Using Order of Operations Calculator for Grade 3

Learn to use order of operations calculator: rules, step-by-step solutions, and detailed explanations.

Calculator Exercises: Exercises 1 to 3
1 Basic Addition and Subtraction
Exercise 1
Solve using calculator: 12 + 5 - 3 + 6
Definition:

Order of Operations: The sequence in which mathematical operations are performed

Addition/Subtraction Rule: When only addition and subtraction are present, perform operations from left to right

Using Calculator Method:
  1. Enter the first number (12)
  2. Press the addition key (+)
  3. Enter the next number (5)
  4. Press the subtraction key (-)
  5. Enter the next number (3)
  6. Press the addition key (+)
  7. Enter the last number (6)
  8. Press equals (=) to get the result
Calculator Input
12+5-3+6
Step 1
17-3+6
Step 2
14+6
Final Answer
20
Step 1: Enter the expression into calculator

Input: 12 + 5 - 3 + 6

Step 2: Calculator processes left to right

12 + 5 = 17

17 - 3 = 14

14 + 6 = 20

Step 3: Final result

The calculator shows: 20

12 + 5 - 3 + 6 = 20
Final answer:

The answer is 20

Applied rules:

• Left-to-Right Rule: Calculator processes addition and subtraction left to right

• Sequential Processing: Calculator updates after each operation

• Correct Entry: Enter expression exactly as written

2 Basic Multiplication and Division
Exercise 2
Solve using calculator: 20 ÷ 4 × 3 ÷ 5
Definition:

Multiplication/Division Rule: When only multiplication and division are present, perform operations from left to right

Higher Precedence: Multiplication and division have higher precedence than addition and subtraction

Calculator Input
20÷4×3÷5
Step 1
5×3÷5
Step 2
15÷5
Final Answer
3
Step 1: Enter the expression into calculator

Input: 20 ÷ 4 × 3 ÷ 5

Step 2: Calculator processes left to right

20 ÷ 4 = 5

5 × 3 = 15

15 ÷ 5 = 3

Step 3: Final result

The calculator shows: 3

Step 4: Verify the calculation

Work backwards: 3 × 5 = 15, 15 ÷ 3 = 5, 5 × 4 = 20 ✓

20 ÷ 4 × 3 ÷ 5 = 3
Final answer:

The answer is 3

Applied rules:

• Left-to-Right Rule: Calculator processes multiplication and division left to right

• Higher Precedence: Calculator handles multiplication/division before addition/subtraction

• Sequential Processing: Calculator updates after each operation

3 Mixed Operations with Multiplication First
Exercise 3
Solve using calculator: 8 + 4 × 3 - 6
Definition:

PEMDAS/BODMAS: Acronym for order of operations (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)

Multiplication Before Addition/Subtraction: Higher precedence operations are performed first

Calculator Input
8+4×3-6
Step 1
8+12-6
Step 2
20-6
Final Answer
14
Step 1: Enter the expression into calculator

Input: 8 + 4 × 3 - 6

Step 2: Calculator processes according to precedence

Calculator performs 4 × 3 = 12 first

Then processes: 8 + 12 - 6

Step 3: Calculator processes left to right

8 + 12 = 20

20 - 6 = 14

Step 4: Final result

The calculator shows: 14

8 + 4 × 3 - 6 = 14
Final answer:

The answer is 14

Applied rules:

• Precedence Order: Calculator automatically performs multiplication before addition/subtraction

• Left-to-Right Within Same Precedence: Calculator processes operations of equal precedence left to right

• Sequential Simplification: Calculator simplifies expression step by step

Calculator Rules and Methods
Calculator: PEMDAS → Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
Calculator Order of Operations
Multiplication/Division
Equal Precedence
Left to right
Addition/Subtraction
Equal Precedence
Left to right
Higher Precedence
Mult/Div vs Add/Sub
Mult/Div first
Key Definitions:

Calculator Order of Operations: The standardized sequence for calculator to perform mathematical operations

PEMDAS: Acronym for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Precedence: The priority level of operations (which to do first)

Left-to-Right Rule: When operations have equal precedence, work from left to right

Higher Precedence: Operations that must be done before others

Expression: A combination of numbers, variables, and operations

Using Calculator Methodology:
  1. Enter expression: Input the entire expression into the calculator
  2. Calculator processes: Calculator automatically applies order of operations
  3. Observe result: Check the calculator's output
  4. Verify manually: Confirm the calculator's result by manual calculation
Tip 1: Always enter the expression exactly as written.
Tip 2: Most calculators follow PEMDAS automatically.
Tip 3: Verify calculator results with manual calculations when learning.
Tip 4: Be careful with the equals (=) button - press it only once at the end.
Common Applications: Multi-step calculations, verifying manual work, complex expressions, scientific calculations.
Key Concepts: Precedence, equality, sequential processing, verification.
Essential Rules:

• Precedence Hierarchy: Calculator processes Multiplication/Division > Addition/Subtraction

• Equal Precedence: Operations of same precedence processed left to right

• Automatic Processing: Calculator applies order of operations automatically

• Verification: Always check calculator results with manual calculations

Calculator Exercises: Exercises 4 to 5
4 Complex Mixed Operations
Exercise 4
Solve using calculator: 15 - 2 × 4 + 10 ÷ 5 × 3
Definition:

Complex Expression: An expression containing multiple operations of different precedence levels

