Write and Interpret Numerical Expressions

Key Concepts

• Evaluate expressions

Evaluate expressions 

How can we evaluate the expression? 

To avoid getting more than one answer, we use the order of operations given below. 

Braces{ }: Symbols that are used to group certain parts of a mathematical expression. 

Brackets [ ]: Symbols that are used to group certain parts of a mathematical expression. 

Numerical Expressions: A numerical expression is mathematical combination of numbers, operations, and grouping symbols. 

Order of Operations: It shows the steps used to evaluate a numerical expression:  

1. Simplify the expressions inside grouping symbols.  

2. Evaluate all powers. 

3. Do all multiplications and/or divisions from left to right.  

4. Do all additions and/or subtractions from left to right. 

Parentheses( ): Symbols that are used to group certain parts of a mathematical expression. 

Example 1: 

Explain the steps involved in evaluating the expression 

 [(6 x 2) – 2] + 6 ÷ 2 x 4. 

Solution: 

Step1: First do the operations inside the parentheses. 

             [(6 x 2) – 2] + 6 ÷ 2 x 4 

                 [12 – 2] + 6 ÷ 2 x 4  

            Then evaluate the terms inside the brackets. 

             [12 – 2] + 6 ÷ 2 x 4 

                                10 + 6 ÷ 2 x 4 

 Step2: Next multiply and divide in order from left to right. 

10 + 6 ÷ 2 x 4 

  10 + 3 x 4 

       10 + 12 

Step3: Finally, add in order from left to right. 

10 + 12 =22 

So, the value of the expression is 22.[Text Wrapping Break]Example2: 

Find the value of 15 + 20−8+(6÷2). 

Solution: 

Step 1: First do the operations inside the parentheses. 

15 + 20−8+(6÷2) 

    15 + 20−8+3 

           15 + 20−11 

Step 2: Subtract from left to right. 

   15 + 20−11 

  15 + 9 

Step 3: Finally, add in order from left to right. 

         15 + 9 = 24 

So the value of the expression is 24. 

Example 3:  

Jordan is working on the expression 25 – [4 + {26 – (28 – 8}]. What is the value of Jordan’s expression? 

Solution: 

Step 1: Subtract 8 from 28 and remove the parenthesis. 

   = 25 – [4 + {26 – (28 – 8}]       

          = 25 – [4 + {26 – 20}]                    

Step 2:   Subtract 20 from 26 and remove the curly brackets. 

   = 25 – [4 + {26 – 20}]                    

          = 25 – [4 + 6]                          

Step 3: Add 4 and 6 and remove the brackets. 

         = 25 – [4 + 6]        

                = 25 – 10                                       

Step 4: Subtract 10 from 25. 

= 25 – 10                                       

= 15 

So, the value of expression is 15. 

Example 4: 

Find the value of [12 + {7 – (8 ÷ 2)}] × 3 

Step1: First do the operations inside the parentheses. 

[12 + {7 – (8 ÷ 2)}] × 3 

= [12 + {7 – 4}] × 3  

    = [12 + 3] × 3  

Step 2: Add 12 and 3 and remove the brackets. 

    = [12 + 3] × 3  

     = 15 × 3  

Step3:  Next, multiply and order from left to right. 

= 15 × 3  

    = 45 

So, the value of expression is 45.

Exercise

Use the order of operations to evaluate the following expressions:

1. [(5×2)-2]+4 = 2 x 5
2. [(6×3)-6]+5 = 5 x 3
3. 8x (20+5)
4. 3+ (4×12)
5. [4x(S-1)] +50
6. 4x (26+7)
7. (8 + 9) x (11×10)
8. 150-30 + 2 x 4
9. 14 x (12+2) = 5

14 x ______ ÷ 5

10. 23 = (12-4) x6

Concept map

What have we learned

• Understanding the numerical expressions.
• Understanding braces, brackets, parentheses to evaluate expressions.
• Understanding how to use order of operations.
• How to evaluate the expressions.