What is 10/6 of 65?

How to calculate 10/6 of 65?

1. Multiply the whole number by the numerator of the fraction: 65 × 10 = 650
2. Divide this result by denominator of the fraction: 650/6 = 108.33333333333
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 650/2 = 325
   • 6/2 = 3
4. Which gives: 325/3

Since 325/3 is an improper fraction, the result could also be expressed as a mixed number: 108 1/3

How does it work?

The principle behind finding a fraction of a number, such as 10/6 of 65, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{6}=\frac{x}{65}$ (where x represents 10/6 of 65)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 65=6x$
2. Which gives: $650=6x$
3. Divide both sides by 6 to isolate x: $\frac{650}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{650}{6}=x$ (or $\frac{325}{3}=x$)

Thus, 10/6 of 65 is equal to 325/3 (or 108.33333333333 in its decimal form).