"BODMAS" Rule
- This rule
depicts the correct sequence in which the operations are to be executed,so as
to find out the value of a given expression.
- Here, ‘B’ stands for ’bracket’
,’O’for ‘of’ , ‘D’ for’ division’ and ‘M’ for ‘multiplication’, ‘A’ for
‘addition’ and ‘S’ for ‘subtraction’.
- Thus, in simplifying an
expression, first of all the brackets must be removed, strictly in the order(),
{} and [].
- After removing the brackets, we
must use the following operations strictly in the order:
- (1)of (2)division (3)
multiplication (4)addition (5)subtraction.
For Example; (6 + 4) × 5
First solve inside ‘brackets’ 6 + 4 = 10, then 10 × 5 = 50.
Next solve the mathematical 'Of'.
For Example; 3 of 4 + 9
First solve ‘of’ 3 × 4 = 12, then 12 + 9 = 21.
Next, the part of the equation is to calculate 'Division' and 'Multiplication'.
We know that, when division and multiplication follow one another, then their order in that part of the equation is solved from left side to right side.
For Example; 15 ÷ 3 × 1 ÷ 5
‘Multiplication’ and ‘Division’ perform equally, so calculate from left to right side. First solve 15 ÷ 3 = 5, then 5 × 1 = 5, then 5 ÷ 5 = 1.
In the last part of the equation is to calculate 'Addition' and 'Subtraction'. We know that, when addition and subtraction follow one another, then their order in that part of the equation is solved from left side to right side.
For Example; 7 + 19 - 11 + 13
‘Addition’ and ‘Subtraction’ perform equally, so calculate from left to right side. First solve 7 + 19 = 26, then 26 - 11 = 15 and then 15 + 13 = 28.
These are simple rules need to be followed for simplifying or calculating using BODMAS rule.
In brief, after we perform "B" and "O", start from left side to right side by solving any "D"or "M" as we find them. Then start from left side to right side solving any "A" or "S" as we find them.
- Here, ‘B’ stands for ’bracket’ ,’O’for ‘of’ , ‘D’ for’ division’ and ‘M’ for ‘multiplication’, ‘A’ for ‘addition’ and ‘S’ for ‘subtraction’.
- Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order(), {} and [].
- After removing the brackets, we must use the following operations strictly in the order:
- (1)of (2)division (3) multiplication (4)addition (5)subtraction.
For Example; (6 + 4) × 5
First solve inside ‘brackets’ 6 + 4 = 10, then 10 × 5 = 50.
Next solve the mathematical 'Of'.
For Example; 3 of 4 + 9
First solve ‘of’ 3 × 4 = 12, then 12 + 9 = 21.
Next, the part of the equation is to calculate 'Division' and 'Multiplication'.
We know that, when division and multiplication follow one another, then their order in that part of the equation is solved from left side to right side.
For Example; 15 ÷ 3 × 1 ÷ 5
‘Multiplication’ and ‘Division’ perform equally, so calculate from left to right side. First solve 15 ÷ 3 = 5, then 5 × 1 = 5, then 5 ÷ 5 = 1.
In the last part of the equation is to calculate 'Addition' and 'Subtraction'. We know that, when addition and subtraction follow one another, then their order in that part of the equation is solved from left side to right side.
For Example; 7 + 19 - 11 + 13
‘Addition’ and ‘Subtraction’ perform equally, so calculate from left to right side. First solve 7 + 19 = 26, then 26 - 11 = 15 and then 15 + 13 = 28.
These are simple rules need to be followed for simplifying or calculating using BODMAS rule.
In brief, after we perform "B" and "O", start from left side to right side by solving any "D"or "M" as we find them. Then start from left side to right side solving any "A" or "S" as we find them.
Order of Operations
Do things in Brackets First. Example:
6 × (5 + 3) = 6 × 8 =
48
6 × (5 + 3) = 30 + 3 =
33
(wrong)
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
5 × 22 = 5 × 4 =
20
5 × 22 = 102 =
100
(wrong)
Multiply or Divide before you Add or Subtract. Example:
2 + 5 × 3 = 2 + 15 =
17
2 + 5 × 3 = 7 × 3 =
21
(wrong)
Otherwise just go left to right. Example:
30 ÷ 5 × 3 = 6 × 3 =
18
30 ÷ 5 × 3 = 30 ÷ 15 =
2
(wrong)
Do things in Brackets First. Example:
| 6 × (5 + 3) | = | 6 × 8 | = |
48
| ||
| 6 × (5 + 3) | = | 30 + 3 | = |
33
| (wrong) |
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:
| 5 × 22 | = | 5 × 4 | = |
20
| ||
| 5 × 22 | = | 102 | = |
100
| (wrong) |
Multiply or Divide before you Add or Subtract. Example:
| 2 + 5 × 3 | = | 2 + 15 | = |
17
| ||
| 2 + 5 × 3 | = | 7 × 3 | = |
21
| (wrong) |
Otherwise just go left to right. Example:
| 30 ÷ 5 × 3 | = | 6 × 3 | = |
18
| ||
| 30 ÷ 5 × 3 | = | 30 ÷ 15 | = |
2
| (wrong) |
How Do I Remember It All ... ? BODMAS !
B
Brackets first
O
Orders (i.e. Powers and Square Roots, etc.)
DM
Division and Multiplication (left-to-right)
AS
Addition and Subtraction (left-to-right)
Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)
After you have done "B" and "O", just go from left to right doing any "D" or "M" as you find them.
Then go from left to right doing any "A" or "S" as you find them.
Note: the only strange name is "Orders". "Exponents" is used in Canada, and so you might prefer "BEDMAS". There is also "Indices" which makes it "BIDMAS". In the US they say "Parentheses" instead of Brackets, so it is "PEMDAS"
B
| Brackets first |
O
| Orders (i.e. Powers and Square Roots, etc.) |
DM
| Division and Multiplication (left-to-right) |
AS
| Addition and Subtraction (left-to-right) |
Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)
|
After you have done "B" and "O", just go from left to right doing any "D" or "M" as you find them.
Then go from left to right doing any "A" or "S" as you find them.
|
Note: the only strange name is "Orders". "Exponents" is used in Canada, and so you might prefer "BEDMAS". There is also "Indices" which makes it "BIDMAS". In the US they say "Parentheses" instead of Brackets, so it is "PEMDAS"
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