Basic Math 1 Section 1.2 United Arab Emirates University University General Requirement Unit.

Basic Math 1Section 1.2

United Arab Emirates University

University General Requirement Unit

is called the quotient of x and y , or x divided by y.

Operations and PropertiesBinary operation: The process of combining two elements of a set to produce a third element is called a Binary operation.

There are 4 operations:

1. Addition

2. Subtraction

3. Multiplication

4. Division

x+ y is called the sum of x and y , or x plus y.

x- y is called the difference of x and y , or x minus y.

xy(or x y ) is called the product of x and y , or x times y.

yxoryx

…Expression: an expression is a meaningful collection of numbers, variables, and operations.

Example 1 2x+3y is an expression that involves numbers, ( 2 and 3 ),

variables ( x and y ) and operations ( addition and multiplication )

Example 2 Write the following statements using symbols

Statement Symbol(s)The sum of 10 and x 10 + x

12 more than p

n increased by 1

The product of m and n

The quotient of b and 2

4 less than the product of r and s

12p

1n

nm

2b

4 sr

…

Statement Symbol(s)

7 times b

The sum of c and 4, divided by d

x square

4 less than the square of m

The square of the sum of x and y

s divided by 4

Class Exercise

b7

d

c 4

2x

42 m

2yx

4

s

Order Of OperationRules and Properties: Order of operations1. Simplify within innermost grouping symbol, and work outward until all grouping symbols are

removed.

2. Evaluate any expressions involving exponents.

3. Perform any multiplication and division, working from left to right.

4. Then do any addition and subtraction, again working from left to right.

Example 1 Evaluate each expression

342) a

3 8

11Multiply first

Then do the addition

342) b 72 14

Simplify within the grouping symbols

Then multiply

… 2342)c 272

492

98

Add inside parentheses

Evaluate the power

Multiply

32.53) 3d 3853

3403

343

40

Evaluate the power

Multiply

Add and then subtract from left to right

…Class Exercise Evaluate each expression

8650) a

20253) b

220253) c

33217) d

71)

75)

15)

2)

Answerd

Answerc

Answerb

Answera

Properties of Addition and Multiplication over Real numbers

RcandbaLet ,,

Inverse

Identity

Commutative

Associative

Closure

MultiplicationAdditionProperty

Rba Rba

cbacba cbacba

a b b a

abba

aaa 00 aaa 11

0 aa 0,11

aa

a

Example Property Example Property43 overClosure 43 overClosure

tionMultiplicaforandAdditionforuseusLet

432432 overeAssociativ

3443 overeCommutativ

61616 overIdentityis0

033 over Inverse

432432 overeAssociativ

3443 overeCommutativ

60606 overIdentityis1

over Inverse

13

13

Rules and Properties

Rules and Properties:Distributive Property

a ( b + c ) = ab + ac

Example 1 Use the distributive property to simplify each expression

545) aa 5545 a

2520 a

First Use Distributive property

Simplify

Class Exercise Use the distributive property to simplify each expression

xxb 524) 2 xxAnswer 208 2

…

4237) yxb 472737 yx

281421 yx

Class Exercise

cba 7346 cbaAnswer 421824

Combining Like Terms

Like Terms: If two or more terms have the same variable and same power( exponent), then, these terms are called like terms.

Example 1 3x and 8x are like terms

7y and –5y are like terms

3x2 and 5x2 are like terms

Unlike Terms: If two or more terms have different variable or different powers ( exponents ), then these terms are called unlike terms

Example 2 2x and 4y are unlike terms because they have different variables

…

4x and 2x2 are unlike terms because they have different powers

Class Exercise Check if these terms in the table below are like terms (Type Yes ) or unlike terms ( Type No ).

Terms Like Terms

2m and 15m

3n and 4y

2x and 3x and 4x2

6n and –3n

No

No

Yes

Yes

Adding Like Terms

To add ( or subtract ) two like terms, we add ( or subtract ) their coefficients.

Example 3 Add or subtract.

573) xxa 510 x

nnb 53) n2

yxc 26) same x and y are unlike terms

xxxd 572) xx 59 x4

Class Exercise Add or subtract.

bbbii

xxi

311)

326)

bii

xi

Answers

15)

29)

Home Work

Do the Home Work Exercises as written in the Syllabus