Download Module 4 - PDF Format - Portage la Prairie School Division

Self-Directed Course: Transitional Math
Pre-Algebra
Lesson #1: Review of Integers and BEDMAS
Before we move into Algebra, we need to review several important terms.
1) Integers: any number that is not a fraction
2) BEDMAS: an acronym that will help remind you that order of operation
Brackets, Exponents, Divide or Multiply (whichever comes first), Add or Subtract (whichever
comes first)
The following exercises that we will work on do not have letters attached to them. To get comfortable
working with the concept of BEDMAS, we will just use integers with no variables. Let’s look at following
examples.
Adding with Positive Integers
14 + 8 = 22
3 + 11 = 14
5 + 7 = 12
–8 + 5 =
(–24) + (–12) =
Adding with Negative Integers
12 + (–4) =
Before we can answer these questions, we have to understand how they work. We have two different
types of numbers. One is positive and the other is a negative number. The easiest way to remember if
your answer is going to be a positive or negative, is to see which has more charges.
Opposite charge will cancel each other out. For example: –4 + 7
In this example, we have 4 negative charges and 7 positive charges.
– – – – and + + + + + + +
One negative charge will cancel a positive charge, leaving you with 3 positive charges
– – – – and + + + + + + + = 3 or +3 (they mean the same thing)
12 + (–4) =
There are 12 positive charges and 4 negative charges. Cancel them out, and you will get your answer.
12 + (–4) = 8
–8 + 5 =
There are 8 negative charges and 5 positive charges. Cancel them out, and you will get your answer.
–8 + 5 = –3
Property of: Portage la Prairie School Division
Self-Directed Course: Transitional Math
Pre-Algebra
(–24) + (–12) =
There are 24 negative charges and 12 negative charges. When they are both negative, you add them
together and keep the negative sign.
(–24) + (–12) = –36
Subtracting with Positive Integers
21 – 4 = 17
8 – 12 = –4
10 – 17 = –7
Notice that with the last two examples we get negative numbers.
10 – 17 =
If we break the 17 into 10 and 7 and rewrite the question, we will see:
10 – 10 – 7 =
10 – 10 = 0
0 – 7 = –7
Subtracting with Negative Integers
21 – (–4) =
8 – (–14) =
8 – 17 =
The brackets are just used to separate the negative signs.
Many students get confused when subtracting negative integers because they are not as comfortable
when subtracting and find it easier to add integers. So to make it easier for yourself, rewrite the
question so you are adding instead of subtracting. In order to do this, you have to change the last two
signs to its opposite. In the end, you will be adding the opposite and get the same answer.
21 – (–4) =
21 + 4 = 25
8 – (–14) =
8 + 14 = 22
Property of: Portage la Prairie School Division
8 – 17 =
8 + (–17) = –9
Self-Directed Course: Transitional Math
Pre-Algebra
Multiplying Integers
When multiplying integers, remember the following chart:
+
+
–
–
x
x
x
x
+
–
+
–
=
=
=
=
+
–
–
+
2x4=8
8 x (–2) = –16
(–5) x 4 = –20
(–6) x (–3) = 18
Dividing Integers
When dividing integers, remember the following chart:
+
+
–
–
÷
÷
÷
÷
+
–
+
–
12 ÷ 4 = 3
=
=
=
=
+
–
–
+
15 ÷ (–3) = –5
Property of: Portage la Prairie School Division
(–6) ÷ 2 = –3
(–28) ÷ (–7) = 4
Self-Directed Course: Transitional Math
Pre-Algebra
Order of Operation
The last part that we will look at is order of Operation. Here we will apply the rule of BEDMAS:
Brackets, Exponents, Divide or Multiply (whichever comes first), Add or Subtract (whichever comes first).
Always remember to read the question from left to right.
Brackets: divide before add
Finish brackets
Divide
(5 + 14 ÷ 2) ÷ 2
(5 + 7) ÷ 2
12 ÷ 2
6
Multiply first
Divide
(7 x 6 ÷ 2)
42 ÷ 2
21
Brackets: multiply before add
Finish brackets
Divide
(8 x 5 + 8) ÷ 2
(40 + 8) ÷ 2
48 ÷ 2
24
Brackets: multiply before subtract
Finish brackets
Multiply before adding together
Add
(24 – 8 x 2) + 8 x 6
(24 – 16) + 8 x 6
8 + 42
50
Property of: Portage la Prairie School Division
Self-Directed Course: Transitional Math
Pre-Algebra
Assignment #1: Review of Integers and BEDMASS
Solve the following.
1) 20 – (–7)
__________
18) 17 – 11
__________
2) 5 + 12
__________
19) 28 – 6
__________
3) –8 + (–3)
__________
20) 35 – (–7)
__________
4) 9 + 14
__________
21) 4 – 20
__________
5) –7 + (–6)
__________
22) 6 x 11
__________
6) 3 + 20
__________
23) 3 x 10
__________
7) 17 – 6
__________
24) 7 – (–9)
__________
8) 14 x 15
__________
25) –6 x (–4)
__________
9) 7 x 17
__________
26) 5 – 16
__________
10) 7 x 20
__________
27) 21 x 4
__________
11) –8 – 10
__________
28) –4 + 11
__________
12) 14 + 14
__________
29) 17 – 3
__________
13) –4 – (–5)
__________
30) 8 x (–8)
__________
14) –8 + 13
__________
31) –3 + (–12)
__________
15) 9 ÷ (–3)
__________
32) 11 – 6
__________
16) 8 – 10
__________
33) 3 + (–5)
__________
17) 11 + 6
__________
34) 5 x 11
__________
Property of: Portage la Prairie School Division
Self-Directed Course: Transitional Math
Pre-Algebra
1) (9 – 1 + 5)
__________
19) (12 + 5) – 2
__________
2) (7 + 8 ÷ 8) ÷ 4
__________
20) (5 ÷ 25) + 7
__________
3) (6 x 4 ÷ 2)
__________
21) 4 x (2 x 23) ÷ 4
__________
4) (4 x 4) ÷ 2
__________
22) (43 + 5 – 2)
__________
5) (24 ÷ 3 ÷ 2) + 9 x 6
__________
23) (6 x 3) x 2 + 9
__________
6) 8 – (11 – 2) + 5 x 6
__________
24) (42 – 23 – 4)
__________
7) (4 x 5) x 6
__________
25) (53 + 6) x 2
__________
8) (7 + 8 – 3)
__________
26) 14 – (8 + 22 ÷ 2)
__________
9) (9 x 3 ÷ 3) + 9 + 9
__________
27) 16 – (3 + 82 x 13) + 6
__________
10) (6 + 7 – 4)
__________
28) (2 ÷ 6 x 5)
__________
11) (15 – 18) + 9
__________
29) 18 – (4 + 43) x 6
__________
12) (13 + 11) x 2
__________
30) 3 x (23 – 6) x 7
__________
13) (22 – 3) – 7
__________
31) (8 x 9 + 6)
__________
14) (6 + 5) x 6
__________
32) (11 + 14 – 5)
__________
15) (21 x 2 – 7 x 3)
__________
33) 6 x (4 ÷ 12 + 7)
__________
16) (9 + 7 – 5)
__________
34) (4 – 72 + 6 – 3)
__________
17) 12 + (18 – 4 – 7)
__________
35) 22 ÷ (6 ÷ 12) – 5
__________
18) (6 + 12 x 3)
__________
36) (5 + 12 + 6)
__________
Property of: Portage la Prairie School Division