Download MA 0090 Section 01 - Arithmetic Operations 01/23/2017 Objectives

MA 0090 Section 01 - Arithmetic Operations
01/23/2017
Objectives: Review symbols and words for addition, subtraction, multiplication, and division on integers.
Also negation and double negation.
Review of Basic Operations
We’ll be using the basic operations addition, subtraction, multiplication, and division extensively. Let’s look
at some of examples to get us started.
Addition. Addition is indicated with a +-sign.
(1)
2+5 =7
(2)
5+2 =7
(3)
7 + 10 = 17
We might say, “the sum of 2 and 5,” “2 plus 5,” or simply “2 + 5.” These all mean the same thing.
Subtraction. Subtraction is indicated with a −-sign.
(4)
5−2=3
(5)
2 − 5 = −3
(6)
10 − 4 = 6
We might say, “2 taken from 5,” “5 less 2,” “5 minus 2,” or “5 − 2.” These all mean the same thing.
Addition and subtraction. Addition and subtraction go together. In fact, it’s best to think of everything
in terms of addition. For example, when we have
(7)
5 − 2,
we can rewrite this as
(8)
5 + (−2) = 3.
Instead of actually rewriting this, you should just think to yourself that “5 minus 2“ is the same as “5 plus
a negative 2.”
Double negatives. A good way to think of negatives is as a number that you add to get zero. For example,
given the number 2, the number we would add to get zero is −2. It works the other way, too. Given −2, the
number we would add to get zero is 2. Therefore, the negative of −2 must be 2. In symbols,
(9)
−(−2) = 2.
You should read this last equation as “the negative of negative 2 is 2.” In an expression, we would have
things like
(10)
5 − (−2) = 5 + ( −(−2) ) = 5 + 2.
Subtraction is the same as adding the negative.
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MA 0090 Section 01 - Arithmetic Operations
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1. Quiz 01, Part I
Find the following. After you’re done with Part II, enter your answers into Desire2Learn (or on paper in
class).
1.
7+2=
2.
4+5=
3.
8−3=
4.
8 + (−3) =
5.
−2 + (−3) =
6.
5−9=
7.
−(−5) =
8.
8 − (−3) =
2. Multiplication
Multiplication is indicated with a ×-sign, a ·-sign, or by just writing two numbers next to each other.
(11)
2×3= 6
(12)
3 · 5 = 15
(13)
(4)(3) = 12.
Multiplying by negative numbers is kind of like taking a negative.
(14)
(−2)(4) = −8
(15)
(1)(−5) = −5
(16)
(−3)(−2) = 6.
We will say, “2 times 3,” “the product of 2 and 3,” or “(2)(3). These all mean the same thing.
3. Division
Division is indicated by a ÷-sign or a division bar.
(17)
12 ÷ 4 = 3
(18)
9/3 = 3
15
(19)
=5
3
Division is very much like multiplication, and dividing by negative numbers is just like multiplying by
negative numbers.
(20)
12 ÷ (−4) = −3
−20
(21)
= −5
4
2
(22)
= −2
−1
We will say, “the quotient of 12 by 3,” “12 divided by 3,” or “12 ÷ 3. These all mean the same thing.
MA 0090 Section 01 - Arithmetic Operations
4. Quiz 01, Part II
9.
5×4=
10.
2 · 12 =
11.
(7)(−2) =
12.
(−3)(−5) =
13.
(−7) · (4) =
14.
(−1)(−1) =
15.
(−10)(−4) =
16.
12 ÷ 2 =
17.
(−25) ÷ 5 =
18.
24
=
−8
19.
−2
=
−2
20.
−16
=
−4
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MA 0090 Section 01 - Arithmetic Operations
5. Homework 01
After you’re done, enter your answers into Desire2Learn.
1.
8+6=
2.
2+3=
3.
12 − 5 =
4.
7 + (−2) =
5.
−5 + (−6) =
6.
2−7=
7.
−(−11) =
8.
4 − (−7) =
9.
6×5=
10.
3 · 11 =
11.
(6)(−5) =
12.
(−2)(−7) =
13.
(−3) · (11) =
14.
(−2)(−1) =
15.
(−5)(−4) =
16.
16 ÷ 4 =
17.
(−27) ÷ 9 =
18.
12
=
−4
19.
−5
=
−1
20.
−14
=
−2
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