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Just remember these rules:
- Multiplying two negatives results in a positive
- Multiplying two positives results in a positive
- Multiplying a negative with a positive results in a negative
- Multiplying a positive with a negative results in a negative
1) If you are multiplying a positive and a negative number just multiply the numbers and put the negative sign beside the product. The negative sign gives the direction on the number line. For example, if we have, (-2)(3) = -6. It means three times two gives 6 in the negative direction of the number line. Otherwise you can say (-2) + (-2) + (-2) = -6 2) If you are multiplying a negative number with a negative number just multiply the numbers and put the positive sign (probably no sign). There may not be a rigorous proof. But, it could be shown as follows:
Before that remember this: For any number a,
1) a.0 = 0.a = 0
2) a + (-a) = (-a) + a = 0 -a is called as additive inverse or the opposite of a.
3) a(b + c) = a.b + b.c This is called as distributive property.
4) Adding a constant on both the sides of an equation will not affect the equation.
(-1)(0) = (-1)[1 – 1]
0 = (-1)(1) + (-1)(-1)
0 = -1 + (-1)(-1)
0 + 1 = -1 + 1 +(-1)(-1)
1 = (0) + (-1)(-1)1 = (-1)(-1)
Source: www.icoachmath.com
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What is an easy way to add intgers that are negative and positive?
-11+4=
If the discriminant is a perfect square then the answer is this?
If the discriminant is a perfect square, it makes calculation easy on paper. Otherwise, the only property of the discriminant that matters is whether it is positive, negative or zero.
Subtract -10 from -15?
Alright, buckle up buttercup. When you subtract a negative, it's like adding a positive. So, -15 minus -10 is the same as -15 plus 10, which equals -5. There you have it, simple math for your beautiful brain.
Why does the inequality sign change when both sides are multilpied or divided by a negative number?
I bet you're thinking of > and <, the "greater than" and the "less than" signs, and not the "inequality" thing-- the = sign with a / through it. Am I right? Think about the positive integers 3 and 5. It should be easy to see that 3 is smaller than 5. Now here's a trick. If you think about the number line, even if you go back and forth over the zero point, "smaller" is always to the left, and "greater" is always to the right. __________________________________________________________ -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 <-------------- smaller larger ---------------> The weird thing is that when you're moving to the left and you cross zero, the numbers look like they're getting bigger-- except for the negative sign. You have to use your imagination with these negative integers. Say that you have 10 cd's. If I take two of them, I'm really adding "negative 2" to the total. This leaves you with 8 cd's. The "negative 2" made you total smaller, but not by much. I give back the two I took, and now I take 8 of them. I'm really adding "negative 8" to the 10 cd's. This leaves you with only two! So the "negative 8" had the effect of making your collection MUCH smaller than the "negative 2" did. So in a sense, the -8 is "smaller" than the -2. It fits with the number line, and the fact that numbers get smaller as you move to the left. Now back to 3 and 5. Look at the number line. +3 < +5. three is smaller than 5. If I multiply them both by -1, I now have -3 and -5. If you look at the number line, you will see that -5 is to the left of -3! This means that -3 > -5. So to put it simply... when you multiply or divide a number with a negative number, the number becomes a negative number, therefore causing it to be smaller than the original number. Therefore the sign changes accordingly.
Is negative 3 a rational number or irrational number?
'-3' is RATIONAL. IRRATIONAL numbers are those where the decimals go to inifinity AND there is no regular order in the decimal digits. e.g. pi = 3.141592..... is IRRATIONAL but 1/3 = 0.3333.... is RATIONAL. NB Both go to infinity, but '1/3' has the decimals in a regular order .
