What is 10/9 of 30?

How to calculate 10/9 of 30?

1. Multiply the whole number by the numerator of the fraction: 30 × 10 = 300
2. Divide this result by denominator of the fraction: 300/9 = 33.333333333333
3. Simplify by dividing both the numerator and denominator by their GCD (3):
   • 300/3 = 100
   • 9/3 = 3
4. Which gives: 100/3

Since 100/3 is an improper fraction, the result could also be expressed as a mixed number: 33 1/3

How does it work?

The principle behind finding a fraction of a number, such as 10/9 of 30, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{9}=\frac{x}{30}$ (where x represents 10/9 of 30)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 30=9x$
2. Which gives: $300=9x$
3. Divide both sides by 9 to isolate x: $\frac{300}{9}=\frac{9x}{9}$
4. Which gives the result: $\frac{300}{9}=x$ (or $\frac{100}{3}=x$)

Thus, 10/9 of 30 is equal to 100/3 (or 33.333333333333 in its decimal form).