Sequential Processing: Performing operations in the correct order step by step

Calculator Input
15-2×4+10÷5×3
Step 1
15-8+2×3
Step 2
15-8+6
Final Answer
13
Step 1: Enter the expression into calculator

Input: 15 - 2 × 4 + 10 ÷ 5 × 3

Step 2: Calculator processes multiplication and division first

Calculator performs: 2 × 4 = 8

Calculator performs: 10 ÷ 5 = 2

Then: 2 × 3 = 6

Step 3: Calculator processes addition and subtraction

15 - 8 = 7

7 + 6 = 13

Step 4: Final result

The calculator shows: 13

15 - 2 × 4 + 10 ÷ 5 × 3 = 13
Final answer:

The answer is 13

Applied rules:

• Precedence Order: Calculator automatically performs multiplication/division before addition/subtraction

• Left-to-Right Within Same Precedence: Calculator processes operations of equal precedence left to right

• Sequential Simplification: Calculator simplifies expression step by step

5 Verification Challenge
Exercise 5
Solve using calculator: 24 ÷ 4 + 3 × 6 - 12 ÷ 3
Definition:

Verification: Checking that the calculator solution is correct by following the same order of operations

Multi-step Expression: An expression requiring multiple operations to solve

Calculator Input
24÷4+3×6-12÷3
Step 1
6+18-4
Step 2
24-4
Final Answer
20
Step 1: Enter the expression into calculator

Input: 24 ÷ 4 + 3 × 6 - 12 ÷ 3

Step 2: Calculator processes all multiplication and division first

24 ÷ 4 = 6

3 × 6 = 18

12 ÷ 3 = 4

Step 3: Calculator processes addition and subtraction

6 + 18 = 24

24 - 4 = 20

Step 4: Final result

The calculator shows: 20

24 ÷ 4 + 3 × 6 - 12 ÷ 3 = 20
Final answer:

The answer is 20

Applied rules:

• Precedence Order: Calculator automatically processes multiplication/division before addition/subtraction

• Left-to-Right Within Same Precedence: Calculator processes operations of equal precedence left to right

• Verification: Double-check calculator results with manual calculations

Complete Guide: Using Calculator for Order of Operations
Calculator: PEMDAS → P-E-MD-AS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)
Calculator Order of Operations Hierarchy
Key definitions:

Calculator Order of Operations: A standardized sequence for calculator evaluating mathematical expressions

PEMDAS: Acronym for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Precedence: The priority level determining which operations to perform first

Left-to-Right Rule: When operations have equal precedence, evaluate from left to right

Higher Precedence: Operations that must be completed before lower precedence operations

Expression: A mathematical phrase containing numbers, variables, and operators

Evaluation: Finding the value of an expression by performing operations

Complete methodology:
  1. Enter the expression: Input the entire expression into the calculator
  2. Calculator applies precedence: Calculator automatically performs operations in order of precedence
  3. Observe the result: Check the calculator's output
  4. Verify manually: Confirm the calculator's result with manual calculation
Tip 1: Always enter the expression exactly as written into the calculator.
Tip 2: Most calculators follow PEMDAS automatically.
Tip 3: Press the equals (=) button only once at the end of the expression.
Tip 4: Verify calculator results with manual calculations when learning.
Real-Life Applications: Calculating bills, following recipes, measuring materials, budgeting, time management.
Common Mistakes: Entering operations in the wrong order, pressing equals multiple times, forgetting calculator follows PEMDAS.
Essential formulas to remember:

• Calculator PEMDAS: Parentheses → Exponents → Multiplication/Division → Addition/Subtraction

• Multiplication and Division: Equal precedence, left to right

• Addition and Subtraction: Equal precedence, left to right

• Higher precedence operations performed first

• Verification: Check calculator results with manual calculations

Visualizing Calculator Operations
Exercise 6: Operation Precedence Levels
Visual representation of operation precedence:
• Highest: Parentheses and Exponents
• Medium: Multiplication and Division
• Lowest: Addition and Subtraction

Analysis: The chart shows the hierarchy of operations in mathematical expressions.

  • Operations with higher precedence are performed first
  • Operations with equal precedence are performed left to right
  • This ensures consistent evaluation of expressions

Questions & Answers

Question: Why do I need to learn order of operations if I have a calculator?

Answer: Great question! You still need to understand order of operations because:

• Calculators follow order of operations, so you need to know how to enter expressions correctly

• You need to verify calculator results to make sure they're correct

• Understanding the rules helps you solve problems without a calculator

• It builds your mathematical reasoning skills

Think of it like knowing how to drive a car - even if GPS helps navigate, you still need to understand traffic rules!

Question: Should I let my child use a calculator for order of operations?

Answer: Calculators can be helpful tools for learning order of operations:

• Use calculators to verify manual calculations

• Helps students see the importance of following the correct order

• Allows focus on understanding the concept rather than computation

• Provides immediate feedback

However, ensure children understand the manual process first before relying heavily on calculators.

Question: My calculator gave me a different answer than expected. What happened?

Answer: This usually happens because:

• You entered the expression incorrectly (wrong order)

• You pressed equals (=) at the wrong time

• The calculator followed order of operations correctly, but you expected a different result

Always double-check your entry and remember that calculators follow PEMDAS automatically. If you're not sure, try solving manually first to verify.