What is 10/4 of 77?

How to calculate 10/4 of 77?

1. Multiply the whole number by the numerator of the fraction: 77 × 10 = 770
2. Divide this result by denominator of the fraction: 770/4 = 192.5
3. Simplify by dividing both the numerator and denominator by their GCD (2):
   • 770/2 = 385
   • 4/2 = 2
4. Which gives: 385/2

Since 385/2 is an improper fraction, the result could also be expressed as a mixed number: 192 1/2

How does it work?

The principle behind finding a fraction of a number, such as 10/4 of 77, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{4}=\frac{x}{77}$ (where x represents 10/4 of 77)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 77=4x$
2. Which gives: $770=4x$
3. Divide both sides by 4 to isolate x: $\frac{770}{4}=\frac{4x}{4}$
4. Which gives the result: $\frac{770}{4}=x$ (or $\frac{385}{2}=x$)

Thus, 10/4 of 77 is equal to 385/2 (or 192.5 in its decimal form).