Question 1

Craig uses a ruler to determine the length of two pieces of metal. He records the length of each piece of metal as a rational number. Which statement BEST explains whether the sum of the two lengths Craig recorded must also be a rational number?

Accepted Answer

When adding two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, the sum is $\frac{ad+bc}{bd}$, and both the numerator and denominator are integers. Therefore, the sum must be a rational number.

Answer

When adding two rational numbers a $\frac{a}{b}$ and $\frac{c}{d}$, the common denominator $bd$ does not have to be an integer. Therefore, the sum does not have to be a rational number.

Answer

When adding two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, the sum is$ \frac{ac}{bd}$,  and both the numerator and denominator are integers. Therefore, the sum must be a rational number.

Answer

When adding two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, the numerators a and c do not have to be integers. Therefore, the sum does not have to be a rational number.

Question 2

Which number is irrational?

Accepted Answer

$9\sqrt3$

Answer

$9\sqrt4$

Answer

$4\sqrt9$

Answer

$3\sqrt9$

Question 3

Which statement describes values of $x$ and $y$ such that $\frac{x}{y}$could be an irrational number?

Accepted Answer

The value of $x$ is the square root of an integer, and the value of $y$ is an integer
greater than zero

Answer

The value of $x$ is zero, and the value of $y$ is an integer less than zero.

Answer

The value of $x$ is a square root that can be simplified to an integer, and the value of $y$ is an
integer less than zero.

Answer

The value of $x$ is an integer less than zero, and the value of $y$ is an integer greater than zero.

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