What is 7/3 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 7/3 of 78? We'll show you a straightforward method to achieve that.

How to calculate 7/3 of 78?

  1. Multiply the whole number by the numerator of the fraction: 78 × 7 = 546
  2. Divide this result by denominator of the fraction: 546/3 = 182
  3. Simplify by dividing both the numerator and denominator by their GCD (3):
    • 546/3 = 182
    • 3/3 = 1
  4. Which gives: 182/1

How does it work?

The principle behind finding a fraction of a number, such as 7/3 of 78, is rooted in the method of cross-multiplication.

Consider the following proportion: 7 3 = x 78 (where x represents 7/3 of 78)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 7 × 78 = 3 x
  2. Which gives: 546 = 3 x
  3. Divide both sides by 3 to isolate x: 546 3 = 3 x 3
  4. Which gives the result: 546 3 = x (or 182 1 = x )

Thus, 7/3 of 78 is equal to 182/1 (or 182 in its decimal form).