What is 2/3 of 84?

How to calculate 2/3 of 84?

1. Multiply the whole number by the numerator of the fraction: 84 × 2 = 168
2. Divide this result by denominator of the fraction: 168/3 = 56
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 168/3 = 56
   • 3/3 = 1
4. Which gives: 56/1

How does it work?

The principle behind finding a fraction of a number, such as 2/3 of 84, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{2}{3}=\frac{x}{84}$ (where x represents 2/3 of 84)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $2\times 84=3x$
2. Which gives: $168=3x$
3. Divide both sides by 3 to isolate x: $\frac{168}{3}=\frac{3x}{3}$
4. Which gives the result: $\frac{168}{3}=x$ (or $\frac{56}{1}=x$)

Thus, 2/3 of 84 is equal to 56/1 (or 56 in its decimal form).