CONFIDENTIAL 1
Good Afternoon!Today we will be learning about
Review of Expressions, Variables, equations &
FunctionsLet’s warm up :
1) Simplify: 4 x 5 + (18 ÷ 2)
2) Is (15 ÷ 5) + 9 equal to 6 + 14 - 3 ?
Evaluate the given expressions:
3) 5 + 2n when n = 3.
4) n + 7 = 16
5) Find the value of y = 7x + 3, when x = 4.
1) 29
2) <
3) 11
4) n = 9
5) 31
CONFIDENTIAL 2
Order of Operations
Evaluate 3 + 4 x 2
3 + 4 x 2 = 7 x 2 = 14
or
3 + 4 x 2 = 3 + 8 = 11
Two people may interpreted the problem differently this problem like
Here, the correct answer is 11.Let’s see how.
CONFIDENTIAL 3
ARITHMETIC EXPRESSION: It is an expression consisting of numbers, grouping symbols and arithmetic operation symbols.
To evaluate these expressions, a specific Order of Expressions is followed.
When a numerical expression involves two or more operations, there is a specific order in which these operations must be
performed.
4 – (3 + 2) is an arithmetic expression.
Parenthesis, Exponents, (Multiplication/Division) then (Add/Subtract)OR that is, PEMDAS for short .
Please Excuse (My Dear) (Aunt Sally).
This phrase will help you understand the order.
CONFIDENTIAL 4
To solve an expression you need to follow the rules for the Order of Operation.
Evaluate: 3 + (3 x 4) - 1
Rule 1:
First, do operations inside the parenthesis ( ).
3 + (3 x 4) - 1
Rule 2:
Then do multiplication and division in order from left to right.
3 + 12 - 1
Rule 3:
Finally, do addition and subtraction in order from left to right.
15 - 1
14
There is no more
multiplication or
division.
Evaluate: 2 x 8 - 3
13
CONFIDENTIAL 5
Is 8 x (3 + 6) equal to 7 x (17 - 6) ?
The value 8 x (3 + 6) = 72 is less than 7 x (17 - 6) = 77.
Hence, not equal.
First of all, we evaluate
8 x (3 + 6)
= 8 x 9
= 72
Then, we evaluate
7 x (17 - 6)
= 7 x 11
= 77
CONFIDENTIAL 6
We learnt about the following terms:
Variable: It is a letter that represents a number.
Since a variable represents a number, it is treated just like a number when doing various mathematical
operations .
x is a very common variable that is used in algebra, but you can use any letter (a, b, c, d, ....) to be a variable.
Algebraic expression: It is a mathematical statement which contains at least one number and at least one variable along with at least one
arithmetic operation.
The following are examples of expressions:
2 × y + 5
z + 3 × (8 - z)
Number stories & expressions
CONFIDENTIAL 7
Evaluating an Expression
You can evaluate an expression by replacing the variable with the given number and performing the indicated operation
Value of an Expression
When you are asked to find the value of an expression, that means you are looking for the result that you get when you evaluate the
expression.
Evaluate simply means that we want to find an answer.
CONFIDENTIAL 8
Evaluate the expression 12 – n for n = 4
Given the expression 12 – n.
Here we will replace the occurrence of n with the number 4
Hence, 12 – n becomes
= 12 – 4
= 8
nis
replaced by 4.
Evaluate the expression 3 x m for m = 5
15
CONFIDENTIAL 9
Evaluate the expression 3a for a = 4
STEP 1:Write the expression.
3a.
STEP 2:
Replace a with 4.3 x 4.
STEP 3:
Simplify the expression.
3 x 4.= 12.
So, the value of the expression is 12.
CONFIDENTIAL 10
Translating an English Phrase Into an Algebraic Expression
Sometimes, you will be having to write out your own algebraic expression based on the wording of a problem.
In that situation, you should:
read the problem carefully,
pick out key words and phrases and determine their equivalent mathematical meaning,
replace any unknowns with a variable, and
put it all together in an algebraic expression.
CONFIDENTIAL 11
When converting word problems to equations, certain "key" words tell you what kind of operations to use.
Word Operation
sum addition
difference subtraction
product multiplication
times multiplication
less than subtraction
total addition
more than addition
CONFIDENTIAL 12
Write an algebraic expression for the sum of n and 5.
The word sum means add.
So the algebraic expression would be ( n + 5 ).
This is an algebraic expression because it contains at least one number (5), at least one variable (n), and at
least one arithmetic operation (subtraction).
Write an algebraic expression for the difference of n and 3.
n -3
CONFIDENTIAL 13
We know that variable is a letter that represents a number.
Equation: It is a mathematical statement that has an expression on
the left side of the equals sign (=) with the same value as the
expression on the right side.
The examples of an equation is:
5 + x = 12
2t - 29 = 7
Variables & equations
CONFIDENTIAL 14
One of the terms in an equation may not be known and needs to be determined.
The unknown term may be represented by a letter such as “x”. (e.g. 2 + x = 4).
The equation is solved by finding the value of the unknown “x” that makes the two sides of the equation have the same value. Use the Inverse Operations to find the value of the variable in the addition equations.
Solution A value, such that, when you replace the variable with it, it makes
the equation true. (the left side comes out equal to the right side)
CONFIDENTIAL 15
The equality of two expressions gives an equation.
