Lesson 2: What does it mean to subtract a negative number? #4

[Video title slide is displayed. It says “Subtract a negative number” and it is highlighted in yellow. Has a whiteboard where she writes down the math equations she is talking about.]

Narrator: So what does it mean to subtract a negative number? Let’s start with an example. 1 - ⁻3. Now I’ve put the negative on the 3 up a little higher just to make sure that you see the difference between the two. Sometimes people will write it as 1- (⁻3) just so that you don’t get the two negative signs blended together. Now what does this mean? Well, we know that the negative means to go in the opposite direction.

[Draws a numberline that goes from  ⁻11 to 11 and then shortly after circles the 1 in blue.]

So if we have our numberline, let’s pull up our numberline. We are starting-let’s get a starting color-we’re starting at one.

 [Draws an arrow starting at 1 in the numberline that is heading to the left]

And now we think, “Ok we gotta go in the opposite direction”, but then we hit this other negative sign that says go in the opposite direction which turns us around. So we were going left and then this one says, “Nope, go the opposite direction again”, so now we’re headed right.

[Draws an arrow on top of the former arrow that is pointing to the right.]

And then we go three; so one, two, three.

[Draws lines like arches that go from 1 to 2, 2 to 3, and 3 to 4 and stops at 4 and circles it in red and adds an =4 to the 1- (⁻3) from earlier.]

So our answer is 4. Well this, the answer four is just the same as 1+3=4 [draws that equation above]. So here we see that a negative and a negative turn into a positive. So 1 - (⁻3) can just be written as a plus sign and a lot of times when you see a negative and a negative together, or even like with  parenthesis around it, you can just make it into a plus sign.

[Draws a 1-3 but then the - sign becomes positive since there were two negative signs consecutively together and then draws another minus sign and then makes it into a positive one to further illustrate the concept that two negatives make one positive.]

Let’s do one more just to practice. So this time let’s start at ⁻5 and we will subtract ⁻2 and this time I’m going to put parentheses around this just so that you can see that this negative sign is different from this negative sign.

[Draws a parenthesis around ⁻2.]

So in this case we start at ⁻5 [circles -5]; the first negative sign tells us to head to the left, but then the second negative sign tells us to head back to the right on the numberline and then we add two; one, two.

[Arrow goes left but consecutive double signs then make it so another arrow is drawn and turns to the right. Then arches are drawn from -5 to -4, and from -4 to -3 to illustrate the movement illustrated in the equation. She draws the same arches in the numberline in red bottom of the ones she made in blue and then at the bottom states -5+2=-3 and he -3 is in red.]

So our answer is ⁻3. And recall that this is the same as ⁻5+2 because in the case of ⁻5+2 we would start at ⁻5, again, and add two, meaning go to the right two places; one, two which equals ⁻3. So once again, the ⁻5 - ⁻2 is just the same as ⁻5+2.  

[End of video]