What is 10/8 of 82?
Often, in mathematics or everyday life, we need to find a fraction of a given number. For instance, how would you quickly calculate 10/8 of 82? We'll show you a straightforward method to achieve that.
How to calculate 10/8 of 82?
- Multiply the whole number by the numerator of the fraction: 82 × 10 = 820
- Divide this result by denominator of the fraction: 820/8 = 102.5
- Simplify by dividing both the numerator and denominator by their GCD (4):
- 820/4 = 205
- 8/4 = 2
- Which gives: 205/2
Since 205/2 is an improper fraction, the result could also be expressed as a mixed number: 102 1/2
How does it work?
The principle behind finding a fraction of a number, such as 10/8 of 82, is rooted in the method of cross-multiplication.
Consider the following proportion: (where x represents 10/8 of 82)
- Using the cross-multiplication method, multiply both numerators by their opposite denominators:
- Which gives:
- Divide both sides by 8 to isolate x:
- Which gives the result: (or )
Thus, 10/8 of 82 is equal to 205/2 (or 102.5 in its decimal form).