Using this idea, (−2) − (−9) would mean the distance between −2 and −9, which is 7. If we wrote 2 − 5 instead, it wouldn't work, because distance can't be negative. However, you need to write the greater number first! You can think of the difference as the distance between the two numbers on the number line.
![integer numbers help integer numbers help](https://codingfinder.com/wp-content/uploads/2020/04/string-into-integer.jpeg)
Remind the students that 5 − 2 denotes the difference of 5 and 2, which is 3. Now, we can take away three negatives, which leaves +8. We cannot take away three negative counters, so we'll add three negative-positive pairs (which amounts to adding zero). How do you do that? The trick is to first add enough negative-positive pairs to the situation, which amounts to adding zero, so it is allowed. For example, in 5 − (−3), you start out with 5 positive counters, but you are supposed to take away 3 negative counters when you don't have any. In other situations, you may not initially have the counters that you are supposed to take away. For example, with (−4) − (−2), you start out with 4 negative counters and you take away two negative counters. The basic idea is to interpret subtraction as "taking away". Counters are trickier to use with subtraction, but we can do it.Students are led to discover the shortcut that two negatives turns into a positive! Observe the pattern and see what happens: 3 − 3 = The last pattern I show here actually justifies the rule for subtracting a negative integer, such as 7 − (−2). This is of course conceptually the same as number line jumps. (−4) − 8 means the temperature is −4° now and drops 8 degrees. Ask the students to observe the answers, and then continue the pattern: (−4) + 2 =Īnother great idea is to use a change in temperature: 5 − 9 means the temperature is 5° and drops 9 degrees. Do a little pattern for the student to solve, and observe what happens with the answers: 3 − 1 = First, consider subtracting a positive integer. Patterns can be used to justify the common rules for subtracting integers.Please also see these animations that illustrate adding and subtracting integers on a number line.
![integer numbers help integer numbers help](https://www.math-drills.com/integers/images/integers_addition_all_parentheses_-09to09_001_300.002.jpg)
![integer numbers help integer numbers help](http://www.math.com/school/subject1/images/S1U1L11EX.gif)
![integer numbers help integer numbers help](https://media.cheggcdn.com/media/705/7053c4ca-4e44-49f8-b61c-d9a3a53179a6/phpqX3my8.png)
Problem such as −4 − (−8) would mean that you start at −4, you get ready to move 8 units to the left (the "minus sign"), but the second minus sign reverses your direction, and you go 8 units to the right instead, ending at 4. Subtracting a negative integer using number line movements is a bit trickier. This is identical to interpreting the addition −4 + (−3) on the number line. Similarly, −4 − 3 would mean that you start at −4 and move 3 units to the left, ending at −7. This is identical to interpreting the addition 2 + (−5) on the number line. Here, 2 − 5 would mean that you start at 2 and move 5 units to the left, ending at −3. Personally, when subtracting a positive integer, I think in terms of jumps on the number line, and when subtracting a negative integer ("the double negative"), I change those to additions.
Integer numbers help how to#
You have several options how to present subtraction of integers. For example: + + + + + − − −Įach plus-minus pair cancels, so the answer is positive 2.Įach plus-minus pair cancels, so the answer is −5. These are represented as little circles with + or − signs drawn inside them, or something similar.