 9 to isolate x: 780 9 = 9 x 9
  4. Which gives the result: 780 9 = x (or 260 3 = x )

Thus, 10/9 of 78 is equal to 260/3 (or 86.666666666667 in its decimal form).