What is 7/8 of 82?

How to calculate 7/8 of 82?

1. Multiply the whole number by the numerator of the fraction: 82 × 7 = 574
2. Divide this result by denominator of the fraction: 574/8 = 71.75
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 574/2 = 287
   • 8/2 = 4
4. Which gives: 287/4

Since 287/4 is an improper fraction, the result could also be expressed as a mixed number: 71 3/4

How does it work?

The principle behind finding a fraction of a number, such as 7/8 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{7}{8}=\frac{x}{82}$ (where x represents 7/8 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $7\times 82=8x$
2. Which gives: $574=8x$
3. Divide both sides by 8 to isolate x: $\frac{574}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{574}{8}=x$ (or $\frac{287}{4}=x$)

Thus, 7/8 of 82 is equal to 287/4 (or 71.75 in its decimal form).