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Subtracting Integers on a Number Line

By Kathleen Knowles, 07 Oct 2020

Subtracting integers on a number line is easy as pie! All you need is a number line, some numbers, and a reason to subtract. It's really that easy. Let's start by reviewing some key terms.

What is an Integer?

Integers are countable, whole numbers. Positive and negative whole numbers are integers. Examples include 3, -3, 5, 0, etc. If you cannot write a number as a whole number, it is not an integer. That means that fractions and decimals are not integers.

You can write integers using set notation.

{ … -3, -2, -1, 0, 1, 2, 3, … }

The ellipsis means that the numbers continue in both directions and keep going and going...

What is a Number Line?

A number line is a handy tool! It is a horizontal line that shows consecutive numbers in equal intervals. The center of the line is at the zero mark, and it is called the Origin of the number line. On the right of the zero mark is the positive side, while the left of the zero mark is the negative side. You write negative numbers with a minus sign in front of them, e.g., -5. All number lines have arrowheads at one or both ends of the line to show that the numbers continue.

Although a number line includes all real numbers, our number line for this article uses only integers. A number line helps you visualize and understand the concept of numbers less than zero, subtraction, and addition.

Finding Numbers On The Number Line

Now let's see how to find integers on a number line.

Example 1

Today is your first day at your new school. Your mum gave you two biscuits for lunch. How can you locate the two biscuits on the number line?

  1. The first step is to draw your number line.
  2. Next, mark the Origin of your number line with zero. Then, write numbers 1-5 to the right of the Origin.
  3. You have a positive number of biscuits since they have not been eaten. (Even if they have been eaten, you can only go down to zero.) Count two places to the right on your number line, and you will end at 2.
  4. That is the position of your biscuits on the number line!

Example 2

Now imagine again that your dad gave you and your brother some apples. But you like apples a lot, so you ate all your apples. The next day, while going to school, you had no apples while your brother still had 5 apples. So you took 2 apples from him and promised to give him 2 the next time you got apples. How do you show the debt you owe to your brother on the number line?

  1. Once again, draw your number line. This time, you don't have any apples, and the 2 apples you are going to eat in school are not yours. They are your brother's. This means that the 2 apples are not positive but negative. Negative numbers are less than 0.
  2. So, write out the integers -1 to -5 to the left of your Origin.
  3. Now, count 2 spaces to the left on your number line. You will land on -2!

Subtracting Integers Using a Number Line

If you want to subtract integers using a number line, you are finding the difference between two numbers. You may also think of it as finding the distance between the two numbers. Measuring this distance is subtraction. Three things to remember:

  • When you subtract from a positive number, count to the left.
  • When you subtract from a negative number with a positive, you count to the left. You create a bigger negative.
  • When you subtract from a negative number with another negative, you count to the right. You increase the number.

Now that you can locate your numbers on the number line subtracting numbers should be a breeze!

Example 1

Subtract 3 from 7 using the number line.

This means

7 – 3

The first step is to locate 7 on the number line. If you start at 7 and count 3 steps to the left, you will end at 4. This means that 7 – 3 = 4.

You can think of it this way. You had 7 apples, and you gave your friend 3. You will have 4 apples left.

Example 2

Subtract 2 from -5.

This means

-5 – 2

The first step here is also to locate -5 on your number line. The 2 is positive. So since you are subtracting a positive number, you will count 2 steps to the left. This also means that you are decreasing the initial number by 2. Two steps to the left, and you will end at -7.

-5 – 2 = -7

Think of it this way. You already owe someone 5 mangoes. Then your sister is hungry, and she wants to eat two mangoes. But you don't have any mangoes! What should you do so your sister stops crying for mangoes? You borrow two more mangoes to give her. So you now owe a total of 7 mangoes.

Example 3

Subtract -2 from -6.

This means

-6 – ( - 2 )

The first step is to locate -6 on the number line. The number you are subtracting now is -2, which is a negative number, so you count 2 steps to the right. You will end at -4. The double negative signs turn the -2 into a positive 2.

-6 – ( - 2 ) = ?

-6 + 2 = -4

The best way to think of this subtraction of negative numbers is to imagine that you owe your friend $6. But your friend is very kind and decides to forgive $2 of the debt. Now, you only have to pay back $4.

Wrapping Up

And that's all there is to it! With practice, you can confidently handle subtracting integers using a number line. It is an excellent tool to help you visualize the math.

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