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Negative numbers are a little crazy the first time you think about
them, but you will see that they are needed in math. In 4th grade, I
asked my teacher what five minus ten was. She told me that there
was no answer. What? I asked her how that was, but she did not
want to pursue it. Most kids will become confused if you teach them
something like this, and they will mix it up with the simple math
they are learning at the time. The answer to five minus ten is negative five. A negative number has a "Minus" operator in front of it, but there is no space between the "Minus" and the number. One number below zero is negative one. Two numbers below zero is negative two. This goes on to infinity. Look at this: -5 -4 -3 -2 -1 0 1 2 3 4 5 -+---+---+---+---+---+---+---+---+---+---+ This is a simple scale. You can use it to add and subtract. Lets use it to add 1 + 1. Find one on the line. Since we are adding,
we will move to the right one number. We land on 2. If
we subtract, we move to the left. Let us explore 1 - 1.
Find one on the line, now count over to the left one. We land on
zero. This is true. If I have one rock, and someone takes one rock
from me, I have zero rocks left. Now lets look at this one 1 - 3. First lets think about
this. Say I have one rock. Someone walks up and says give me three
rocks. I can't. I have only one rock. No matter how much I would like
to, I can not give more than I have. In math, this is not an
impossibility, it is, in fact necessary. Let's go to the number line. Start
on the one, because I have one rock. Now, we are subtracting, so we
move left, and we are subtracting three, so we move left three
numbers. 1... 0... -1... -2. The answer is negative
two. This can apply in the real world when you think about money.
urn my rocks into dollars, and say the bank needs three dollars. I
end up owing the bank two dollars. I have negative two dollars.There must be negative numbers for a lot of reasons. One of the most important reasons is so that the manipulation of equations can take place. Most equation manipulation is only useful when solving, so I cover that in the Problem Solving lesson, Lesson 2. You can also add, multiply and divide negative numbers. You can do anything to a negative number that you can do to a positive number. Say you want to add two negative numbers. -5 + -5 = x.
We can go back to out number line. Here is a bigger one for
reference: -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 -+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+--- Start at negative five. Now, we are adding, so we will be moving to the right. But we are adding a negative number, so this reverses the direction. We now go left five numbers. We get negative ten. This would be like if I owed the bank five bucks. Then I go and buy a five dollar rock, and pay by check. The bank would add negative five to my account. I now owe ten. You may notice that -5 + -5 is exactly the same as
-5 - 5. This is true! Try it on the number line. If your second number is negative, change the direction you count on the number line. Matters become complicated when multiplying with negative numbers. Imagine seven people. Each owes the bank ten dollars. They all get together and decide how much they all owe together. 7 * -10 = x They would eventually find that x = -70, meaning they owed a total of $70. They could have made the equation like this: -10 * 7 = x They would have gotten the same number. When multiplying integers, if one of the numbers is negative, and one is positive, the result (answer) will always be negative. That's really all you need to know to master negative multiplication. Two positive integers multiplied yield a positive number, and two negative integers multiplied yield a positive number. -10 * -10 = 100If you want to know why -10 times -10 is +100, go ask someone. It is too lengthy of an explanation to include in this tutorial. Division is very similar to multiplication. In fact is just the same. Remember that if there is a negative number and a positive, the result is negative. If both are positive, or both are negative, the result will be positive.
10 / 2 = 5When multiplying or dividing, I completely ignore all positive or negative signs, until I know the result. Then I look to see if there are two different signs involved. If so, I make my answer negative. |