What is 5/8 of 84?

How to calculate 5/8 of 84?

1. Multiply the whole number by the numerator of the fraction: 84 × 5 = 420
2. Divide this result by denominator of the fraction: 420/8 = 52.5
3. Simplify by dividing both the numerator and denominator by their GCD (4):
   • 420/4 = 105
   • 8/4 = 2
4. Which gives: 105/2

Since 105/2 is an improper fraction, the result could also be expressed as a mixed number: 52 1/2

How does it work?

The principle behind finding a fraction of a number, such as 5/8 of 84, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{8}=\frac{x}{84}$ (where x represents 5/8 of 84)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 84=8x$
2. Which gives: $420=8x$
3. Divide both sides by 8 to isolate x: $\frac{420}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{420}{8}=x$ (or $\frac{105}{2}=x$)

Thus, 5/8 of 84 is equal to 105/2 (or 52.5 in its decimal form).