Download Unit 2: Rational Numbers Study Guide – Answer Key

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Unit 2: Rational Numbers
Study Guide
Topic 1: Classifying Numbers:
1. Classify each number below. Use a  to indicate that a number belongs in a given category. Leave a
space blank if it does not belong to the category.
Natural
Number
Whole
Number
Rational
Number
Integer
Irrational
Number
Real
Number
-22
7
2.̅
√
2. Determine whether each statement below is true or false. If the statement is false, provide a
counterexample.
a.
b.
c.
d.
e.
___________ If a number is an integer, it cannot be a whole number.
___________ All rational numbers are real numbers.
___________ All irrational numbers are real numbers.
___________ All whole numbers are natural numbers.
___________ All rational numbers are integers.
Topics 2 and 3: Adding and Subtracting Rational Numbers
3.
19.4 – 23.1
5. -4.87 – (-2.5)
4. -31.488 + (-19.96)
6.
2.995 - 7
7.
+
9.
8.
10.
Topics 4 and 5: Multiplying and Dividing Rational Numbers
11.
9.5  0.25
12. 5.82(-3.5)
13. 363(-16.5)
15.

17.
(
)
14.
58.275  ( 6.3)
16.
(
18.
(
)
)
Topic 6: The Distributive Property
Use the distributive property to simplify each expression. Then, if possible, combine like terms.
19.
(12x + 8)
20.
(10 – 15a)
21.
(6 + 3x) – 8
22.
2 + (9x – 15)
23.
2 – 6 ( – x) + 6
24.
5 – (2x + 3)
Unit 2: Rational Numbers
Study Guide – Answer Key
1.
Natural
Number
-22
7
2.̅
Whole
Number


Integer
Rational
Number


Irrational
Number









√
2.
a.
b.
c.
d.
e.
False: 2 is an integer and a whole number
True
True
False: 0 is a whole number that is not a natural number
False: -2.5 is a rational number but not an integer.
Topics 2 and 3: Adding and Subtracting
Rational Numbers
15.
16.
3.
-3.7
4.
-51.448
5.
-2.37
6.
-4.005
17.
18.
Topic 6: Distributive Property
7.
8.
9.
10.
Topics 4 and 5: Multiplying and Dividing
Rational Numbers
11.
12.
20.37
13.
22
14.
25
Real
Number
19.
9x + 6
20.
9a – 6
21.
2x – 4
22.
3x – 3
23.
6x + 5
24.
-2x + 2