Name: _________________________________
Study Guide
Unit 1: Adding & Subtracting Rational Numbers
Opposites
1) The opposite of −4
4) The opposite of 289
Absolute Value
1) |−4|
1
4) |1 2|
2) The opposite of − 3
3) The opposite of 3.45
4) What is another word for
opposite?
5) What happens when you add
a pair of opposites together?
2) |19|
3) |−5.7|
5) |9 − 4|
6) |−4 + 1|
2
7) Define absolute value:
Changing fractions to decimals
7
1) 10
1
4) 5 100
2
1
2) 5
3) − 7
13
5) −2 25
Changing decimals to fractions (Remember to simplify)
1) 0.65
2) 0.6
4) 4.11
5) -2.8
2
6) 16 9
3) -0.250
6) 14.64
Adding Rational Numbers
1) −5.6 + (−9.72)
3) 18 + (−22.45)
3
4
2) −7.79 + 9.55
2
1
4) − 3 + 8
1
5
5) −2 4 + (−1 5)
6) 3 3 + (− 6)
7) −209 + 987
8) −566 + (−455)
3
9) 5.6 + (−2 5)
3
10) −0.5 + (−8 4)
Subtracting Rational Numbers
1) 19 − 34
2) −99 − (−36)
3) −107 − 107
4) 90.55 − 100.54
5) 8.11 − (−93.4)
6) −65.23 − (−13.576)
7) 0.45 − 4
8) 4 3 − 2 7
7
4
9) 8 − 3 5
1
5
1
1
10) − 4 − (− 6)
Graphing Equations
1) Graph the following equation on the number line below and solve: −5 + (−2)
2) Graph the following equation on the number line below and solve: 7 + (−11)
3) Graph the following equation on the number line below and solve: −2 − 4
4) Determine what equation best represents the graph below:
5) Determine what equation best represents the graph below:
6) Determine what equation best represents the graph below:
Problem Solving
1) Describe the difference between whole numbers and positive integers
2) For a negative number, x, is the absolute value of x a positive number or a negative number? Explain.
3) Identify whether each statement below is true or false:
 If a number is a positive integer, then the number is a whole number. _______
 If a number is negative, then its absolute value is negative. ____________
 If a number is positive, then its opposite is positive. ____________
4) Without actually adding, how can you tell if the sum of two numbers will be zero? Give an example.
5) In four plays a football team gains 3 yards, loses 7 yards, loses 2 yards, and gains 15 yards. How
many yards did the team gain after four plays?
Properties
Write an equivalent expression to the equations below and list which property allows you to do this.
1) (−4) + (−5) =
2) (54 + 62) + 28 =
3) 1 + 4 + 5 + 9 + 6 =
4) (−2) + 5 + (−4) + 5 =
5) 9 + (−6 + 4) + 5 =
6) 15 + 15 + 43 + 15 =
7) 10 + (25 + 94)
8) 1 4 + (1 4 + 8) =
1
1
3