I have four numbers: 9, -0.83, 3/10, and -5 1/3. I‘m supposed to use two of them to illustrate distributive property. I know how to do that, but the next step is, Give the additive inverse of one of your numbers. Then, in a separate problem, I‘m guessing, Give the multiplicative inverse of one of your numbers. I‘m really confused. What are additive and multiplicative inverses? Thanks.
Additive inverse is also known as the opposite the additive inverse of 12 is -12 12+-120 multiplicative inverse of 12 is 1/12 12*1/121
Additive inverse is just a fancy way of saying the negative of a number. For example, the negative of 5 is -5. The negative of -47 is 47. You get it by putting a negative sign infront of the number and simplifying (two negatives make a positive). The multiplicative inverse is just a fancy way of saying reciprocal. What exactly is a reciprocal? Well, you can remember by this: - recycle - to start a different cycle in - pro - for - cal - belonging to. It might be confusing at first. But think of it as turning over the fraction. Basically, when you divide one by a number, you'll get the reciprocal. The reciprocal of 5 is 1/5. The reciprocal of 1/2 is 2. The combination of them, the negative inverse, is used if you want to find the slope of a line perpendicular to another, the slope of the second line is the negative reciprocal of the first one (-1/m, where m is the slope of the line with the equation, y mx + b). But you probably don't need that until you start calculus. In the example you gave, you have x which is -4/7: - The negative (-x) is 4/7. - The reciprocal (1/x) is -7/4, which simplifies to -1 and 3/4. - The negative reciprocal (-1/x) is 7/4 or 1 and 3/4. The fractions could be simplified further into decimals, but I don't have any good way of rendering repeating decimals on here so I won't.
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The additive inverse is the number that, when added to your original number, gives you zero. This is just the negative of the number. The multiplicative inverse is the number that you multiply your original number by to get 1. This is 1/x, x being your number. so 1/9, 10/3 etc.
