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.