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Rational or Irrational?
Objective: _________________________________________________________________________
Do Now: Sort the numbers into two categories: rational numbers and irrational numbers.
RATIONAL
IRRATIONAL
Lesson: Rational or Irrational?
Directions – Think about each of the following statements and determine whether each statement is 1)
always true, 2) sometimes true, or 3) never true. Provide examples and justify your reasoning.
A) The sum of two rational numbers is a rational number.
B) The product of two irrational numbers is an irrational number.
C) The sum of a rational number and an irrational number is a rational number.
D) The product of a non-zero rational number and an irrational number is an irrational number.
E) Challenge: Between two rational numbers there is an irrational number.
F) Challenge: The hypotenuse of a right triangle is an irrational number.
Name: ___________________________________________________ Date: __________________
Homework – Rational or Irrational?
a) Circle the rational numbers below.
13
3
3
49
26 
1
2
7 7
8
5
23
9
4 9
2
5  45
b) For the following statements, determine whether each statement is always true, sometimes true, or
never true. Provide at least two examples that back up your answer.
I) The product of two irrational numbers is an irrational number.
II) The sum of a rational number and an irrational number is an irrational number.
Name: ___________________________________________________ Date: __________________
Homework – Rational or Irrational?
a) Circle the rational numbers below.
13
3
3
49
26 
1
2
7 7
8
5
23
9
4 9
2
5  45
b) For the following statements, determine whether each statement is always true, sometimes true, or
never true. Provide at least two examples that back up your answer.
I) The product of two irrational numbers is an irrational number.
II) The sum of a rational number and an irrational number is an irrational number.
3.14
5

2
1
2
1 
0.1
0.1212
6
5 6
3 2
2.718...
4
7
1
10
3

3.14
5
7

2
1
2
1 
0.1
2 8
0.1212
6
5 6
3 2
2.718...
4
7
1
10
3
5 6
16
5 6
16

7
2 8
2
3 2
2
3 2