Question

For $x = 7,$ which of the following is the smallest?

$\dfrac{6}{x}$

$\dfrac{6}{x+1}$

$\dfrac{6}{x-1}$

$\dfrac{x}{6}$

$\dfrac{x+1}{6}$

Answer: B

Concepts:substitution fraction

Difficulty rating: 450

Small Hint:

Substitute $x = 7$ first.

Big Hint:

With equal numerators, compare denominators.

Solution:

Substituting $x = 7$ gives the five values $\dfrac{6}{7},$ $\dfrac{6}{8},$ $1,$ $\dfrac{7}{6},$ and $\dfrac{4}{3}.$

The first two are the only values less than $1.$ Because they have the same numerator, the fraction with the larger denominator is smaller. Thus, the correct answer is B .

1998 AMC 8 Problem 1

Answer: B

Difficulty rating: 450

Small Hint:

Big Hint:

Solution:

Problem 1 in Other Years