Interpreting numeric expressions example

- Which of the following is a correct interpretation of the expression one plus six? Well before I even read this, let's just think about what's happening in one plus six on the number line. I'm going to start at one, which is going to be one to the right of zero. And then I'm going to add another six. I'm going to go six more to the right of zero to end up at seven, which is going to be seven to the right of zero. The number that is six to the left of one on the number line. Now six to the left of one, in this type of a number line, which is the standard number line, where to the right is positive and to the left is negative. If you move six to the left that means you're subtracting six from one so that's not right. We're adding six. The number that is six to the right of one on the number line. Yeah, that's exactly right. We're going six to the right. If you're adding six you're moving to the right. You're going to increase. So that's definitely going to be the choice. Let's keep going. Which of the following is a correct interpretation of the expression three plus negative seven? So before I even look at these choices, one way I would think about it is I would start at three and then I would move seven to the left of three. I'm adding negative sevens. So this is the same thing as three minus seven. So I'd move seven to the left of three. So let's see they would say. Start at seven on the number line and move three to the left. Well that doesn't make sense. I want to start at three. And let's skip over to here. Start at three on the number line and move seven to the left. Yeah, that's exactly right. We're going to start at three, and then we're going to move seven in the negative direction into the left, if our convention, which is our standard convention, that to the left is negative and to the right is more positive. So that's going to be exactly right. Let's do one more. So now they have three minus negative four. Well one way to think about it is three minus negative four is the same thing if you subtract a negative, it's the same thing as adding the positive version. So it's the same thing as three plus four. And so I would want to start at three and then move four to the right. Because once again this is the same thing as three plus four. Three minus negative four is the same thing as three plus four. So I want to start at three and move four to the right. Start at three and move four to the right. This would be the same thing as three plus four which is the same thing as that expression.