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
