## How do I enter math?

For the most part, entering math into our calculator will be just about the same as entering math in any other calculator you've ever used. That said, there are a few things you should consider.

### Absolute Values

Absolute values and absolute value equations are supported by the calculator. To enter an absolute value, you simply surround the expression with abs(). So, let's say, you wanted to express $\left | x-4 \right |=15$, then you would enter abs(x-4)=15. If you try to enter it as |x-4|=15 (with vertical line characters surrounding the expression), it won't work and you'll get an error.

### Entering Variables

You can enter any standard variable from a to z. Variables are case-insensitive, meaning, that $A+a+A$ and $a+a+a$ will both be interpreted as the same.

### Exponents

There are two ways you can express an exponent: first, using the caret symbol (^); second, using two multiplication signs (**). Both will be interpreted as the same. So, if you wanted to write $x^2$ you could write either x^2 or x**2. Important: be sure to set parentheses accordingly. Let's say you wanted to use a fraction as an exponent. If you would write $x^{\frac{1}{2}}$ you would need to write x^(1/2), because if you had omitted the parentheses and just wrote x^1/2 the expression would have been interpreted as $\frac{x^1}{2}$.

### Square Roots

If you wanted to take the root of an expression, you would enter sqrt(x), which would take the square root of the variable x. Of course, instead of x, you can enter any other expression you need. Mathematically, roots can be expressed as exponents. So, if you wanted to take the square root $\sqrt{x}$, you could also write $x^\frac{1}{2}$, which would be the same mathematically. But usually, when writing mathematical expressions, most people tend to prefer the root symbol (also known as a radical symbol) over the exponential notation. In fact, one of the simplification rules built into our calculators, is to bring exponential notation into radical form.

### Cube Roots and higher

As mentioned earlier, there exists a special relationship between exponents and radicals: one can be written as the other. In fact, finding roots and converting them to exponent form is a relatively common operation in algebra. Roots are expressed as **fractional exponents**, when they are converted to exponential form. Taking the square root of x (so: $\sqrt{x}$) would be the same as raising x to the power of $\frac{1}{2}$ (so: $x^\frac{1}{2}$). Analogously, the cube root of x (usually written as $\sqrt[3]{x}$) could be expressed in exponential form as $x^\frac{1}{3}$, with a base of x and an exponent of $\frac{1}{3}$. So, if you wanted to take the cube root of x, you would enter x^(1/3).

This relationship can be illustrated further by taking a look at the Laws of Exponents:

The **Power of a Power** states, that $\left ( b^n \right )^m = b^{n\cdot m}$. We know that taking the square root of a number is the inverse operation of squaring that number. So, if $n=2$ and $m=\frac{1}{2}$, then $n\cdot m = 1$ and every number to the power of one is the number itself.

### Decimal Numbers

Of course, numbers are supported! If you enter a decimal though, it will be converted into a fraction (simplified to lowest terms). So, if you enter x+0.25, our calculator will convert the decimal 0.25 into $\frac{1}{4}$ and instead of $x+0.25$ you will see $x+\frac{1}{4}$.

### Brackets, Parentheses

Brackets and parentheses are used to group expressions. Please use parentheses ( ) and not square brackets [ ].

### Implied Multiplication

Implied multiplication (“multiplication without a symbol”) is fully supported. Implied multiplication is an important concept in algebra and mathematics in general. Instead of the need to write a multiplication sign after each part of an expression, you can simply enter them in one. For example, the expressions 2x and 2*x would be considered equal by our calculators. Some textbooks and mathematical software will treat expressions written with implied multiplication higher than ones using regular multiplication of division. Our calculator treat implied multiplication the same as regular multiplication. So, if you entered 1/2x, it would be interpreted as $\frac{1}{2}\cdot x$ and not as $\frac{1}{2\cdot x}$.

### Inequalities

Solving an inequality is (nearly) just like solving an equation: isolate the variable of interest and bring it to one side of the inequality. Nearly, at least. There is one important difference you need to keep in mind when working with inequalities: When you multiply or divide both sides by a negative you need to switch the direction of the sign. Of course, our calculators know these rules and apply them accordingly. You can enter inequalities like a regular equation, but substituting the equals sign for one of the following:

- < Less-than, e.g. $x-4<5$
- > Greater-than, e.g. $x-4>5$
- <= Less-than or equal, e.g. $x-4\leq 5$
- >= Greater-than or equal, e.g. $x-4\geq 5$

## Interpreting the Solution

As you may have already noticed, the solution you get is organized in a hierarchy. Let's have a look at an example below:

- Take the root of both sides of , to eliminate the exponent on the left side
- Take the root of both sides of
**Simplify****Simplify**the root**Simplify****Simplify**the root

- Resolve the plus-minus-sign: replace in the equation with or

There are two main steps involved in solving this problem. The first main step is that you take the root of both sides of the equation to eliminate the exponent on the left side. The second main step is, that you resolve the plus-minus-sign in the equation. If you want to know more about how to take the root of both sides of the equation, you can step into the hierarchy and have a look how it's done. Again, taking the root of both sides of the equation involves two separate steps: first, you would take the actual root of both sides of the equation. which would yield a new equation (which you can see in light gray right next to the step). Second, you would have to simplify the actual equation. Again, simplification can be broken down into several steps and these steps can be seen directly below in the hierarchy. The result of each step is shown in light gray directly next to it.

### Steps of Calculation

Mathematics is a simple language that can do complicated stuff and you want to know how to get from A to B. To really understand what's going on while solving an equation or factoring or simplifying an expression, you will want to know what parts of the expressions have been transformed and how. Of course, our calculators also provide this information. To see how an expression or part of it was transformed, simply move your mouse over one of the steps. As you do so, you will notice a little tooltip window popping up. For the most cases, this window will contain two expressions: first, the original expression, with the parts highlighted that will be transformed; second, the resulting expression, with the results of the transformation highlighted. For very simple operations, you might just see a single expression instead of two in the pop-up, like when we're only dropping a term or two terms cancel each other out.

## What happens when no steps can be provided?

Sometimes it will happen, that our calculator won't be able to provide the steps involved in calculation. Thankfully, this doesn't happen too often! If for any reason it should happen, our calculator will still provide you with the solution, just without the steps.

## Your calculator says: the solutions are XXX or YYY – shouldn't it be 'and' instead of 'or'?

Actually, no. ;-) 'And' would imply that both conditions have to be met, whereas 'or' says that only one condition has to met, for the equation to be true.