What is 10/8 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 10/8 of 46? We'll show you a straightforward method to achieve that.

How to calculate 10/8 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: 460/8 = 57.5
  3. Simplify by dividing both the numerator and denominator by their GCD (4):
    • 460/4 = 115
    • 8/4 = 2
  4. Which gives: 115/2

Since 115/2 is an improper fraction, the result could also be expressed as a mixed number: 57 1/2

How does it work?

The principle behind finding a fraction of a number, such as 10/8 of 46, is rooted in the method of cross-multiplication.

Consider the following proportion: 10 8 = x 46 (where x represents 10/8 of 46)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 10 × 46 = 8 x
  2. Which gives: 460 = 8 x
  3. Divide both sides by 8 to isolate x: 460 8 = 8 x 8
  4. Which gives the result: 460 8 = x (or 115 2 = x )

Thus, 10/8 of 46 is equal to 115/2 (or 57.5 in its decimal form).