What is 6/7 of 46?

How to calculate 6/7 of 46?

1. Multiply the whole number by the numerator of the fraction: 46 × 6 = 276
2. Divide this result by denominator of the fraction: 276/7 = 39.428571428571

Since 276/7 is an improper fraction, the result could also be expressed as a mixed number: 39 3/7

How does it work?

The principle behind finding a fraction of a number, such as 6/7 of 46, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{7}=\frac{x}{46}$ (where x represents 6/7 of 46)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 46=7x$
2. Which gives: $276=7x$
3. Divide both sides by 7 to isolate x: $\frac{276}{7}=\frac{7x}{7}$
4. Which gives the result: $\frac{276}{7}=x$

Thus, 6/7 of 46 is equal to 276/7 (or 39.428571428571 in its decimal form).