What is 9/4 of 74?

How to calculate 9/4 of 74?

1. Multiply the whole number by the numerator of the fraction: 74 × 9 = 666
2. Divide this result by denominator of the fraction: 666/4 = 166.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 666/2 = 333
   • 4/2 = 2
4. Which gives: 333/2

Since 333/2 is an improper fraction, the result could also be expressed as a mixed number: 166 1/2

How does it work?

The principle behind finding a fraction of a number, such as 9/4 of 74, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{9}{4}=\frac{x}{74}$ (where x represents 9/4 of 74)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $9\times 74=4x$
2. Which gives: $666=4x$
3. Divide both sides by 4 to isolate x: $\frac{666}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{666}{4}=x$ (or $\frac{333}{2}=x$)

Thus, 9/4 of 74 is equal to 333/2 (or 166.5 in its decimal form).