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Adding and Subtracting Integers

Integers can be positive or negative numbers. Adding positive integers is relatively straightforward.

Adding With Negative Integers

Think of a situation where one person has six dollars and the other owes (or was in debt) two dollars. If they got together, what is the total amount of money they have between them?

Owing (being in debt) $2 can be represented by -2. Adding -2 and 6 together can be shown like this:-2 + 6 = 4

Adding To a Negative Integer

Integer line showing -2 + 6  = 4

The example above shows adding a positive integer to a negative integer by moving to the right on a number line.

Adding a Negative Integer

The example below shows adding a negative integer to a positive integer by moving to the left on a number line.

Integer line showing adding -2 to 6 to give 4

Think of adding a negative number the same as being given a fine – the end result is that you will have less!

More Examples of Adding With Negative Integers

Subtracting With Negative Numbers

Subtracting From Negative Integers

When subtracting positive numbers using a number line we move to the left on the line.

Number line illustrating -4 - 3

Subtracting Negative Integers

When subtracting negative numbers we move to the right. Moving to the left by a negative number is the same as moving to the right by the opposite positive number.

What would you do if someone asked you to walk -3 miles to the north?

You could walk 3 miles to the south!

When explaining the subtraction of negative numbers do not use phrases like “take away” as it does not make any sense to take away a negative number. You can relate subtraction of negative numbers to situations where subtraction is used to find the difference between two values. e.g. the temperature difference between 8 degrees and -4 degrees can be shown as 8 – (-4) = 12.

Changes in Temperature

Depending where you live you might experience temperatures below zero degrees. In such cases integers are useful for showing temperature and changes in temperature. For example, if the temperature during the day is 16 degrees and overnight it falls to -9 degrees, by how much did the temperature change?

-9 – 16 = -25

Another way is to think how far -9 is from zero and how far 16 is from zero.

Once we work out these as being 9 and 16 we can add them together to get a difference of -25 (we use the negative sign because the temperature is falling.)

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