PEMDAS rule

PEMDAS rule can be used to simplify complicated  numerical expressions with more than operations.

Very simply way to remember PEMDAS rule!

P ----> Parentheses

E ----> Exponent 

M ----> Multiply

D ----> Divide

A ----> Add

S ----> Subtract

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. Multiplication does not always come before division. 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.

Evaluate each of the following numerical expressions.

Problem 1 :

(3 * (4 + 2)) * 5

Solution :

= (3 *  (4 + 2)) * 5

= (3 * 6) * 5

= 18 * 5 

= 90

Problem 2 :

(4 * (16 – 1)) – 6

Solution :

(4 * (16 – 1)) – 6

= (4 * 15) – 6

= 60 - 6

= 54

Problem 3 :

5 + (6 + (7 * 2)) // 5

Solution :

= 5 + (6 + (7 × 2)) // 5

= 5 + (6 + 14) // 5

= 5 + 20 // 5

= 5 + 4

 = 9

Problem 4 :

3 – (-2 + 7) + 4

Solution :

= 3 – (-2 + 7) + 4

= 3 – 5 + 4

= -2 + 4

= 2

Problem 5 :

(18 // 3) * (-2)

Solution :

= (18 // 3) * (-2)

= 6 * (-2)

= -12

Problem 6 :

2(7 – 13) – (6 - 12)

Solution :

= 2(7 – 13) – (6 - 12)

= 2(-6) – (-6)

= -12 + 6

= -6

Problem 7 :

-6 * (2 – 7)

Solution :

= -6 * (2 – 7)

= -6 * (-5)

= 30

Problem 8 :

–(14 – 8) // (-2)

Solution :

= –(14 – 8) // (-2)

= -6 // (-2)

= 3

Problem 9 :

-18 – (8 – 15)

Solution :

= -18 – (8 – 15)

=-18 – (-7)

= -18 + 7

= -11

So, the answer is -11.

Problem 10 :

-52 // (6 – 19)

Solution :

= -52 // (6 – 19)

= -52 //  (-13)

= 4

Problem 11 :

(38 - (-4))/(6 * (-7))

Solution : 

= (38 - (-4))/(6 * (-7))

= (38 + 4)/(-42)

= 42/(-42)

= -1.0

Problem 12 :

(28 - (-3 * 4))/(10 * (-2))

 

Solution :

= (28 - (-3 * 4))/(10 * (-2))

= (28 - (-12))/(-20)

= (28 + 12)/(-20)

= 40/(-20)

= -2.0

 

Input Equation: = 14+18/2*18-7 = 14+9.0*18-7 = 14+162.0-7 = 176.0-7 = 169.0	Input Equation: = 10-9*24/8*6 = 10-216/8*6 = 10-27.0*6 = 10-162.0 = -152.0
Input Equation: = 15*18+12/3+9 = 270+12/3+9 = 270+4.0+9 = 274.0+9 = 283.0	Input Equation: = 10/5+10-9*11 = 2.0+10-9*11 = 2.0+10-99 = 12.0-99 = -87.0
Input Equation: = 8*4+9-9+18 = 32+9-9+18 = 41-9+18 = 32+18 = 50	Input Equation: = 3*19*14+18/2 = 57*14+18/2 = 798+18/2 = 798+9.0 = 807.0
Input Equation: = 11*11-6*17+4 = 121-6*17+4 = 121-102+4 = 19+4 = 23	Input Equation: = 10*12-14/2+15 = 120-14/2+15 = 120-7.0+15 = 113.0+15 = 128.0
Input Equation: = 2-1+5*4*11 = 2-1+20*11 = 2-1+220 = 1+220 = 221	Input Equation: = 14/2-1+3 = 7.0-1+3 = 6.0+3 = 9.0
Input Equation: = 16*7*15+11+17 = 112*15+11+17 = 1680+11+17 = 1691+17 = 1708	Input Equation: = 9+15/5*13 = 9+3.0*13 = 9+39.0 = 48.0
Input Equation: = 12/3*12+10 = 4.0*12+10 = 48.0+10 = 58.0	Input Equation: = (11+42-5)/(11-4) = (53-5)/(11-4) = (48)/(11-4) = 48/(11-4) = 48/(7) = 48/7 = 6.8571428571429 (use only 1 or 2 decimal)
Input Equation: = 16*15/5+12 = 240/5+12 = 48.0+12 = 60.0	Input Equation: = (9+33-6)/6-3**2 = (42-6)/6-3**2 = (36)/6-3**2 = 36/6-3**2 = 36/6-9 = 6.0-9 = -3.0
Input Equation: = (6+3)**2+(9-10/5) = (9)**2+(9-10/5) = 9**2+(9-10/5) = 9**2+(9-2) = 9**2+(7) = 9**2+7 = 81+7 = 88.0	Input Equation: = (24+21*(12%9)+12-6)+36 = (24+21*3+12-6)+36 = (24+63+12-6)+36 (87+12-6)+36 = (99-6)+36 = 93+36 =129
Input Equation: =(1+4)**2-(2*9%6+8) =5**2-(2*9%6+8) =25-(2*9%6+8) =25-(18%6+8) =25-(0+8) =25-8 =17	Input Equation: = 20 * 4 * 2 *7 - (18%14*6) = 20 * 4 * 2 *7 - (4*6) = 20 * 4 * 2 *7 - (24) = 80 * 2 *7 - (24) = 160 *7 - (24) = 1120-24 = 1096
Input Equation: =120 + ((9/3) % (72/8))**2 = 120 + ((9/3) % (9))**2 = 120 + ((9/3) % (9))**2 = 120+(3.0%9)**2 = 120+3.0**2 = 120+9.0 = 129.0	Input Equation : = 120 + ((9%3) % (72/8))**2 = 120 + ((9%3) % (9.0)**2 = 120 + ((0) % (9.0))**2 = 120 +(0.0)**2 = 120 + 0.0 = 120.0
Input Equation: = 18%12//24*23-12+8*6 = 18%12//24*23-12+48 = 6//24*23-12+48 = 0*23-12+48 = 0-12+48 = -12+48 = 36	Input Equation: = 18%12%24*23-12+8*6 = 6%24*23-12+8*6 = 6*23-12+8*6 = 138-12+8*6 = 126+8*6 = 126+48 = 174

