ALGEBRA
where letters (example: X, V or U) and other general symbols are used to represent numbers and quantities in equations. The letters are also called variables.
Why do we use variables?
It is a symbol that we use to represent a number that we don’t know yet.
Usually, u, x or y is being used.
ALGEBRAIC EXPRESSIONS
Combining of numbers, symbols/alphabets (variables) and operators (+, -, ×, ¸) to give a certain representation.
Example
3U + 1
When do we use algebraic expression?
Situations:
Example 1
Three more than a number X
How do we form the expression?
Three more than a number X
Method
Step1: X is the number that we do not know
Step2: What is the situation?
Three more than number X => add 3 to the number X => + 3
Step3: Forming the expression
X + 3
Example 2
Four less than a number
Method
Step1: Let’s use U to represent the number that we do not know.
Step2: What is the situation?
Four less than a number U => minus 4 from the number U => - 4
Step3: Forming the expression
U - 4
Example 3
Five times a number Y
Method
Step1: Y is the variable.
Step2: What is the situation?
Five times a number Y => multiply Y by 5 => 5Y
Step3: Forming the expression
5Y
Example 4
Sum of a number Z and 8
Method
Step1: Z is the variable.
Step2: What is the situation?
Sum of a number Z and 8 => Sum is Add (+) => Add Z and 8
Step3: Forming the expression
Z + 8
Practice:
1. One-half of X
2. Product of S and 6
3. A number 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:
W N
Danny U
Mother
Father
Step2:
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.
Harold has W – 8 bottles left.
Example
Each
of a square is K cm. What is the perimeter of the square?
Method
Step1:
W N
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
Step1:
W N
Mary Avg
Step2:
W N
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
Step1:
W N
Alex (Sun)
Step2:
W N
Step3: Alex sells 3K + 1 + 3K + 1 + K = 7K
+ 2 tickets
=========================================================
Notes: Just in case...
~~~~ End ~~~~ :)
