What is 10/6 of 46?

Often, in mathematics or everyday life, we need to find a fraction of a given number. For instance, how would you quickly calculate 10/6 of 46? We'll show you a straightforward method to achieve that.

How to calculate 10/6 of 46?

  1. Multiply the whole number by the numerator of the fraction: 46 × 10 = 460
  2. Divide this result by denominator of the fraction: 460/6 = 76.666666666667
  3. Simplify by dividing both the numerator and denominator by their GCD (2):
    • 460/2 = 230
    • 6/2 = 3
  4. Which gives: 230/3

Since 230/3 is an improper fraction, the result could also be expressed as a mixed number: 76 2/3

How does it work?

The principle behind finding a fraction of a number, such as 10/6 of 46, is rooted in the method of cross-multiplication.

Consider the following proportion: 10 6 = x 46 (where x represents 10/6 of 46)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 10 × 46 = 6 x
  2. Which gives: 460 = 6 x
  3. Divide both sides by 6 to isolate x: 460 6 = 6 x 6
  4. Which gives the result: 460 6 = x (or 230 3 = x )

Thus, 10/6 of 46 is equal to 230/3 (or 76.666666666667 in its decimal form).