Mad Math On Monday

One of the foundational concepts in mathematics is "Order of Operations". A useful mnemonic that often helps us to solve complex equations is: Please Excuse My Dear Aunt Sally.

P = Parentheses
E = Exponents
M/D = Multiplication / Division
A/S = Addition/Subtraction

In a given equation, any portion of the problem that is within the parentheses should be simplified first. The order of operations should also be followed within the parentheses.

Next, if there are exponents present, these should be simplified.

Multiplication and Division are handled together, in the order in which they appear in the equation, from left to right.

Similarly, addition and subtraction are handled together, from left to right, across the equation.

Let's try a few.....
1) 3^3 + (6 X 2) - 10 / 2
Parentheses 3^3 + 12 - 10 / 2
Exponents 9 + 12 - 10/2
Mult / Div 9 + 12 - 5
Add/Sub 21 - 5
16

2) (6 + 4) / 2 + 2^2 - 5
Parenthesis 10 / 2 + 2^2 - 5
Exponents 10 / 2 + 4 - 5
Mult / Div 5 + 4 - 5
Add / Sub 9 - 5
4

3) (10-8)^3 + 12 X 2 - 10
Parenthesis 2 ^3 + 12 X 2 - 10
Exponents 8 + 12 X 2 - 10
Mult/Div 8 + 24 - 10
Add / Sub 32 - 10
22

4) (10 X 2 - 5) + (3 + 4) X (4 x 2)
Parenthesis (5 - 5) + 7 X 8
0 + 7 X 8
Exponents
Mult/Div 0 + 56
Add/Sub 56


Need additional practice?
Try these on your own and check back tomorrow for the solutions.
1) 4^2 + 12 - (5 X 10)
2) 10 - 5 X 10^2
3) (6 + 6)^2 + (8 -4) X (6-2)
4) (6 - 3/3) + 4 - 4 + 12
5) 10^4 - 10^2 X 5 / 500


Robin Hinmon, owner, Brandywine Academic Services
http://www.BrandywineAcademicServices.com