Type in your sum to see how to solve it step by step. Examples: 2+3*4 or 3/4*3
Description
Just type in sums like these (see Order of Operations for more detail):
Examples:
- 1+2*3
- 7 + (6 * 5^2 + 3)
- cos(1.2^2)+3
- (5−3)(5+3)
- ( −6 + √(6²−4×5×1) ) / (2×5)
- sqrt(3^2+4^2)
You will see what the calculator thinks you entered (which may be a little different to what you typed), and then a step-by-step solution.
Note: there can be more than one way to find a solution.
The calculator is still under development and may get things wrong, so be careful!
Tree View
Press the "tree" button to see your sum as a tree. You would do the calculations from the top down ... sometimes you have a choice which calculation to do first.
All Functions
Operators
+ | Addition operator |
- | Subtraction operator |
* | Multiplication operator |
/ | Division operator |
^ | Exponent (Power) operator |
Functions
sqrt | Square Root of a value or expression. |
sin | sine of a value or expression |
cos | cosine of a value or expression |
tan | tangent of a value or expression |
asin | inverse sine (arcsine) of a value or expression |
acos | inverse cosine (arccos) of a value or expression |
atan | inverse tangent (arctangent) of a value or expression |
sinh | Hyperbolic sine of a value or expression |
cosh | Hyperbolic cosine of a value or expression |
tanh | Hyperbolic tangent of a value or expression |
exp | e (the Euler Constant) raised to the power of a value or expression |
ln | The natural logarithm of a value or expression |
log | The base-10 logarithm of a value or expression |
floor | Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer. |
ceil | Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer. |
abs | Absolute value (distance from zero) of a value or expression |
sign | Sign (+1 or −1) of a value or expression |
Constants
pi | The constant π (3.141592654...) |
e | The Euler constant (2.71828...), the base for the natural logarithm |
Learning Outcomes
- Use the order of operations to simplify mathematical expressions
- Simplify mathematical expressions involving addition, subtraction, multiplication, division, and exponents
Simplify Expressions Using the Order of Operations
We’ve introduced most of the symbols and notation used in algebra, but now we need to clarify the order of operations. Otherwise, expressions may have
different meanings, and they may result in different values.
For example, consider the expression:
4+3⋅74+3\cdot 7
Some students say it simplifies to 49.Some students say it simplifies to 25. 4+3⋅7 Since 4+3 gives 7.7⋅7 And 7⋅7 is 49.494+3⋅7Since 3⋅7 is 21.4 +21And 21+4 makes 25.25 \begin{array}{cccc}\qquad \text{Some students say it simplifies to 49.}\qquad & & & \qquad \text{Some students say it simplifies to 25.}\qquad \\ \begin{array}{ccc}& & \qquad 4+3\cdot 7\qquad \\ \text{Since }4+3\text{ gives 7.}\qquad & & \qquad 7\cdot 7\qquad \\ \text{And }7\cdot 7\text{ is 49.}\qquad & & \qquad 49\qquad \end{array}& & & \begin{array}{ccc}& & \qquad 4+3\cdot 7\qquad \\ \text{Since }3\cdot 7\text{ is 21.}\qquad & & \qquad 4+21\qquad \\ \text{And }21+4\text{ makes 25.}\qquad & & \qquad 25\qquad \end{array}\qquad \end{array}
Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.
Order of Operations
When simplifying mathematical expressions perform the operations in the following order:
1. Parentheses and other Grouping Symbols
- Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.
2. Exponents
- Simplify all expressions with exponents.
3. Multiplication and Division
- Perform all multiplication and division in order from left to right. These operations have equal priority.
4. Addition and Subtraction
- Perform all addition and subtraction in order from left to right. These operations have equal priority.
Students often ask, "How will I remember the order?" Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase. Please Excuse My Dear Aunt Sally.
Please | Parentheses |
Excuse | Exponents |
My Dear | Multiplication and Division |
Aunt Sally | Addition and Subtraction |
It’s good that ‘My Dear’ goes together, as this reminds us that multiplication and division have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.
Similarly, ‘Aunt Sally’ goes together and so reminds us that addition and
subtraction also have equal priority and we do them in order from left to right.
example
Simplify the expressions:
4+3⋅74+3\cdot 7
(4+3)⋅7\left(4+3\right)\cdot 7
Solution:
1. | |
4+3⋅74+3\cdot 7 | |
Are there any parentheses? No. | |
Are there any exponents? No. | |
Is there any multiplication or division? Yes. | |
Multiply first. | 4+3⋅74+\color{red}{3\cdot 7} |
Add. | 4+214+21 |
2525 |
2. | |
(4+3)⋅7(4+3)\cdot 7 | |
Are there any parentheses? Yes. | (4+3)⋅7\color{red}{(4+3)}\cdot 7 |
Simplify inside the parentheses. | (7)7(7)7 |
Are there any exponents? No. | |
Is there any multiplication or division? Yes. | |
Multiply. | 4949 |
try it
example
Simplify:
18÷9⋅2\text{18}\div \text{9}\cdot \text{2}
18⋅9÷2\text{18}\cdot \text{9}\div \text{2}
Show Solution
try it
example
Simplify:
18÷6+4(5−2)18\div 6+4\left(5 - 2\right)
.
Show Solution
try it
In the video below we show another example of how to use the order of operations to simplify a mathematical expression.
When there are multiple grouping symbols, we simplify the innermost parentheses first and work outward.
example
Simplify: 5+23+3[6−3(4−2)]\text{Simplify: }5+{2}^{3}+3\left[6 - 3\left(4 - 2\right)\right]
.
Show Solution
try it
In the video below we show another example of how to use the order of operations to simplify an expression that contains exponents and grouping symbols.
example
Simplify:
23+34÷3−52{2}^{3}+{3}^{4}\div 3-{5}^{2}
.
Show Solution
try it
Licenses and Attributions
CC licensed content, Shared previously
- Ex: Evaluate an Expression Using the Order of Operations. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution
- Example 3: Evaluate An Expression Using The Order of Operation. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution
- Question ID: 144748, 144751, 144756, 144758, 144759, 144762. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax. License: CC BY: Attribution. License terms: Download for free at //cnx.org/contents/[email protected]