What is 4/9 of 84?

How to calculate 4/9 of 84?

1. Multiply the whole number by the numerator of the fraction: 84 × 4 = 336
2. Divide this result by denominator of the fraction: 336/9 = 37.333333333333
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 336/3 = 112
   • 9/3 = 3
4. Which gives: 112/3

Since 112/3 is an improper fraction, the result could also be expressed as a mixed number: 37 1/3

How does it work?

The principle behind finding a fraction of a number, such as 4/9 of 84, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{4}{9}=\frac{x}{84}$ (where x represents 4/9 of 84)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $4\times 84=9x$
2. Which gives: $336=9x$
3. Divide both sides by 9 to isolate x: $\frac{336}{9}=\frac{9x}{9}$
4. Which gives the result: $\frac{336}{9}=x$ (or $\frac{112}{3}=x$)

Thus, 4/9 of 84 is equal to 112/3 (or 37.333333333333 in its decimal form).