Integer Calculator

This integer calculator can be used for adding and subtracting integers and decimals. The calculator works with positive and negative numbers and finds the solution for any number of consecutive operations (for example, you can enter 5 + - + - + - + - - - + + 3, and the calculator will identify the final operation sign, +, perform the calculation, and return the final answer, 8).

Directions for use

To use the calculator to add and subtract integers and decimals, enter the given equation and press “Calculate.” The calculator will return the final answer and a step-by-step solution algorithm, identifying the final sign for each operation. The input field accepts the following symbols:

• Integers, for example, 3, 6, 144, -15.
• Decimals, where the decimal point separates the whole number part and the decimal part. For example, 3.0, 8.978, 123.901, -12.36.
• Operation sign for addition, +.
• Operation sign for subtraction, –.
• Brackets, (). The brackets, or parentheses, should always come in pairs, i.e., the equation should contain both the opening and the closing bracket. For example, 3 + (-4), -98 - (-5.67). You cannot input 5 + (-3, since this equation contains only one bracket. The symbols enclosed in brackets should always end with a number, not an operation sign. For example, (3 - 4 + 5) is a valid input, while (3 - 4 +) 5 is not. Square brackets, [], or curly brackets, {}, can also be used. The calculator will automatically convert them into parentheses ().

You can use as many consecutive operation signs as necessary without separating them by spaces or symbols. The calculator will identify and demonstrate the final operation sign for each operation. Below are some valid input examples:

• -33 + 15 - 1- - 2 (equals -17)
• (-33) + 15 - 1 - (-2) (equals -17)
• (-33 + 15 -1) - - 2 (equals -17)
• -33 + 15 - 1- - - - - + 2 (equals -21)

The input field accepts up to 60 symbols.

Positive and negative integers

Positive and negative integers are best visualized on the number line, as shown in the image below:

“-” is the negative sign, marking the numbers below zero or to the left of zero on the number line; “+” is the positive sign, marking the numbers above zero, i.e., to the right of zero on the number line. When writing down the numbers, the + sign is usually omitted, and the number is written without any sign. For example, +7 = 7.

Integers addition and integers subtraction

Adding and subtracting integers means moving to the right or left on the number line. To add an integer, move the corresponding number of steps to the right (for positive integers) or to the left (for negative integers) on the number line. To subtract an integer, add the opposite integer. Integers are called opposite if they have the same absolute value but a different sign. For example, 4 and -4, 12 and -12, 1 and -1.

Adding positive numbers

Adding positive numbers is a simple addition operation. For example, adding 3 means taking 3 steps along the number line in the positive direction (to the right). Adding 14 means you need to take 14 steps in the positive direction, and so on. Some examples of adding positive integers are demonstrated below:

0 + 3 = 3

4 + 3 = 7

-1 + 12 = 11

-5 + 1 = -4

Subtracting positive numbers

Subtracting positive numbers is a simple subtraction operation. To subtract a positive number, move a corresponding number of steps along the number line in the negative direction (to the left). Examples of subtracting positive integers are demonstrated below:

0 - 1 = -1

12 - 9 = 3

44 - 46 = -2

-5 - 5 = -10

Adding negative numbers

Negative numbers represent the movement in the negative direction (to the left) on the number line. This means that adding a negative number will be performed by moving along the number line to the left:

5 + (-2) = 3

14 + (-12) = 2

-2 + (-13) = -15

Since adding a negative number is performed by moving along the number line in the negative direction, this operation is equivalent to subtracting a positive number:

3 + (-3) = 3 - 3 = 0

Subtracting negative numbers

To subtract a negative number, add the opposite of that number. This means subtracting a negative number is equivalent to adding the corresponding positive number. For example:

-4 - (-11) = -4 + 11 = 7

Rules for adding and subtracting integers

The rules for integer addition and subtraction can be summarized as follows:

• Two like signs (+ + or - -) result in a positive sign, +.
• Two unlike signs (+ - or - +) result in a negative sign, -.

Real-life examples

Integer addition and subtraction are widely used daily for almost every activity. Counting the change, counting the number of people, counting the number of recipe ingredients, and plenty of other examples.

Number of people in the queue

Imagine you are in a long queue, counting the number of people before you. When you came, there were 13 people in front of you. Later, it turned out that one person was holding the spot for a group of people, and 4 other people joined. After that, the couple right in front of you got annoyed and left the queue altogether. How many people are there currently in front of you?

Solution

We need to create and solve an equation to find the answer to that problem. We are given the initial number of people, 13. Then 4 people joined, which can be written down mathematically as +4. Then a couple, or 2, people left. That can be mathematically expressed as -2. Finally, we get the following equation:

13 + 4 - 2 = 15

Answer

There are 15 people in front of you.