# 4.6. Operations¶

## 4.6.1. Operators and Operands¶

Now that we can store data in variables, let's explore how we can generate new data from existing data.

An operator is one or more characters that represents a computation like addition, multiplication, or division. The values an operator works on are called operands.

The following are all legal JavaScript expressions whose meaning is more or less clear:

• `20 + 32`
• `hour - 1`
• `hour * 60 + minute`
• `minute / 60`
• `5 ** 2`
• `(5 + 9) * (15 - 7)`

For example, in the calculation `20 + 32`, the operator is `+` and the operands are `20` and `32`.

The symbols `+` and `-`, and the use of parentheses for grouping, mean in JavaScript what they mean in mathematics. The asterisk (`*`) is the symbol for multiplication, and `**` is the symbol for exponentiation. Addition, subtraction, multiplication, and exponentiation all do what you expect.

Example

 ```1 2 3 4 5``` ```console.log(2 + 3); console.log(2 - 3); console.log(2 * 3); console.log(2 ** 3); console.log(3 ** 2); ```

Console Output

```5
-1
6
8
9
```

We use the same terminology as before, stating that `2 + 3` returns the value `5`.

When a variable name appears in the place of an operand, it is replaced with the value that it refers to before the operation is performed. For example, suppose that we wanted to convert 645 minutes into hours. Division is denoted by the operator `/`.

Example

 ```1 2 3``` ```let minutes = 645; let hours = minutes / 60; console.log(hours); ```

Console Output

```10.75
```

In summary, operators and operands can be combined to create expressions that are evaluated upon execution. Let's discuss some specific types of operators

## 4.6.2. Arithmetic Operators¶

Some of most commonly-used operators are the arithmetic operators, which carry out basic mathematical operations. These behave exactly as you are used to, though the modulus operator (`%`) may be new to you.

Arithmetic operators
Operator Description Example
Addition (`+`) Adds the two operands `2 + 3` returns `5`
Subtraction (`-`) Subtracts the two operands `2 - 3` returns `-1`
Multiplication (`*`) Multiplies the two operands `2 * 3` returns `6`
Division (`/`) Divides the first operand by the second `6 / 2` returns `3`
Modulus (`%`) Aka the remainder operator. Returns the integer remainder of dividing the two operands. `7 % 5` returns `2`
Exponentiation (`**`) Calculates the base (first operand) to the exponent (second operand) power, that is, baseexponent

`3 ** 2` returns `9`

`5 ** -1` returns `0.2`

Increment (`++`) Adds one to its operand. If used before the operand (`++x`), returns the value of its operand after adding one; if used after the operand (`x++`), returns the value of its operand before adding one. If `x` is `2`, then `++x` sets `x` to `3` and returns `3`, whereas `x++` returns `2` and, only then, sets `x` to `3`
Decrement (`--`) Subtracts one from its operand. The return value is analogous to that for the increment operator. If `x` is `2`, then `--x` sets `x` to `1` and returns `1`, whereas `x--` returns `2` and, only then, sets `x` to `1`

While the modulus operator (`%`) is common in programming, it is not used much outside of programming. Let's explore how it works with a few examples.

The `%` operator returns the remainder obtained by carrying out integer division of the first operand by the second operand. Therefore, `5 % 3` is `2` because 3 goes into 5 one whole time, with a remainder of 2 left over.

Examples

• 12 % 4 is 0, because 4 divides 12 evenly (that is, there is no remainder)
• 13 % 7 is 6
• 6 % 2 is 0
• 7 % 2 is 1

The last two examples illustrate a general rule: An integer x is even exactly when x % 2 is 0 and is odd exactly when x % 2 is 1.

Note

The value returned by `a % b` will be in the range from `0` to `b` (not including `b`).

Tip

If remainders and the modulus operator seem tricky to you, we recommend getting additional practice at Khan Academy.

## 4.6.3. Order of Operations¶

When more than one operator appears in an expression, the order of evaluation depends on the rules of precedence. JavaScript follows the same precedence rules for its arithmetic operators that mathematics does.

1. Parentheses have the highest precedence and can be used to force an expression to evaluate in the order you want. Since expressions in parentheses are evaluated first, `2 * (3 - 1)` is 4, and `(1 + 1) ** (5 - 2)` is 8. You can also use parentheses to make an expression easier to read, as in `(minute * 100) / 60`, even though it doesn't change the result.
2. Exponentiation has the next highest precedence, so `2 ** 1 + 1` is 3 and not 4, and `3 * 1 ** 3` is 3 and not 27. Can you explain why?
3. Multiplication, division, and modulus operators have the same precedence, which is higher than addition and subtraction, which also have the same precedence. So `2 * 3 - 1` yields 5 rather than 4, and `5 - 2 * 2` is 1, not 6.
4. Operators with the same precedence are evaluated from left-to-right. So in the expression `6 - 3 + 2`, the subtraction happens first, yielding 3. We then add 2 to get the result 5. If the operations had been evaluated from right to left, the result would have been `6 - (3 + 2)`, which is 1.

Tip

The acronym PEMDAS can be used to remember order of operations:

P = parentheses

E = exponentiation

M = multiplication

D = division

S = subtraction

Note

Due to an historical quirk, an exception to the left-to-right rule is the exponentiation operator `**`. A useful hint is to always use parentheses to force exactly the order you want when exponentiation is involved:

 ```1 2 3 4 5``` ```// the right-most ** operator is applied first console.log(2 ** 3 ** 2) // use parentheses to force the order you want console.log((2 ** 3) ** 2) ```

Console Output

```512
64
```

Question

What is the value of the following expression?

```16 - 2 * 5 / 3 + 1
```
1. 14
2. 24
3. 3
4. 13.666666666666666

Question

What is the output of the code below?

```console.log(1 + 5 % 3);
```

Question

What is the value of the following expression?

```2 ** 2 ** 3 * 3
```
1. 768
2. 128
3. 12
4. 256