What is 10/8 of 30?

How to calculate 10/8 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: 300/8 = 37.5
3. Simplify by dividing both the numerator and denominator by their GCD (4):
   • 300/4 = 75
   • 8/4 = 2
4. Which gives: 75/2

Since 75/2 is an improper fraction, the result could also be expressed as a mixed number: 37 1/2

How does it work?

The principle behind finding a fraction of a number, such as 10/8 of 30, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{8}=\frac{x}{30}$ (where x represents 10/8 of 30)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 30=8x$
2. Which gives: $300=8x$
3. Divide both sides by 8 to isolate x: $\frac{300}{8}=\frac{8x}{8}$
4. Which gives the result: $\frac{300}{8}=x$ (or $\frac{75}{2}=x$)

Thus, 10/8 of 30 is equal to 75/2 (or 37.5 in its decimal form).