To illustrate the sum −2 + 4 on the number line, we start at −2 and jump 4 steps to the right. We practice this idea with several examples, including some with two jumps. Then we look at subtraction. For example, 3 − 4 means you start at 3 and jump 4 steps to the left (towards smaller numbers).
In this second part, we look at adding or subtracting a negative integer. First, adding a negative integer turns out to be the same as subtraction. For example, 4 + (−5) is the same as 4 − 5.
Subtracting a negative integer on a number line is an interesting situation. For example, if you compare 2 − (−6) with 2 − 6, surely the two cannot be the same. In 2 − 6, we start at 2 and go 6 steps to the left. In 2 − (−6), we also start at 2. The subtraction means we'd go to the left, BUT since it's a NEGATIVE number we're subtracting, that as if turns us the opposite way and we go RIGHT instead. So, it ends up being the same as 2 + 6.
Math Mammoth Integers — a self-teaching worktext with explanations & exercises for all operations with integers
Math Mammoth Grade 7 complete curriculum