What is 9/4 of 82?

How to calculate 9/4 of 82?

1. Multiply the whole number by the numerator of the fraction: 82 × 9 = 738
2. Divide this result by denominator of the fraction: 738/4 = 184.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 738/2 = 369
   • 4/2 = 2
4. Which gives: 369/2

Since 369/2 is an improper fraction, the result could also be expressed as a mixed number: 184 1/2

How does it work?

The principle behind finding a fraction of a number, such as 9/4 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{9}{4}=\frac{x}{82}$ (where x represents 9/4 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $9\times 82=4x$
2. Which gives: $738=4x$
3. Divide both sides by 4 to isolate x: $\frac{738}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{738}{4}=x$ (or $\frac{369}{2}=x$)

Thus, 9/4 of 82 is equal to 369/2 (or 184.5 in its decimal form).