Addition and Subtraction
Numbers lines are particularly useful with addition and subtraction problems. Remember that apple piracy I mentioned? That's a great way to learn subtraction if you happen to have a bunch of apples handy. But, you can do that problem with a number line.
I said you had eight apples. So, find the 8 on the line below. Then, I took five. Since this is subtraction, we go to the left. Why? Because when you subtract, your number's left. Okay, count back 5. We're at 3. So, you have three apples left! That's enough for a tart, right?
You can use a number line for subtraction.
Now, what if I gave you back four apples? Okay, this is addition, so move to the right. Why? Because getting more numbers is just right. Okay, count one, two, three, four. And, we're at 7. I think we're back in pie territory.
Negative Numbers
Number lines are a great way to work with negative numbers. You can't have -4 apples. I may be an apple thief, but I'm not that good. But, on a number line, you can solve problems involving negatives.
What's -8 + 5? Start at -8 below and move 5 which way? It's addition, so go right. One, two, three, four, five: -3. -8 + 5 = -3.
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You can use a number line to solve problems that have negative numbers.
What about 2 - 9? Start at 2 and move 9 to the left - for subtraction. One, two, three, four, five, six, seven, eight, nine. We're at -7, so 2 - 9 = -7.
Sometimes, you'll need to bounce back and forth between the positive and negative sides of the origin. But, the principle of what you're doing doesn't change. What is 9 - 12 + 4 - 2?
Whoa. This would be a mess with apples. But, we can do it with a number line. Start at 9 below, then move 12 - where? Your number's left, so go left. Now, we're at -3. If we add 4, we go which way? Getting more is right, so go right. Now, we're at positive 1. Then, we go left 2, and we're at -1. So, 9 - 12 + 4 - 2 = -1. With a number line, that wasn't so bad, was it?