 

 

Solve the following advanced order of operations problems:

1. (24+21*(12//9)+12-6)+36 = (24+21*(12//9)+12-6)+36 = (24+21*(1)+12-6)+36 = (24+21*1+12-6)+36 = (24+21+12-6)+36 = (45+12-6)+36 = (57-6)+36 = (51)+36 = 87	2. 20-12-4-2+5(8+9)**2 Input Equation can be rewritten: = 20-12-4-2+5*(8+9)**2 = 20-12-4-2+5*(17)**2 = 20-12-4-2+5*17**2 = 20-12-4-2+5*289 = 20-12-4-2+1445 = 8-4-2+1445 = 4-2+1445 = 2+1445 = 1447
3. (1+4)**2-(2*9/6+8) Input Equation: = (1+4)**2-(2*9/6+8) = (5)**2-(2*9/6+8) = 5**2-(2*9/6+8) = 5**2-(18/6+8) = 5**2-(3.0+8) = 5**2-(11.0) = 5**2-11.0 = 25-11.0 = 14.0	4. 20 * 4 * 2 *7 - (18//14*6) Input Equation: = 20*4*2*7-(18//14*6) = 20*4*2*7-(1*6) = 20*4*2*7-(6) = 20*4*2*7-6 = 80*2*7-6 = 160*7-6 = 1120-6 = 1114
5. 120 + ((9/3) / (72/8))**2 Input Equation: = 120+((9/3)/(72/8))**2 = 120+((3.0)/(72/8))**2 = 120+(3.0/(72/8))**2 = 120+(3.0/(9))**2 = 120+(3.0/9)**2 = 120+(0.0)**2 = 120+0.0**2 = 120+0.0 = 120.0	6. (1+12*4)**2 - (22*4-12)**2 Input Equation: = (1+12*4)**2-(22*4-12)**2 = (1+48)**2-(22*4-12)**2 = (49)**2-(22*4-12)**2 = 49**2-(22*4-12)**2 = 49**2-(88-12)**2 = 49**2-(76)**2 = 49**2-76**2 = 49**2-5776 = 2401-5776 = -3375
7. 18/12//24*23-12+8*6 Input Equation: = 18/12//24*23-12+8*6 = 1.5//24*23-12+8*6 = 0.0*23-12+8*6 = 0-12+8*6 = 0.0-12+48 = 36.0	8. (40 - 3 - 5)**2 + (12/4*6)**2 Input Equation: = (40-3-5)**2+(12/4*6)**2 = (37-5)**2+(12/4*6)**2 = (32)**2+(12/4*6)**2 = 32**2+(12/4*6)**2 = 32**2+(3.0*6)**2 = 32**2+(18.0)**2 = 32**2+18.0**2 = 32**2+324.0 = 1024+324.0 = 1348.0
9. ((12//8-4)**2)**2 - 12**2 Input Equation: = ((12//8-4)**2)**2-12**2 = ((1-4)**2)**2-12**2 = ((-3)**2)**2-12**2 = (9)**2-12**2 = 81-12**2 = 81-144 = -63