Evaluate numerical expressions involving integers

key notes:

1. 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.
2. 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

1. Step 1: Parentheses
   • Solve expressions inside parentheses first.
   • Example: (3+4)×2
2. Step 2: Multiplication and Division
   • Perform all multiplication and division from left to right.
   • Example: 3+4×2
3. Step 3: Addition and Subtraction
   • Perform all addition and subtraction from left to right.
   • Example: 3+(4×2)

Example Problems

1. Simple Example:
   • 5+3×2
     • First, multiply: 3×2=6
     • Then, add: 5+6=11
2. With Parentheses:
   • (2+3)×4
     • First, solve inside parentheses: 2+3=5
     • Then, multiply: 5×4=20
3. 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!