If two expressions are not equal, an inequality is created.
The inequality symbols used at this grade level are ≠ (is not equal to), > (is greater than), and < (is less
than).
It may also be stated that an equation is ‘two expressions set equal to each
other’.
Solution A value, such that, when you replace the variable with it, it makes
the equation true. (the left side comes out equal to the right side)
CONFIDENTIAL 16
Solve: n + 5 = 9
WAY 1:
WAY 2:
There are different ways of to solve a problem.
Use an addition fact.
n + 5 = 9
n = 4
n + 5 = 9
n + 5 -5 = 9 – 5
n = 4
Use the Inverse Operations.
Subtract 5 from each side.
Think:4 + 5 = 9
So ‘n’ must be
4.
Review
CONFIDENTIAL 17
We need to use the Inverse Operations to find the value of the variable in the equations.
If the problem has Addition, use Subtraction to solve.
a + 4 = 7a + 4 - 4 = 7 - 4
a = 3
If the problem has subtraction , use Addition to solve.
b - 4 = 5b - 4 + 4 = 5 + 4
b = 9
If the problem has Multiplication ,
use Division to solve.
5c = 155c ÷ 5 = 15 ÷ 5
c = 3
If the problem has Division , use Multiplication to solve.
d ÷ 4 = 4d ÷ 4 x 4 = 4 x4
d = 16
Remember to Use Inverse Operations
CONFIDENTIAL 18
The sum of twice a number and 13 is 75. Find the number.
STEP1: Let the number be denoted by “n”.
So, the equation will be as follows:
2n + 13 = 75
STEP2: Solve the equation.
2n + 13 = 75
2n + 13 - 13 = 75 -13
2n = 622 2
n = 31
Divide both sides
by 2.
Subtract 13 from
both sides.
Hence, the number is 31.
CONFIDENTIAL 19
BREAK
CONFIDENTIAL 20
GAME
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CONFIDENTIAL 21
FUNCTION : It is a relationship in which one quantity depends upon another quantity.
In other words, Functions are rules that describe the relationship between two variables.
For example, y = x + 4.
The two variables in a function have names that explain how they relate to one another.
One variable, usually x, is known as the input or independent variable. This is the variable upon which the operation or operations are performed.
The other variable, usually y, is called the output or dependent variable. The value of this variable is dependent upon the value of the independent variable.
Functions
CONFIDENTIAL 22
Functions are also displayed or described in the form of function tables or graphs.
A Function Table is a table of ordered pairs that follow the rule for that function.
Function tables can be made up of an infinite number of ordered pairs. A Function Table for the equation y = 2x + 6 is shown
below.
ORDERED PAIR : Two numbers that give the location of a point on a graph or map are called the Ordered Pair.
x 1 2 3 4
y 8 10 12 14
independent variable
dependent variable
Rule y = 2x + 6
CONFIDENTIAL 23
Solve the problem with the help of a function table. Then write the
equation.
One number is 2 more than 3 times another number.
You can write the equation with the help of the given statement.
We are given thatOne number is 2 more than 3 times another
number.
Let the smaller number be ‘x’ and, greater number be ‘y’.
Then the equation will be:y = 3x + 2
We will now solve the problem with the help of Function Table.
STEP1:
CONFIDENTIAL 24
STEP2:We find the values of ‘y’ by
putting the values of ‘x’ in the equation.
When x = 1, y = 3 x 1 + 2,
y = 3 + 2 = 5
When x = 2, y = 3 x 2 + 2, y = 6 + 2 = 8
When x = 3, y = 3 x 3 + 2,
y = 9 + 2 = 11
When x = 4, y = 3 x 4 + 2, y = 12 + 2 =
14
Input (x) 1 2 3 4
Output (Y)
5 8 11 14
Rule y = 3x + 2
STEP3:We now make the function table’ by putting the values of ‘x’ and
‘y’ .
CONFIDENTIAL 25
Assignments
Simplify:
1) (24 ÷ 6) + (2 x 3) - 8
2) 9 x 2 + 3 - 7
3) Is 2 x 7 -6 equal to 25 ÷ 5 + 3 ?
1) 2 2) 14
3) Yes
CONFIDENTIAL 26
4) 8a - 3 when a = 5.
5) 7 + 9b when b = 4.
Evaluate the given expressions:
6) c ÷ 5 + 7 when c = 35.
4) 37
5) 43
6) 14
CONFIDENTIAL 27
7) 8d = 48 8) 4e + 7 = 63
Evaluate the given equation:
7) 6 8) 14
CONFIDENTIAL 28
Question
number
Rule: y = x - 3
Input (x) Output (y)
9) 6
10) 2
11) 8
12) 4
Complete the function tables according to the given rules:
9) 3
10) 5
11) 5
12) 7
CONFIDENTIAL 29
13) The sum of thrice a number and 2 is 44. Find the number.
14) Sean has twice as many pencils than the number of pens. He has 7 pencils. He gave 3 pens to his friend.
Write the equation. How many pens does he have now?
13) 3n + 2 = 44
n = 14
14) y = 2x -311 pens
CONFIDENTIAL 30
You have done a nice job.See you in the next session.