What is 10/6 of 46?

How to calculate 10/6 of 46?

1. Multiply the whole number by the numerator of the fraction: 46 × 10 = 460
2. Divide this result by denominator of the fraction: 460/6 = 76.666666666667
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 460/2 = 230
   • 6/2 = 3
4. Which gives: 230/3

Since 230/3 is an improper fraction, the result could also be expressed as a mixed number: 76 2/3

How does it work?

The principle behind finding a fraction of a number, such as 10/6 of 46, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{6}=\frac{x}{46}$ (where x represents 10/6 of 46)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 46=6x$
2. Which gives: $460=6x$
3. Divide both sides by 6 to isolate x: $\frac{460}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{460}{6}=x$ (or $\frac{230}{3}=x$)

Thus, 10/6 of 46 is equal to 230/3 (or 76.666666666667 in its decimal form).