Don\’t Use Calculator 5×3-2+1×2

Step	Operation	Expression	Result
1	Multiplication (Left)	5 × 3	15
2	Multiplication (Right)	1 × 2	2
3	Subtraction	15 – 2	13
4	Addition	13 + 2	15

What is ‘don’t use calculator 5×3-2+1×2’?

The phrase “don’t use calculator 5×3-2+1×2” is a popular challenge meant to test and emphasize the importance of understanding the order of operations in mathematics. It’s not just about finding the answer, but about knowing *how* to find it correctly without blindly trusting a calculator. The correct way to solve this expression is by following a specific set of rules, often remembered by the acronyms PEMDAS or BODMAS. Many people get this wrong by simply calculating from left to right, which leads to an incorrect answer. The expression is a perfect example of why these rules are critical for accuracy in math. This concept is fundamental for students, programmers, and anyone who works with formulas.

The PEMDAS/BODMAS Formula and Explanation

To solve the expression 5×3-2+1×2, we use the PEMDAS/BODMAS rule. This rule dictates the sequence for solving operations to ensure everyone gets the same, correct answer.

P/B – Parentheses/Brackets: Solve everything inside parentheses first. (None in this expression).
E/O – Exponents/Orders: Next, solve any exponents or square roots. (None in this expression).
MD – Multiplication and Division: These have equal priority. Solve them from left to right as they appear.
AS – Addition and Subtraction: These also have equal priority. Solve them from left to right as they appear.

Applying this to 5 × 3 – 2 + 1 × 2:

Multiplication First: We have two multiplication operations. We solve them from left to right.
- 5 × 3 = 15
- 1 × 2 = 2
The expression becomes: 15 - 2 + 2
Addition/Subtraction Next: Now we only have addition and subtraction. We solve them from left to right.
- 15 - 2 = 13
The expression becomes: 13 + 2
Final Step:
- 13 + 2 = 15

The final answer is 15. The common mistake is to calculate 15 - 2 = 13, then 13 + 1 = 14, and finally 14 * 2 = 28, which is incorrect because it ignores the precedence of multiplication. For more details on the rules, our PEMDAS rule explained article is a great resource.

Variables Table

These variables are unitless numbers used in the expression.
Variable	Meaning	Unit	Typical Range
A, B, C, D, E	The numbers in the arithmetic expression	Unitless	Any real number

Practical Examples

Understanding the order of operations is key. Let’s see it in action with two more examples.

Example 1: 10 + 4 × 2 – 6 ÷ 3

Inputs: 10, 4, 2, 6, 3
Units: Unitless
Steps:
1. Multiplication: 4 × 2 = 8. Expression is now 10 + 8 - 6 ÷ 3.
2. Division: 6 ÷ 3 = 2. Expression is now 10 + 8 - 2.
3. Addition: 10 + 8 = 18. Expression is now 18 - 2.
4. Subtraction: 18 - 2 = 16.
Result: 16

Example 2: 7 × (3 + 2) – 5²

Inputs: 7, 3, 2, 5
Units: Unitless
Steps:
1. Parentheses: 3 + 2 = 5. Expression is now 7 × 5 - 5².
2. Exponents: 5² = 25. Expression is now 7 × 5 - 25.
3. Multiplication: 7 × 5 = 35. Expression is now 35 - 25.
4. Subtraction: 35 - 25 = 10.
Result: 10

For more practice, you can use a scientific calculator which correctly follows the order of operations.

How to Use This Order of Operations Calculator

Our interactive tool is designed to help you learn, not just to give an answer. Here’s how to use it effectively:

Enter Your Values: The calculator is pre-filled with the numbers from 5×3-2+1×2. You can change these numbers in the input fields (Value A through E) to see how the result changes.
Observe the Calculation: As you change the numbers, the “Calculation Steps” and the final “Primary Result” update in real-time, showing you exactly how the answer is derived.
Analyze the Chart: The bar chart provides a visual representation of the intermediate steps, helping you understand the magnitude of each part of the calculation.
Reset to Default: Click the “Reset” button at any time to return to the original problem.

By experimenting with different numbers, you can build a strong intuition for how the order of operations works. Understanding these common math mistakes is the first step to avoiding them.

Key Factors That Affect the Result

The final answer of an arithmetic expression is highly sensitive to several factors related to the order of operations.

Presence of Parentheses: Anything inside parentheses must be solved first, which can completely change the outcome.
Location of Multiplication/Division: Since these are solved left-to-right, their order matters. `8 / 4 * 2` is 4, but `8 / (4 * 2)` is 1.
Location of Addition/Subtraction: Similar to the above, these are also solved left-to-right. `10 – 5 + 2` is 7, not 3.
Exponents and Roots: These operations take high precedence and are performed before multiplication, division, addition, or subtraction.
Misinterpreting PEMDAS: A common error is thinking Multiplication *always* comes before Division, and Addition *always* before Subtraction. They actually have equal priority and should be evaluated from left to right.
Calculator Entry Method: Basic calculators solve as you type, ignoring the order of operations. A scientific calculator follows PEMDAS, which is why the same keystrokes can yield different answers.

Frequently Asked Questions (FAQ)

Why is the answer to 5×3-2+1×2 not 28?

The answer isn’t 28 because that result comes from solving the expression strictly from left to right, ignoring the order of operations. The rules of math (PEMDAS/BODMAS) state that multiplication must be done before addition and subtraction.

What does PEMDAS stand for?

PEMDAS is an acronym for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It’s a mnemonic used to remember the order of operations.

Is BODMAS different from PEMDAS?

No, they represent the same set of rules. BODMAS stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction. “Brackets” are the same as “Parentheses” and “Orders” are the same as “Exponents.” They are used interchangeably in different regions.

Do you always do multiplication before division?

No. Multiplication and division have equal priority. You should solve whichever one appears first when reading the expression from left to right.

What if I enter 5×3-2+1×2 into a basic calculator?

A simple, non-scientific calculator will likely give you an incorrect answer because it calculates each operation as it’s entered. It would calculate 5 * 3 = 15, then 15 – 2 = 13, then 13 + 1 = 14, and finally 14 * 2 = 28. A scientific calculator would give the correct answer of 15. A BODMAS calculator can help illustrate this.

Are there any units involved in this calculation?

No, the numbers in this specific expression are abstract and unitless. They are pure numbers used to demonstrate a mathematical principle.

Where can I learn more about basic math rules?

Our learning guides, such as our article on basic algebra, are a great place to start building a strong mathematical foundation.

Can I use this calculator for other expressions?

This specific tool is designed to demonstrate the expression `A * B – C + D * E`. While you can change the numbers, it does not parse arbitrary expressions. For that, you would need a more advanced math expression solver.

Related Tools and Internal Resources

If you found this tool helpful, you might be interested in our other calculators and guides:

Scientific Calculator: A full-featured calculator that respects the order of operations.
What is PEMDAS?: A detailed article explaining the rules of operator precedence.
Percentage Calculator: Useful for a wide range of percentage-based problems.
Common Math Mistakes: Learn about frequent errors in arithmetic and how to avoid them.
Fraction Calculator: A tool for performing arithmetic with fractions.
Basic Algebra Guide: A primer on the fundamental concepts of algebra.

Don\’t Use Calculator 5×3-2+1×2

Order of Operations Calculator

Interactive Expression Demonstrator

Calculation Steps (Intermediate Values)

Visualizing the Operations

Order of Operations Breakdown