What is 1/4 of 82?

How to calculate 1/4 of 82?

1. Multiply the whole number by the numerator of the fraction: 82 × 1 = 82
2. Divide this result by denominator of the fraction: 82/4 = 20.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 82/2 = 41
   • 4/2 = 2
4. Which gives: 41/2

Since 41/2 is an improper fraction, the result could also be expressed as a mixed number: 20 1/2

How does it work?

The principle behind finding a fraction of a number, such as 1/4 of 82, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{1}{4}=\frac{x}{82}$ (where x represents 1/4 of 82)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $1\times 82=4x$
2. Which gives: $82=4x$
3. Divide both sides by 4 to isolate x: $\frac{82}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{82}{4}=x$ (or $\frac{41}{2}=x$)

Thus, 1/4 of 82 is equal to 41/2 (or 20.5 in its decimal form).