What is 7/4 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 7/4 of 82? We'll show you a straightforward method to achieve that.
How to calculate 7/4 of 82?
- Multiply the whole number by the numerator of the fraction: 82 × 7 = 574
- Divide this result by denominator of the fraction: 574/4 = 143.5
- Simplify by dividing both the numerator and denominator by their GCD (2):
- 574/2 = 287
- 4/2 = 2
- Which gives: 287/2
Since 287/2 is an improper fraction, the result could also be expressed as a mixed number: 143 1/2
How does it work?
The principle behind finding a fraction of a number, such as 7/4 of 82, is rooted in the method of cross-multiplication.
Consider the following proportion: (where x represents 7/4 of 82)
- Using the cross-multiplication method, multiply both numerators by their opposite denominators:
- Which gives:
- Divide both sides by 4 to isolate x:
- Which gives the result: (or )
Thus, 7/4 of 82 is equal to 287/2 (or 143.5 in its decimal form).