Final answer:
The correct equation that represents 'The quotient of 13 and a number is 1/3' is 13/x = 1/3, where x is the unknown number.
Step-by-step explanation:
The equation that represents the statement 'The quotient of 13 and a number is 1/3' is option A, which is 13/x = 1/3. To understand why, consider that a quotient is the result of division. The phrase 'quotient of 13 and a number' means you are dividing 13 by some number (let's call it x). The statement completes by stating that this quotient equals 1/3.
In algebra, to maintain an equality, you can perform the same operation on both sides of the equation. For instance, if you have the fraction 100 cm/1 m, and you divide both the numerator and the denominator by 1 m, you get that the fraction equals 1, because the numerator and denominator are the same. Applying this principle, let's verify that the right equation is chosen. If you multiply both sides of equation A by x, you get 13 = x/3. Then, if you multiply both sides by 3, you will find the number x that when divided into 13 yields a quotient of 1/3.