Order of Operations Help

Subject Areas

Tools / Misc

bCalc

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scrnGC2: Calc Input

scrnGC3: f(x) Plot Input

scrnGC4: g(x) Plot Input

The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.

gCalc

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Select precision* of answer:

Select angle mode:

Enter expression to evaluate here:

The answer is shown below:

Enter function to be plotted:

f(x) =

Enter 2nd function, if needed:

g(x) =

Change or reset the x-y scaling below:

x_min =

x_max =

y_min =

y_max =

Accuracy Disclaimer

The javascript math object methods used for this calculator are not accurate for very large or very small numbers. In particular, the trigonometric functions may yield very small answers that should actually be zero or very large answers that should be infinite. This typically occurs at 90° or pi/2 intervals.

DO NOT USE WHERE HIGH PRECISION IS REQUIRED. USE AT YOUR OWN RISK.

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Order of Operations Help - PEMDAS

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Need a crutch to help you remember the order of operations?

Try this: "Please Excuse My Dear Aunt Sally"

The first letters of this little catch phrase spell PEMDAS, which spells out the order of operations as shown at the left. Anything contained within parenthesis must be solved first, followed by exponents, multiplication, division, addition and subtraction. Multiplication and division have equal priority and addition and subtraction have equal priority. Whenever you have operators of equal priority, work from left to right.

The following example illustrates the steps one would follow in solving a problem:

Problem: x = 9 + 8 × 7 + 6 ² + 5(4 + 3) ÷ 2 - 1

Step 1: x = 9 + 8 × 7 + 6 ² + 5( 7 ) ÷ 2 - 1 Solve what's in the parenthesis (4+3).

Step 2: x = 9 + 8 × 7 + 36 + 5( 7 ) ÷ 2 - 1 Solve the exponent (6² = 6 × 6).

Step 3: x = 9 + 56 + 36 + 5( 7 ) ÷ 2 - 1 Multiply or divide working left to right (8 × 7).

Step 4: x = 9 + 56 + 36 + 35 ÷ 2 - 1 Multiply or divide working left to right (5 × 7).

Step 5: x = 9 + 56 + 36 + 17.5 - 1 Multiply or divide working left to right (35 ÷ 7).

Step 6: x = 65 + 36 + 17.5 - 1 Add or subtract working left to right (9 + 56).

Step 7: x = 101 + 17.5 - 1 Add or subtract working left to right (65 + 36).

Step 8: x = 118.5 - 1 Add or subtract working left to right (101 + 17.5).

Step 9: x = 117.5 Add or subtract working left to right (118.5 - 1).

Note how methodically we worked through the whole process using PEMDAS. If you had typed the original expression into a calculator, you would have obtained the same answer because calculators follow the order of operations just as methodically. Understanding PEMDAS will also help you understand your calculator better.

One final note, if you encounter parenthesis within parenthesis, always start with the innermost set of parenthesis and keep working out until you have evaluated everything contained within the parenthesis.