What is 6/8 of 46?

How to calculate 6/8 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: 276/8 = 34.5
3. Simplify by dividing both the numerator and denominator by their GCD (4):
   • 276/4 = 69
   • 8/4 = 2
4. Which gives: 69/2

Since 69/2 is an improper fraction, the result could also be expressed as a mixed number: 34 1/2

How does it work?

The principle behind finding a fraction of a number, such as 6/8 of 46, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{8}=\frac{x}{46}$ (where x represents 6/8 of 46)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 46=8x$
2. Which gives: $276=8x$
3. Divide both sides by 8 to isolate x: $\frac{276}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{276}{8}=x$ (or $\frac{69}{2}=x$)

Thus, 6/8 of 46 is equal to 69/2 (or 34.5 in its decimal form).