by PEMDAS math rule, Definition and PEMDAS examples
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What is ‘PEMDAS’ ?
PEMDAS rule, Definition and PEMDAS examples
‘PEMDAS’ is an acronym for the order of operations. Each letter represent an operation to calculate the value of mathematical expressions. The operations included in the PEMDAS are performed from left to right. PEMDAS Stands for P: Parentheses, E: Exponents , M:Multiplication , D: Division, A: Addition and S: Subtraction
| P | E | M/D | A/D |
| Parentheses
{} , [] , () |
Exponents
|
multiplication /division (perform left to right depending on which operation comes first) |
addition/subtraction
(perform left to right depending on which operation comes first) |
The following rule must be followed if you want to use PEMDAS correctly.
PEMDAS RULE
(i) Perform operations inside of parentheses (brackets) before you do anything else.
(ii) After performing operations inside of parentheses , solve the exponents (if there are any).
(iii) After the parentheses and the exponents, perform multiplication or division from left to right depending on which operation comes first.
- Note: Just because M comes before D in the PEMDAS rule doesn’t mean that you will always perform multiplication before division.
(iv) Finally, after multiplication and division, perform addition and subtraction from left to right depending on which operation comes first. The following acronym will help you remember the PEMDAS Rule.
Please Excuse My Dear Aunt Sally
The following examples show how to correctly apply PEMDAS rule while solving mathematical operations.
PEMDAS EXAMPLES WITH ANSWERS (solved)
(i) 28 ÷
Sol. 28 ÷ =28 ÷
( solving parentheses first : 9-7=2)
= 28 ÷4 ( solving exponents =4)
=7 ( finally division)
(ii) 75-10 x 6
Sol. 75-10 x 6= 75- 60 ( solving multiplication first 10 x 6=60)
= 15 ( performing subtraction)
(iii) 8 x 8 ÷ 16
Sol. There are only two operations in the given mathematical expressions , multiplication and division. According to PEMDAS , perform multiplication or division from left to right depending on which operation comes first. So in the given problem , we will solve multiplication first then division as follows.
8 x 8 ÷ 16 = 64 ÷ 16
=4
(iv) 6 x 4 ÷ 12 +72÷ 8-9
Sol. 6 x 4 ÷ 12 +72÷ 8-9 = 24 ÷ 12 +72÷ 8-9 ( performing multiplication)
= 2 +9 -9 (performing division)
= 11-9 (solving addition)
=2 (performing subtraction)
(v) + (2 +12 x 2) -16 ÷ 4
Sol. + (2 +12 x 2) -16 ÷ 4 =
+ 26-16 ÷ 4 ( Solving operations inside parentheses)
= 9+ 26-16 ÷ 4 (solving exponent )
=9+ 26-4 ( performing division)
= 35-4 (performing addition)
= 31
(vi) 8+14 ÷ 7 x 3-5
Sol. 8+14 ÷ 7 x 3-5 = 8+2 x 3-5 (performing division first)
= 8+6-5 (performing multiplication)
= 14-5
=9
(vii) 12 – 8 + 4 + 9 × (40 ÷ 4)
Sol. 12 – 8 + 4 + 9 × (40 ÷ 4) = 12-8+4+9 x 10 (solving division inside parentheses 40 ÷4=10)
= 12 – 8+4 +90 (multiply 9 x 10 )
= 4+4+90 (subtracting 12-8 )
=98
(viii) (42 ÷ 7 ) + 7 + ( 17 – 9 ) × 8
Sol. (42 ÷ 7 ) + 7 + ( 17 – 9 ) × 8 = 6 + 7 + ( 17 – 9 ) × 8 (Solving division 42 ÷ 7 )
= 6 + 7 + 8 × 8 (performing subtraction 17-9 )
= 6+7 +64 (multiplying 8 x 8 )
= 77
(ix) (10+43-5) ÷ 6+
Sol. (10+43-5) ÷ 6+ = 48 ÷ 6+
(Solving the expressions inside the parentheses)
=48 ÷ 6+25 (solving the exponent )
= 8+25 (performing 48 ÷ 6)
= 33
(x) +(9-10÷ 5)
Sol. +(9-10÷ 5) =
+(9-10÷ 5)
= +(9-2)
= + 7
= 81+7 = 88
(XI) 3 x 19 x 14 +18 ÷ 2
Sol. 3 x 19 x 14 +18 ÷ 2= 57 x 14 +18 ÷ 2
=798+18 ÷ 2
=798+9
= 807
(XII) 8 × 9 − 8 ÷ 2 + 14
Sol. 8 × 9 − 8 ÷ 2 + 14= 72 − 8 ÷ 2 + 14 (performing multiplication)
=72 − 4+ 14 (dividing 8 ÷ 2 )
=68+14
=82
(XIII) 7 + 4 × 4 − 36 ÷ 9
Sol. 7 + 4 × 4 − 36 ÷ 9 = 7 + 16 − 36 ÷ 9 (performing multiplication)
= 7 + 16 − 4 (solving division)
=23-4
=19
(XIV)
Sol. (solving the subtraction lying inside the small brackets)
= (solving exponent
)
= (performing multiplication inside the parentheses)
=[21-6] x 6
=15 x 6
=30
(XV)
Sol.
=62- 2 x 16 +1
=62- 32 +1
=30+1
=31
PEMDAS EXAMPLES WITH ANSWERS (Unsolved)
(i) 10 ÷ (3+2) x 4 + +6-9 Ans. 30
(ii) 25- +3 x 4 Ans. 21
(iii) 3+ [6(11+1-4)]÷ 8 x 2 Ans. 15
(iv) 3 x (3+7) – ÷2 Ans. 22
(v) 2 x ÷(26-1) Ans. 33
(vi) (4+3) x 10 ÷ 2 +(5+6) Ans. 46
(vii) Ans. 142
(viii) Ans. 148
(ix) (10-7) + (2 x 14 ÷ 4) Ans. 10
(x) (10+2) ÷ 4 x [(15÷ 3)-4] Ans. 3
(xi) 4(15÷ 3) +(6 x 3) – Ans. 34
(xii) 4 × 6 ÷ 2 − + 15 Ans. -37
(xiii) 8 − + 4 × 64 ÷
Ans . 20
(xiv) Ans. 95
(xv) (22 ÷11) –
Ans. -60
PEMDAS examples worksheet with answers PDF
PEMDAS QUIZ
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