What is 10/4 of 69?

How to calculate 10/4 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: 690/4 = 172.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 690/2 = 345
   • 4/2 = 2
4. Which gives: 345/2

Since 345/2 is an improper fraction, the result could also be expressed as a mixed number: 172 1/2

How does it work?

The principle behind finding a fraction of a number, such as 10/4 of 69, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{4}=\frac{x}{69}$ (where x represents 10/4 of 69)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 69=4x$
2. Which gives: $690=4x$
3. Divide both sides by 4 to isolate x: $\frac{690}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{690}{4}=x$ (or $\frac{345}{2}=x$)

Thus, 10/4 of 69 is equal to 345/2 (or 172.5 in its decimal form).