Chapter 1 - Introduction - What is an algebraic expression?

1.1a - The following are simple algebraic expressions:

A variable is any letter that represents an unknown number. In the following examples, x is the variable.

Operation Expression Reading
Addition x + 5 x plus 5
sum of x and 5
5 added to x
5 more than
x
x increased by 5
Subtraction x - 5 x minus 5
5 subtracted from x
5 less than x
x
decreased by 5
Multiplication 5x 5 times x
product of 5 and x
x
multiplied by 5
Division x divided by 5
one-fifth of x

1.1b - Evaluating an expression means to find the number it represents.

Ex 1.1a Evaluate x + y + 5 when x = 1 and y = 2

x + y + 5
1 + 2 + 5
    = 8

  Ex 1.1b Evaluate 5xy when
x = 2 and y = 3

5xy
5(2)(3)
    = 30


Chapter 1 - Introduction - Orders of Operation

1.2a - Rules To Follow

            - To evaluate an expression, use the standard order of operations.
            - You can use the word PEMDAS to help you remember.
                        P - parentheses
                        E - exponents
                        M - multiplication
                        D - division
                        A - addition
                        S - subtraction
                - 1) Always go from left to right.
                - 2) When doing M and D, do them at the same time going from left to right.
                - 3) When doing A and S, do them at the same time going from left to right.

Ex 1.2a Evaluate 18 + 2 6 + - 3 7
The answer you should have gotten is 12.

Here are the detailed steps:

 

Ex 1.2b

Chapter 1 - Introduction - Expressions with parentheses and divisions

1.3 - Grouping symbols like parentheses or divisions are used in expressions to indicate that certain operations are to be done first.

Notes:
- Do operations inside parentheses and above/below division bars.
- Then do the rest using the PEMDAS rule.

Ex 1.3a 2 3 + 1      1. Multiply.
   6 + 1        2. Add.
      7
  Ex 1.3b 2(3 + 1)         1. Add inside parentheses.
  2 4             2. Multiply.
     8
 
Ex 1.3c   1. Add on top.


  2. Divide.
  Ex 1.3d 1. Divide the fraction.

2. Add.
 
Ex 1.3e

Chapter 1 - Introduction - Solving Algebraic Equations

1.4 - Here is are examples of how to solve algebraic equations.

Ex 1.4a 1. Subtract 18 on both sides.

2. Divide both sides by 2.
     
Ex 1.4b 1. Subtract 100 and add 6d to both sides.

2. Switch around, and divide by 6.

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