What is 3/8 of 84?

How to calculate 3/8 of 84?

1. Multiply the whole number by the numerator of the fraction: 84 × 3 = 252
2. Divide this result by denominator of the fraction: 252/8 = 31.5
3. Simplify by dividing both the numerator and denominator by their GCD (4):
   • 252/4 = 63
   • 8/4 = 2
4. Which gives: 63/2

Since 63/2 is an improper fraction, the result could also be expressed as a mixed number: 31 1/2

How does it work?

The principle behind finding a fraction of a number, such as 3/8 of 84, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{3}{8}=\frac{x}{84}$ (where x represents 3/8 of 84)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $3\times 84=8x$
2. Which gives: $252=8x$
3. Divide both sides by 8 to isolate x: $\frac{252}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{252}{8}=x$ (or $\frac{63}{2}=x$)

Thus, 3/8 of 84 is equal to 63/2 (or 31.5 in its decimal form).