Are You Smarter Than a 7th Grader...

[handy]

I'm homeschooling the kids now.

Which is all good except when it comes to my son's math.

I'm pretty much horrible at math, even 7th grade math.

Steve is working with Tom now to help him figure out +/- integers.

Adding +/- is no problem for me, but I seriously cannot understand subtraction of negative numbers.

For instance, here is the example from his textbook that caused me to simply put math away for the day until Daddy came home:

17 - -9= 26

Now, I can fully understand why 300 + -100 = 200... no problems there.

I can understand it because I can visualize it. If I have $300.00 in one account, but I am $100.00 overdrawn in another account, I only have $200.00.

When I can visualize something in this way, I have no problem both understanding and teaching the concept.

But, I simply cannot visualize a "real world" example of 17 - -9= 26.

Can anyone who is good at this sort of thing give me a way to visualize what it happening here?

 

[providence]

But, I simply cannot visualize a "real world" example of 17 - -9= 26.

Subtraction has a geometric interpretation.

Imagine a number line like that on http://en.wikipedia.org/wiki/Number_line. Place a dot at location 17 and another dot a location -9 on the number line. The distance between these dots is 26. You may think of A - B as the distance due east a car must travel to arrive at point A when starting at point B. So, 17 - -9 = 26. However, you get the negative of that result if you subtract in the reverse direction: -9 - 17 = -26. That occurs because traveling -26 units east is interpreted as traveling 26 units west. The point at -9 is west of the point 17.

Here's two more examples: -5 - -7 = 2 and -7 - -5 = -2.

It's also useful to know that subtracting a negative number is the same as adding a positive number. The two adjacent negatives cancel. So, 17 - -9 is the same as 17 + 9 = 26. It's kind-of like how saying "I'm not not going to the store" is logically equivalent to saying "I'm going to the store." You can verify this because the distance to point 17 from point -9 on the number line is equivalent to the sum of two separate distances (9 and 17), as if the car makes a stop at the origin (point 0 on the number line) in the middle of the trip.

Just as 17 - -9 = 26 can be understood as the distance traveled east to arrive at point 17 from point -9, you can also understand it as the amount of $ you need to add to a bank account that is $9 overdrawn so that the balance is $17.

 

[Milk-Drops]

I remembered the concept by just remembering that a Double Negative in math equals a positive. Subtracting a negative is adding a positive.

A real world example could be. Jimmy is 200 dollars in Debt (-200). His bank decides to help him out with a grant that will subtract 90 dollars(-90) of his debt. Jimmy ends up with only 110 dollars of debt.(-110).

The equation would look like -200 - -90 = -110 or -200 + 90 = -110

I hope that helps.