What is 9/4 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 9/4 of 46? We'll show you a straightforward method to achieve that.

How to calculate 9/4 of 46?

  1. Multiply the whole number by the numerator of the fraction: 46 × 9 = 414
  2. Divide this result by denominator of the fraction: 414/4 = 103.5
  3. Simplify by dividing both the numerator and denominator by their GCD (2):
    • 414/2 = 207
    • 4/2 = 2
  4. Which gives: 207/2

Since 207/2 is an improper fraction, the result could also be expressed as a mixed number: 103 1/2

How does it work?

The principle behind finding a fraction of a number, such as 9/4 of 46, is rooted in the method of cross-multiplication.

Consider the following proportion: 9 4 = x 46 (where x represents 9/4 of 46)

  1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: 9 × 46 = 4 x
  2. Which gives: 414 = 4 x
  3. Divide both sides by 4 to isolate x: 414 4 = 4 x 4
  4. Which gives the result: 414 4 = x (or 207 2 = x )

Thus, 9/4 of 46 is equal to 207/2 (or 103.5 in its decimal form).