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# Write and Interpret Numerical Expressions

Sep 28, 2022

## 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.
1. Evaluate all powers.
1. Do all multiplications and/or divisions from left to right.
1. 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

1. 23 = (12-4) x6

### 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.

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