What is 10/9 of 69?

How to calculate 10/9 of 69?

1. Multiply the whole number by the numerator of the fraction: 69 × 10 = 690
2. Divide this result by denominator of the fraction: 690/9 = 76.666666666667
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 690/3 = 230
   • 9/3 = 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 10/9 of 69, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{9}=\frac{x}{69}$ (where x represents 10/9 of 69)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 69=9x$
2. Which gives: $690=9x$
3. Divide both sides by 9 to isolate x: $\frac{690}{9}=\frac{9x}{9}$
4. Which gives the result: $\frac{690}{9}=x$ (or $\frac{230}{3}=x$)

Thus, 10/9 of 69 is equal to 230/3 (or 76.666666666667 in its decimal form).