How to change subtraction of integers into an addition — and WHY it works

In this pre-algebra or grade 7 math lesson, I show how integer subtraction works, first of all, based on two simple patterns. If we continue them logically, we see that subtracting an integer works the same as adding the opposite of that integer. The second pattern makes it especially easy to see WHY subtracting a negative integer changes into addition. It's the shortcut of a double negative turning into a positive.

Then I solve several simple examples, such as −6 − (−2) and others. Next, I show how subtraction of integers works on a NUMBER LINE (as jumps).

In the latter part, we study more complex examples of mixed integer additions and subtractions. With those, you can either solve the operations one by one (from left to right) — or convert each subtraction into an addition first, then add all the positives separately and all the negatives separately, and lastly add the two sums.

Tengo una versión español de este video también.

See also

Addition of integers — a video lesson

Multiplication of integers — a video lesson

Math Mammoth Integers — a self-teaching worktext with explanations & exercises for all operations with integers

Math Mammoth Grade 7 complete curriculum

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