Mathematics Education

Is BODMAS or PEMDAS correct?

By Dogi 4 min read
In this article13 sections
    Quick answer

    Both BODMAS and PEMDAS are correct acronyms used to remember the order of operations in mathematics. They serve the same purpose: to ensure everyone solves mathematical expressions consistently and arrives at the same answer. The difference lies only in the specific words used in the acronyms, reflecting slight variations in regional terminology.

    BODMAS vs. PEMDAS: Understanding the Order of Operations

    When tackling mathematical problems, especially those involving multiple operations like addition, subtraction, multiplication, and division, a standardized order is crucial. This is where acronyms like BODMAS and PEMDAS come into play. They are not competing systems but rather different mnemonic devices for the same fundamental mathematical rule.

    What Does BODMAS Stand For?

    BODMAS is commonly used in the UK and some other Commonwealth countries. It stands for:

    • Brackets (Parentheses)
    • Orders (Powers and Square Roots)
    • Division
    • Multiplication
    • Addition
    • Subtraction

    This means you first solve anything inside brackets. Then, you deal with any orders (like exponents or roots). After that, you perform division and multiplication, working from left to right. Finally, you handle addition and subtraction, also from left to right.

    What Does PEMDAS Stand For?

    PEMDAS, also known as the Parentheses, Exponents, Multiplication, Division, Addition, Subtraction order, is widely taught in the United States and Canada.

    • Parentheses (Brackets)
    • Exponents (Orders/Powers)
    • Multiplication
    • Division
    • Addition
    • Subtraction

    As you can see, the order is identical to BODMAS. The terms "Parentheses" and "Exponents" are simply different words for "Brackets" and "Orders," respectively. The critical aspect is that division and multiplication have equal priority and are performed from left to right, as are addition and subtraction.

    Why is the Order of Operations Important?

    Imagine solving the expression 2 + 3 * 4. If you perform addition first, you get 5 * 4 = 20. However, if you follow the order of operations (multiplication before addition), you calculate 3 * 4 = 12, and then 2 + 12 = 14. The order of operations ensures a consistent and unambiguous result. Without it, mathematical communication would be chaotic.

    Key Similarities and Differences

    The primary "difference" between BODMAS and PEMDAS is purely linguistic. Both acronyms represent the same hierarchy of mathematical operations.

    Operation BODMAS Term PEMDAS Term Priority Level
    Grouping Brackets Parentheses 1st
    Powers Orders Exponents 2nd
    Multiplication Multiplication Multiplication 3rd (Left-to-Right)
    Division Division Division 3rd (Left-to-Right)
    Addition Addition Addition 4th (Left-to-Right)
    Subtraction Subtraction Subtraction 4th (Left-to-Right)

    The most common point of confusion arises with multiplication and division, and addition and subtraction. These pairs are performed in the order they appear from left to right, not strictly in the order listed in the acronym. For example, in 10 / 2 * 5, you divide first (10 / 2 = 5), then multiply (5 * 5 = 25).

    Practical Examples

    Let’s solve a few problems using both BODMAS and PEMDAS to illustrate their identical application:

    Example 1: (5 + 3) * 2

    • BODMAS: Brackets first: 8 * 2 = 16.
    • PEMDAS: Parentheses first: 8 * 2 = 16.

    Example 2: 4^2 + 10 / 2

    • BODMAS: Orders (powers) first: 16 + 10 / 2. Then Division: 16 + 5 = 21.
    • PEMDAS: Exponents first: 16 + 10 / 2. Then Division: 16 + 5 = 21.

    Example 3: 12 - 3 * 2 + 4

    • BODMAS: Multiplication first: 12 - 6 + 4. Then Addition/Subtraction from left to right: 6 + 4 = 10.
    • PEMDAS: Multiplication first: 12 - 6 + 4. Then Addition/Subtraction from left to right: 6 + 4 = 10.

    Other Acronyms for Order of Operations

    You might also encounter other acronyms, such as BEDMAS or BIDMAS. These are simply variations of BODMAS, with "E" for Exponents or "I" for Indices sometimes used interchangeably with "O" for Orders. Regardless of the acronym, the underlying mathematical principle remains the same.

    People Also Ask

    What is the correct order of operations?

    The correct order of operations is to first solve expressions within grouping symbols like parentheses or brackets. Next, evaluate exponents or powers. Then, perform multiplication and division from left to right. Finally, carry out addition and subtraction from left to right.

    Is it PEMDAS or BODMAS?

    Both PEMDAS and BODMAS are correct and refer to the same order of operations. PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) is common in North America, while BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is used in the UK and other regions.

    Does the order of multiplication and division matter?

    Yes, the order of multiplication and division matters because they have the same priority. You perform them from left to right as they appear in the expression. The same applies to addition and subtraction.

    Why is the order of operations important in math?

    The order of operations is crucial for ensuring that mathematical expressions have a single, unambiguous answer. Without a standardized order, different people could arrive at different results for the same problem, leading to inconsistencies in calculations and communication.

    Can you use BODMAS and PEMDAS interchangeably?

    Yes, you can use BODMAS and PEMDAS interchangeably because they represent the exact same mathematical rule for the order of operations. The only difference is the specific terminology used for each step, such as "Brackets" versus "Parent

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    Dogi

    Dogi writes for the Milwkick editorial team, turning everyday questions about home, pets, health and personal growth into clear, practical guides. How we create our articles.

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