The rule or order that we use to simplify expressions in math is called BODMAS rule.
Very simply way to remember BODMAS rule!
B ----> Brackets
O ----> Of (orders :Powers and radicals)
D ----> Division
M ----> Multiplication
A ----> Addition
S ----> Subtraction
Important Notes :
1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.
2. Division does not always come before multiplication. We have to do one by one in the order from left to right.
3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right.
Examples :
12 ÷ 3 x 5 = 4 x 5 = 20
13 - 5 + 9 = 8 + 9 = 17
In the above simplification, we have both division and multiplication. From left to right, we have division first and multiplication next. So we do division first and multiplication next.
Problem 1 :
Evaluate :
6 + 7 x 8
Solution :
Evaluation = 6 + 7 x 8 = 6 + 56 = 62 |
Operation Multiplication Addition Result |
Problem 2 :
Evaluate :
10^{2} - 16 ÷ 8
Solution :
Evaluation = 10^{2} - 16 ÷ 8 = 100 - 16 ÷ 8 = 100 - 2 = 98 |
Operation Power Division Subtraction Result |
Problem 3 :
Evaluate :
(25 + 11) x 2
Solution :
Evaluation = (25 + 11) x 2 = 36 x 2 = 72 |
Operation Bracket Multiplication Result |
Problem 4 :
Evaluate :
3 + 6 x (5 + 4) ÷ 3 -7
Solution :
Evaluation = 3 + 6 x (5 + 4) ÷ 3 -7 = 3 + 6 x 9 ÷ 3 -7 = 3 + 54 ÷ 3 -7 = 3 + 18 -7 = 21 - 7 = 14 |
Operation Bracket Multiplication Division Addition Subtraction Result |
Problem 5 :
Evaluate :
56 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10
Solution :
Evaluation = 56 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10 = 56 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10 = 56 - 2(20 + 3 x 3 - 2 x 2) + 10 = 56 - 2(20 + 9 - 4) + 10 = 56 - 2(29 - 4) + 10 = 56 - 2(25) + 10 = 56 - 50 + 10 = 6 + 10 = 16 |
Operation Bracket Division Multiplication Addition Subtraction Multiplication Subtraction Addition Result |
Problem 6 :
Evaluate :
6 + [(16 - 4) ÷ (2^{2} + 2)] - 2
Solution :
Evaluation = 6 + [(16 - 4) ÷ (2^{2 }+ 2)] - 2 = 6 + [12 ÷ (2^{2 }+ 2)] - 2 = 6 + [12 ÷ (4 + 2)] - 2 = 6 + [12 ÷ 6] - 2 = 6 + 2 - 2 = 8 - 2 = 6 |
Operation Square Bracket Power Bracket Square Bracket Addition Subtraction Result |
Problem 7 :
Evaluate :
(96 ÷ 12) + 14 x (12 + 8) ÷ 2
Solution :
Evaluation = (96 ÷ 12) + 14 x (12 + 8) ÷ 2 = 8 + 14 x 20 ÷ 2 = 8 + 280 ÷ 2 = 8 + 140 = 148 |
Operation Bracket Multiplication Division Addition Result |
Problem 8 :
Evaluate :
(93 + 15) ÷ (3 x 4) - 24 + 8
Solution :
Evaluation = (93 + 15) ÷ (3 x 4) - 24 + 8 = 108 ÷ 12 - 24 + 8 = 9 - 24 + 8 = -15 + 8 = -7 |
Operation Bracket Division Subtraction Subtraction Result |
Problem 9 :
Evaluate :
55 ÷ 11 + (18 - 6) x 9
Solution :
Evaluation = 55 ÷ 11 + (18 - 6) x 9 = 55 ÷ 11 + 12 x 9 = 5 + 12 x 9 = 5 + 108 = 113 |
Operation Bracket Division Multiplication Addition Result |
Problem 10 :
Evaluate :
(7 + 18) x 3 ÷ (2 + 13) - 28
Solution :
Evaluation = (7 + 18) x 3 ÷ (2 + 13) - 28 = 25 x 3 ÷ 15 - 28 = 75 ÷ 15 - 28 = 5 - 28 = -23 |
Operation Bracket Multiplication Division Subtraction Result |
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