2023 CEMC Cayley Problems/Problem 1

Problem

What is the value of $\frac{1}{1} + \frac{2}{2} + \frac{3}{3}$ ?

$\text{ (A) }\ 1 \qquad\text{ (B) }\ 0 \qquad\text{ (C) }\ 3 \qquad\text{ (D) }\ 9 \qquad\text{ (E) }\ 10$

Using the greatest common denominator, we have:

$\frac{1 \times 6}{1 \times 6} + \frac{2 \times 3}{2 \times 3} + \frac{3 \times 2}{3 \times 2}$

$=\frac{6}{6} + \frac{6}{6} + \frac{6}{6} = \frac{18}{6} = 3$

~anabel.disher

If $x \neq 0$ , then $\frac{x}{x} = \frac{x \div x}{x \div x} = \frac{1}{1} = 1$ . Thus, we have:

$1 + 1 + 1 = 3$

~anabel.disher