What is 6/8 of 83?

How to calculate 6/8 of 83?

1. Multiply the whole number by the numerator of the fraction: 83 × 6 = 498
2. Divide this result by denominator of the fraction: 498/8 = 62.25
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 498/2 = 249
   • 8/2 = 4
4. Which gives: 249/4

Since 249/4 is an improper fraction, the result could also be expressed as a mixed number: 62 1/4

How does it work?

The principle behind finding a fraction of a number, such as 6/8 of 83, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{8}=\frac{x}{83}$ (where x represents 6/8 of 83)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 83=8x$
2. Which gives: $498=8x$
3. Divide both sides by 8 to isolate x: $\frac{498}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{498}{8}=x$ (or $\frac{249}{4}=x$)

Thus, 6/8 of 83 is equal to 249/4 (or 62.25 in its decimal form).