Evaluate numerical expressions involving integers

key notes :

Definition:

• A numerical expression is a mathematical phrase that includes numbers and operations (such as addition, subtraction, multiplication, and division) but does not include an equals sign.

Order of Operations:

To correctly evaluate numerical expressions, follow the order of operations, often remembered by the acronym PEMDAS:

• Parentheses
• Exponents (not typically covered in 6th grade, but it’s good to be aware)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Steps to Evaluate Numerical Expressions

Step 1: Parentheses

• Solve expressions inside parentheses first.
• Example: (3+4)×2

Step 2: Multiplication and Division

• Perform all multiplication and division from left to right.
• Example: 3+4×2

Step 3: Addition and Subtraction

• Perform all addition and subtraction from left to right.
• Example: 3+(4×2)

Example Problems

Simple Example:

• 5+3×2
• First, multiply: 3×2=6
• Then, add: 5+6=11

With Parentheses:

• (2+3)×4
• First, solve inside parentheses: 2+3=5
• Then, multiply: 5×4=20

Multiple Operations:

• 6−2×3+4÷2
• First, multiply and divide from left to right:
• 2×3=6
• 4÷2=2
• Then, add and subtract from left to right:
• 6−6+2=0+2=2

Tips for Students

Write Clearly:

• Write each step of your work to avoid mistakes.

Double-Check:

• Always double-check each operation to ensure accuracy.

Use Parentheses:

• When in doubt, use parentheses to clarify the order of operations.

Practice:

• Regular practice with different types of problems helps reinforce the rules.

Learn with an example

Let’s Practice!