Read and you end up at 1.

Read this lesson to learn about the four basic arithmetic operations you can perform with integers. You’ll also learn how you can visualize these operations in your head.

Basic Mathematical Operations

Add, subtract, divide and multiply…oh my! While thinking about working out math problems using these four basic mathematical operations might seem scary, math is actually not as complicated as it may seem. While there are many different types of numbers such as decimals, fractions and percentages, in this lesson we are going to look at using the four basic operations with integers, which are our whole numbers – both positive and negative.Let’s get started with the easiest of all operations – addition.

Addition

Adding integers is pretty straightforward. If it helps, you can think of your integers as dollar bills. Or, if you are comfortable with your number line, you can use that instead. So, a 3 would be $3 or 3 spaces to the right of 0 on the number line. Remember, positive integers go to the right and negative integers go to the left.

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For example, if you add a 2 to your 3, you will be going 2 spaces further to the right. You’ll be at the number 5. If you think in money terms, you are adding $2 more to your current $3.

So, you’ll now have $5.Since your integers can be both positive and negative, it is possible that you’ll be asked to add a negative integer such as this:

  • 3 + ( – 2 )

When you are adding a negative number you are actually subtracting and, therefore, you’ll need to go to the left on the number line. So you go 2 spaces to the left and you end up at 1. Take a look at the image below to see the sign rules for integers.


Integer Sign Rules for Addition and Subtraction
sign_rule_with_examples


It is a great idea to memorize these rules and here is an easy way to do it:

  • Like signs = addition
  • Unlike signs = subtraction

Subtraction

You can actually write the above as a subtraction problem too. By using our sign rules for addition and subtraction, you can see that when you have an addition sign and a negative sign, they combine for a subtraction problem (remember, unlike signs equal subtraction). So, in the above problem, 3 + ( -2 ), the addition sign and negative sign combine for a subtraction problem and can be rewritten as 3 – 2.

  • 3 + ( -2 ) = 3 – 2 = 1

You can also expand a subtraction problem and rewrite it as an addition problem:

  • 4 – 5 = 4 + ( – 5 )

Now you can go ahead and evaluate like you do for addition.

You start at the number 4 and you are subtracting a 5, or adding a negative 5, so you need to go 5 spaces left on the number line. This takes you to -1.

  • 4 – 5 = -1

Now let’s look at subtracting a negative number:

  • 4 – ( – 5 )

Using our sign rules for addition and subtraction, we see that when we have two like signs, they combine to make an addition problem (remember, like signs equal addition). So, our problem can be rewritten to:

  • 4 – ( – 5 ) = 4 + 5

And you’ll solve it like any addition problem.

  • 4 + 5 = 9

Multiplication

When it comes to multiplication, think of it as adding up equal groups of the same amount. So, think of 2 * 3 as adding up two groups of 3 each. This gives you 6.

integer operations


If you figure out your multiplication for all your numbers 1 through 9, you can create a multiplication table that you can use for reference.


integer operations


The more you use it, the better and faster you’ll get at multiplication. Soon, you won’t have to refer to it at all.When you multiply positive and negative integers, you first multiply without paying any attention to your positive and negative signs. When you are done multiplying and have your answer, then you go back and figure out your sign using the very easy rule shown in the chart below:

  • Like signs = positive
  • Unlike signs = negative


Integer Sign Rules for Multiplication and Division
According to these rules, if you multiply two positive or two negative integers (like signs), your answer will be positive, but if one of your integers is positive and the other is negative (unlike signs), then your answer will be negative. Pretty easy, right?

  • 2 * 2 = 4
  • 3 * -2 = -6
  • -5 * – 2 = 10

Division

Think of division as taking a number of items and dividing them into smaller, equal groups. If you see the problem 4 / 2, it is asking you to divide the 4 into 2 small groups.

The answer you get is how many items are in each group.

  • 4 / 2 = 2

And, as we have already stated, the sign rules also apply to division. So,

  • 12 / -3 = -4
  • -18 / -6 = 3

Lesson Summary

Integers are whole numbers, both positive and negative. You can perform four basic math operations on them: addition, subtraction, multiplication, and division.

When you add integers, remember that positive integers move you to the right on the number line and negative integers move you to the left on the number line.Subtraction is the same thing as adding a negative number.

  • 9 – 4 = 9 + ( -4 )

Multiplication is actually the addition of several identical groups. 3 * 2 is asking you to add three groups of 2.Division is the opposite of multiplication.

With division, you are taking one whole group of items and dividing them into smaller groups that each have the same amount. For example, 24 / 8 is telling you to divide 24 items evenly into 8 groups and asking how many items each group will have – in this case, the answer is 3.For all four mathematical operations, it is most important that you pay attention to the signs to ensure that your final answer is correct.

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