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12 Sep 2020, 12:06
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There are several myths relating to PEMDAS vs. BODMAS when it comes to using the correct order of operations. Some people think that since GRE, GMAT, SAT, ACT, PSAT, and such other tests are US-based tests, you must use PEMDAS. Some people are even of the opinion that PEMDAS and BODMAS produce different results.
The truth is that although the manner in which you use PEMDAS differs from the manner in which you use BODMAS, both will always produce the same result. Math is universal. Go ahead and use whichever you are more comfortable with.
There is, however, one more difference. The E in PEMDAS stands for “Exponents” while the O in BODMAS stands for “Of”, but this difference doesn’t pose any problem.
Without much ado, let’s look at an example and see how the two work.
48 ÷ (2 × 3) + \((1 + 3)^2\) ÷ 2 × 2 × 3 ÷ 2 − 4 – 18 + 2=?
Steps using PEMDAS:
Step 1: P (Parentheses)
48 ÷ 6 + \(4^2\) ÷ 2 × 2 × 3 ÷ 2 – 4 – 18 + 2 =
Step 2: E (Exponents)
48 ÷ 6 + 16 ÷ 2 × 2 × 3 ÷ 2 – 4 – 18 + 2 =
Step 3: MD (Multiplication and Division to be done in the same step from left to right)
8 + 24 – 4 – 18 + 2 =
Step 4: AS (Addition and Subscription to be done in the same step from left to right)
12
Thus, PEMDAS should be perceived as PE(MD)(AS).
Those among you who want to go for PEMDAS may be already familiar with the mnemonic:
Please Excuse My Dear Aunt Sally!
Steps using BODMAS:
Step 1: B (Bracket)
48 ÷ 6 +\( 4^2\) ÷ 2 × 2 × 3 ÷ 2 – 4 – 18 + 2 =
You will need to deal with the exponent before you go to the next steps.
48 ÷ 6 + 16 ÷ 2 × 2 × 3 ÷ 2 – 4 – 18 + 2 =
There is no “Of” here; we move to the next Step.
Step 2: D (Division)
8 + 8 × 2 × 1.5 – 4 – 18 + 2 =
Step 3: M (Multiplication)
8 + 24 – 4 – 18 + 2 =
Step 4: A (Addition)
34 – 4 – 18 =
Step 5: S (Subtraction)
12
If you are from India or know Hindi, BODMAS itself is a mnemonic for you; you don’t need any other mnemonic to remember it.
Therefore,
1. PEMDAS and BODMAS both produce the same result, and
2. You can use either, but do commit it to memory.
The truth is that although the manner in which you use PEMDAS differs from the manner in which you use BODMAS, both will always produce the same result. Math is universal. Go ahead and use whichever you are more comfortable with.
There is, however, one more difference. The E in PEMDAS stands for “Exponents” while the O in BODMAS stands for “Of”, but this difference doesn’t pose any problem.
Without much ado, let’s look at an example and see how the two work.
48 ÷ (2 × 3) + \((1 + 3)^2\) ÷ 2 × 2 × 3 ÷ 2 − 4 – 18 + 2=?
Steps using PEMDAS:
Step 1: P (Parentheses)
48 ÷ 6 + \(4^2\) ÷ 2 × 2 × 3 ÷ 2 – 4 – 18 + 2 =
Step 2: E (Exponents)
48 ÷ 6 + 16 ÷ 2 × 2 × 3 ÷ 2 – 4 – 18 + 2 =
Step 3: MD (Multiplication and Division to be done in the same step from left to right)
8 + 24 – 4 – 18 + 2 =
Step 4: AS (Addition and Subscription to be done in the same step from left to right)
12
Thus, PEMDAS should be perceived as PE(MD)(AS).
Those among you who want to go for PEMDAS may be already familiar with the mnemonic:
Please Excuse My Dear Aunt Sally!
Steps using BODMAS:
Step 1: B (Bracket)
48 ÷ 6 +\( 4^2\) ÷ 2 × 2 × 3 ÷ 2 – 4 – 18 + 2 =
You will need to deal with the exponent before you go to the next steps.
48 ÷ 6 + 16 ÷ 2 × 2 × 3 ÷ 2 – 4 – 18 + 2 =
There is no “Of” here; we move to the next Step.
Step 2: D (Division)
8 + 8 × 2 × 1.5 – 4 – 18 + 2 =
Step 3: M (Multiplication)
8 + 24 – 4 – 18 + 2 =
Step 4: A (Addition)
34 – 4 – 18 =
Step 5: S (Subtraction)
12
If you are from India or know Hindi, BODMAS itself is a mnemonic for you; you don’t need any other mnemonic to remember it.
Therefore,
1. PEMDAS and BODMAS both produce the same result, and
2. You can use either, but do commit it to memory.
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13 Sep 2020, 13:26
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Hello, Bandy2020. I am curious, what about the meaning of BODMAS for the non-Hindi speaker? Why would that acronym (?) itself be a mnemonic? I would also like to point out that some more progressive schools in the U.S. are now teaching the order of operations as GEMDAS, with G standing in for "groups" or "grouping(s)," to be more inclusive of other such entities, such as those found within square brackets ([ ]) or absolute value (| |) notation.
Thank you for sharing.
- Andrew
Thank you for sharing.
- Andrew
13 Sep 2020, 20:34
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Hi AndrewN,
I liked your query, comments, and the additional information (GEMDAS).
The post was mainly for those who are not familiar with PEMDAS because most of the US origin GMAT material (naturally) mentions only PEMDAS and people not familiar with PEMDAS start wondering whether they MUST use PEMDAS.
In India (and a few other countries) people -- mostly Hindi speakers -- are familiar with BODMAS because that is what they learn in school.
Therefore, non-Hindi speakers need not learn BODMAS; they can go for PEMDAS or GEMDAS!
By the way, Bodmas (with different spellings -- Budmash or Badmash) has already found a place in English dictionaries!
I liked your query, comments, and the additional information (GEMDAS).
The post was mainly for those who are not familiar with PEMDAS because most of the US origin GMAT material (naturally) mentions only PEMDAS and people not familiar with PEMDAS start wondering whether they MUST use PEMDAS.
In India (and a few other countries) people -- mostly Hindi speakers -- are familiar with BODMAS because that is what they learn in school.
Therefore, non-Hindi speakers need not learn BODMAS; they can go for PEMDAS or GEMDAS!
By the way, Bodmas (with different spellings -- Budmash or Badmash) has already found a place in English dictionaries!
