standard_description: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
problem_activity: Problem 1
Consider the set of numbers
$$6$$
,
$${4 \frac{1}{2}}$$
,
$$2$$
, and
$$5$$
, and answer the questions that follow.
a.   Graph the numbers on the number line and list the numbers in order from least to greatest.
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b.   Write the opposites of each number and graph them on the number line.
c.   Order the opposites from least to greatest.
d.   Is −5 greater than −2? Explain using your number line.
Problem 2
Order the rational numbers below from least to greatest.
$${5, -4, -\frac{1}{3}, \frac{10}{3}, 3, 0, -4\frac{1}{4}, -4\frac{3}{4}}$$
What strategies did you use to determine the correct order?
Problem 3
A student orders three rational numbers from least to greatest as:
$${{{{{{{{{-5}}}}}}}}}$$
,
$${{{{{{{{{-5}}}}}}}}} \frac {1}{3}$$
,
$$6$$
Are the numbers ordered correctly? Choose the best statement below.


aligns: no