![]() Lets say you are an Ancient Philosopher who was building up mathematics who was building mathematics from the ground up And you already have a reasonable of what a negative number could or should represent and you know how to add and subtract negative numbers But now you are faced with a conundrum What happens when you multiply negative numbers? Either when you multiply a positive number times a negative number Or when you multiply two negative numbers So, for example You aren't quite sure what should happen if you were to multiply (and im just picking two numbers where one is positive and one is negative) What would happen if you were to multiply 5 times negative 3 You're not quite sure about this just yet You're also not quite sure what would happen if you multiply two negative numbers. Hope this explains most of the things, and helps you understand your problems At each step, the 7 arrows going toward the right are "pushed back" by two more arrows going toward the left. s twice, but we don't have any available, so end up with -10.Īs a final example, let's start at another value not 0, but is positive. We finish with 7 if we only want the total (instead of subtraction).īy the same reasoning, this is also why - × P and P × - equal negatives.ģ. But the 2 arrows toward the left are saying that the line also moved "backwards" 2 steps. The nine arrows toward the right say the line moved "forward" 9 steps. For example, -2×-4=8, where we take away 4 negative 2s. (I meant to have the zeros lined up so they would be on top of each other, but for some reason, what I typed on the editor and the later displayed format are somewhat different sorry about that.)Ī negative times a negative will equal a positive because what was originally negative has been reversed in direction. Arrows pointing toward the right are positive, and arrows pointing toward the left are negative. Each individual arrow represents a step, the next whole number. The 0 is where the 0 is, the left is negatives (decrease), and the right is positive (increase). Vice versa, if a negative number comes after the subtraction sign, it means you move to the right instead of to the left on the number line.A positive times a positive is positive because the positive value is being increased a positive number of times. That is, if a negative number comes after the addition sign, it means you move to the left instead of the right on the number line. ![]() When a negative number comes after the addition or subtraction sign, it means you have to reverse the normal direction. Or think in terms of giving or receiving cookies. I have to give you what I owe so I end up with only 2 cookies. Starting at -1, move 3 steps to the right on the number line. The plus or addition sign tells us to move to the right on the number line. If I have 1 cookie (1) and I want to give you 3 cookies (-3), that means I owe you 2 cookies (-2). Starting at number 1, move 3 steps to the left on the number line. The subtraction tells us to move to the left on the number line. The other thing to note is that the addition symbol (+) tells us to move to the right of the number line while the subtraction symbol (-) tells us to move to the left of the number line. The negative symbol applies only to the number it is paired with. The subtraction symbol tells us which direction we want to go along the number line. They both look the same but have different meanings. The first thing to understand is the difference in the meaning between the subtraction symbol (-) and the negative number symbol (-). When it comes to using negative numbers in addition and subtraction, using a number line is crucial for understanding how it all works. Therefore, -5 is smaller than -3 because you are further away from zero.Īdding and Subtracting with Negative Numbers.So -3 means you are 3 steps away from 0 and -5 means you are 5 steps away from zero.The negative sign tells you how far away the number is from the zero.To help my students understand better, I tell them to think of negative numbers this way: The negative numbers also increases digitally as you move to the left of the line, but the negative sign means the value of the number actually decreases.The number line has to beginning and no ending, indicated by the arrow on both ends of the line.
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