EVALUATING NUMERICAL EXPRESSIONS

About "Evaluating numerical expressions"

"Evaluating Numerical Expressions" is one of the important basic stuff of algebra. 

A numerical expression is an expression involving numbers and operations.You can use the order of operations to evaluate numerical expressions.

Order of operations can be done by using the following steps. 

1. Perform operations in parentheses.

2. Find the value of numbers with exponents.

3. Multiply or divide from left to right.

4. Add or subtract from left to right.

Evaluating numerical expressions - Examples

Example 1 :

Evaluate  5 + 18 ÷ 3²

Solution :

Here we don't have any number in parentheses. So first we have to find the value of exponent. 

  =  5 + 18 ÷ 9

Now we have two signs division and addition. According to the order of operation we have to do division first.By dividing 18 and 9, we get 2

  =  5 + 2

  =  7

Example 2 :

Evaluate  21 + 3² ÷ 3

Solution :

Here we don't have any number in parentheses. So, first we have to find the value of exponent. 

  =  21 + 9 ÷ 3

Now we have two signs division and addition. According to the order of operation we have to do division first.By dividing 9 and 3, we get 3

  =  21 + 3

  =  24

Example 3 :

Evaluate  6 x 2³ ÷ 3 + 1

Solution :

Here we don't have any number in parentheses. So, first we have to find the value of exponent. 

  =  6 x 8 ÷ 3 + 1

From left to right we have the symbols multiplication, division and addition. According to the order of operation we have to perform multiplication, division and addition respectively.

  =  48 ÷ 3 + 1

  =  16 + 1

  =  17

Let us see some more stuff about order of operation.

What is BODMAS rule ?

The rule or order that we use for evaluating numerical expressions in math is called "BODMAS" rule.

Very simply way to remember  BODMAS rule! 

B -----> Brackets first (Parentheses)

O -----> Of (orders :Powers and radicals) 

D -----> Division

M -----> Multiplication

A -----> Addition

S -----> Subtraction

Important notes :

1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.

2. Division does not always come before multiplication. We have to do one by one in the order from left to right. 

3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right.

Examples : 

12 ÷ 3 x 5  =  4 x 5  =  20

13 - 5 + 9   =  8 + 9  =  17 

In the above simplification, we have both division and multiplication. From left to right, we have division first and multiplication next. So we do division first and multiplication next.

Example 4 :

Evaluate the expression  5 + 2 - 3 

Solution :

In the above problem we have two signs addition and subtraction.

Step 1 :

First add the numbers which are in wither sides of positive sign. 

  =  5 + 2 - 3

Step 2 :

Now, we have to subtract 3 from 7.

  =  7 - 3

  =  4

Example 5 :

Evaluate the expression 6(6 ÷ 2) x 9

Solution :

According to the rule BODMAS, first we have to consider the numbers which are in bracket or parenthesis. 

  =  6(6 ÷ 2) x 9

  =  6 (3) x 9 

Now, we have three numbers which are multiplying. So multiply those numbers 

  =  18 x 9 ==> 162

Example 6 :

Evaluate 6(6) ÷ (2 x 9)

Solution :

According to the rule BODMAS, first we have to consider the numbers which are in bracket. 

  =  6(6)  ÷  18

  =  (6 x  6)/18

  =  2

Now, we have three numbers which are multiplying. So multiply those numbers 

  =  18 x 9 ==> 162

Example 7 :

Evaluate  100 ÷ (16 + 9) x 6

Solution :

According to the rule BODMAS, first we have to consider the numbers which are in bracket. 

  =  100 ÷ (16 + 9) x 6

  =  100 ÷ 25 x 6

=  4 x 6 ==> 24

Example 8 :

Evaluate the expression (2 x 11 + 1) - (3 x 6 + 5)

Solution :

According to the rule BODMAS, first we have to consider the numbers which are in bracket. 

  =  (2 x 11 + 1) - (3 x 6 + 5)

Inside the bracket, we have two signs multiplication and addition. First, we have to perform multiplication then we have to do addition.

  =  23 - 23 ==> 0

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