What is 5/6 of 69?

How to calculate 5/6 of 69?

1. Multiply the whole number by the numerator of the fraction: 69 × 5 = 345
2. Divide this result by denominator of the fraction: 345/6 = 57.5
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 345/3 = 115
   • 6/3 = 2
4. Which gives: 115/2

Since 115/2 is an improper fraction, the result could also be expressed as a mixed number: 57 1/2

How does it work?

The principle behind finding a fraction of a number, such as 5/6 of 69, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{5}{6}=\frac{x}{69}$ (where x represents 5/6 of 69)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $5\times 69=6x$
2. Which gives: $345=6x$
3. Divide both sides by 6 to isolate x: $\frac{345}{6}=\frac{6x}{6}$
4. Which gives the result: $\frac{345}{6}=x$ (or $\frac{115}{2}=x$)

Thus, 5/6 of 69 is equal to 115/2 (or 57.5 in its decimal form).