What is 10/7 of 77?

How to calculate 10/7 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: 770/7 = 110
3. Simplify by dividing both the numerator and denominator by their GCD (7):
   • 770/7 = 110
   • 7/7 = 1
4. Which gives: 110/1

How does it work?

The principle behind finding a fraction of a number, such as 10/7 of 77, is rooted in the method of cross-multiplication.

Consider the following proportion: $\frac{10}{7}=\frac{x}{77}$ (where x represents 10/7 of 77)

1. Using the cross-multiplication method, multiply both numerators by their opposite denominators: $10\times 77=7x$
2. Which gives: $770=7x$
3. Divide both sides by 7 to isolate x: $\frac{770}{7}=\frac{7x}{7}$
4. Which gives the result: $\frac{770}{7}=x$ (or $\frac{110}{1}=x$)

Thus, 10/7 of 77 is equal to 110/1 (or 110 in its decimal form).