What is 6/9 of 76?

How to calculate 6/9 of 76?

1. Multiply the whole number by the numerator of the fraction: 76 × 6 = 456
2. Divide this result by denominator of the fraction: 456/9 = 50.666666666667
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 456/3 = 152
   • 9/3 = 3
4. Which gives: 152/3

Since 152/3 is an improper fraction, the result could also be expressed as a mixed number: 50 2/3

How does it work?

The principle behind finding a fraction of a number, such as 6/9 of 76, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{6}{9}=\frac{x}{76}$ (where x represents 6/9 of 76)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $6\times 76=9x$
2. Which gives: $456=9x$
3. Divide both sides by 9 to isolate x: $\frac{456}{9}=\frac{9x}{9}$
4. Which gives the result: $\frac{456}{9}=x$ (or $\frac{152}{3}=x$)

Thus, 6/9 of 76 is equal to 152/3 (or 50.666666666667 in its decimal form).