# Addition Rule

How to use the addition rule:

Addition: To

To show subtraction using the addition rule: To show for instance 5 - 8, position the zero of the lower ruler under the 8 on the top. The number underneath 5 is then the number which when added to 8 gives 5, or -3. Here are a few more to try: 8 - 7; -2 - 9; 7 - (-4). There's another way of thinking about this subtraction procedure in the case where the first number is bigger than the second: We use the bottom scale as a ruler (in the traditional sense of the word; ignore the negative part to the left) and simply

The addition rule is also a useful tool for coming to terms with algebra. As an illustration, position the 6 of the lower ruler under the 0 of the upper one. Now for any number on the top-- call it NOT ("number on top")-- the number beneath it is NOT + 6. To be even more succinct, abbreviate "NOT" as simply "

If you can think of other uses for the addition rule please let me know.

Addition: To

*illustrate*for example 5 + 7, position, by dragging with the mouse, the 0 (zero) of the lower (red) ruler under the 5 of the upper (blue) ruler. Then, without dragging the rulers past each other, locate the 7 on the lower ruler. The number above it is 5 + 7 = 12. Here are a few more to try: 7 + 2; -8 + 3; 26 + -15. (Helpful hint: you can move the two rulers together by dragging in the middle where they meet.)To show subtraction using the addition rule: To show for instance 5 - 8, position the zero of the lower ruler under the 8 on the top. The number underneath 5 is then the number which when added to 8 gives 5, or -3. Here are a few more to try: 8 - 7; -2 - 9; 7 - (-4). There's another way of thinking about this subtraction procedure in the case where the first number is bigger than the second: We use the bottom scale as a ruler (in the traditional sense of the word; ignore the negative part to the left) and simply

*measure off* the distance (difference) between the two numbers on the upper scale. The procedure is exactly the same. Try 8 - 4 and 6 - (-3).The addition rule is also a useful tool for coming to terms with algebra. As an illustration, position the 6 of the lower ruler under the 0 of the upper one. Now for any number on the top-- call it NOT ("number on top")-- the number beneath it is NOT + 6. To be even more succinct, abbreviate "NOT" as simply "

*n*". Then whatever*n*is, the number beneath it is*n*+ 6. Exercise: Show*n*+ 3 in this way. What about*n* - 2?If you can think of other uses for the addition rule please let me know.