ALGEBRA
where alphabets or other symbols are used to represent a value in a equation. They are also called variables.
Why do we use variables?
It is a symbol that we use to represent a value that we don’t know yet.
Example of symbols : u, x, y, 𝛃, 𝛂
ALGEBRAIC EXPRESSIONS
Combining of numbers, variables and operators (+, -, ×, /) to form a representation.
In Algebra, multiplication of number and variables are represented without the x (multiply) sign.
(1) 5 x u = 5u
(2) y x 2 = 2y (number be 'in front' of the variable)
(3) 1 x z = z (does not need to write the 1)
Example
3 x U + 1 => 3U + 1
3U + 1
- When a number is with a variable, the number is called the coefficient
- A number by itself is called a constant
When do we use algebraic expression?
Example 1
What is the algebraic expression of three more than z
How do we form the expression?
Three more than z
Method
Step1: What is given and required? 3, more than, z
Three more than z => add 3 to z => + 3
z + 3 <Step 2: Forming the expression>
Example 2
Four less than z
Step1: What is given and required? z, 4, less than
Four less than z => minus 4 from z => - 4
z - 4 <Step 2 :Forming the expression>
Example 3
Five times of z
Step1: What is given and required? 5, x(times), z
5z <Step 2: Forming the expression>
Example 4
Sum of z and 8
Method
Step1: What is given and required? z, 8 + (sum)
z + 8 <Step 2 :Forming the expression>
Replacing variables with a value
If z = 5, what are the values in the examples:
Example 1 : z + 3
Step 1: 5 + 3 <Replace z with value given = 5>
Step 2 : 8 <Calculate>
Example 2 : z - 4
= 5 - 4 <Step 1: replace variable with value>
= 1 <Step 2 : calculate>
Example 3 : 5z
= 5 x 5 <Step 1: replace variable with value>
= 25 <Step 2 : calculate>
Example 4 : z + 8
= 5 + 8 <Step 1: replace variable with value>
= 13 <Step 2 : calculate>
Practice:
1. One-half of X
2. Product of S and 6
3. V divided by 5
SIMPLIFYING Algebraic Expression
Example
Simplify 4f + 3g -2f +4g
Method
Step1 CIRCLE
different alphabets/numbers with +/- on left with different shapes
Step2 GROUP
the different shapes together
Step3 SIMPLIFY expression
= 2f + 7g
Example
Simplify 4x + 9 – 3x -7
Step3: = x
- 2
Practices
Simplify:
1. 4t + 5 + t – 2
2. 5x – 2x + x
3. 3m + 6 – 2m
4. 3h + h
5. 8p – 2k – k + 7
WORD PROBLEMS: Writing Algebraic Expression
Example
Anna has 4u + 3 pens. She bought another 3u pens, and then gave 2u pens to Billy. How many pens does she have now?
Method:
Step1: Who and their numbers/variables? Underline/Circle and write
Anna 4u + 3
Step2: What is the story? link and write expression
Bought 3u pen => 4u + 5 + 3u
Gave away 2u + 1 => 4u + 5 + 3u – 2u
Step3: Solve
4u + 5 + 3u – 2u
= 4u + 3u – 2u + 3
= 5u + 3
Example
Jack has U number of apples. Mike has 2 apples more than Jack. How many apples does Mike have?
Method
Step 1: Who and their numbers/variables? Underline/Circle and write
W N
Jack U
Mike
Step 2: What is the story? link and write expression
W N
Jack U
Mike U +2
Step3: Solve: Form the expression
Mike has U+2 apples
Example
Danny
is U years old. His mother is 5 times as old as
Danny. His father is 6 years older than his
mother. Find his father’s age in terms of U.
Step1: Who and their numbers/variables? Underline/Circle and write
W N
Danny U
Mother
Father
Step2: What is the story? link and write expression
Step3:
His father is 5U + 6 years old.
Example
Harold
had W bottles. He gave 8 bottles to his brother. How many bottles had he left?
Method
Step1:
W N
Harold W
brother
Step2:
Step3:
Harold has W – 8 bottles left.
Example
Each
of a square is K cm. What is the perimeter of the square?
Method
Side of Square K
Perimeter
Step2:
W N
Side of Square K
Perimeter 4 x K
Step3:
Perimeter is 4K
Example
Mary
scored K marks for 5 subjects. What was her
average marks for each subject?
Method
Mary Avg
Mary 5 subj K
Mary Average = Total Value / Number of Data
Step3:
Mary Average mark is K/5
Example
Alex
sold (3k + 1) tickets on Saturday. He sold k more tickets on Sunday than on
Saturday. How many tickets did he sell altogether?
Method
Alex (Sun)
Step3: Alex sells 3K + 1 + 3K + 1 + K = 7K
+ 2 tickets
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Notes: Just in case...
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