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What thought process would you use when trying to find the additive or multiplication inverse of a number or expression?
Additive inverse: change all signs. Multiplicative inverse: flip it over.
What is the additive inverse of a over 3?
It is -a/3
Multiplicative inverse of -3?
The multiplicative inverse of -3 is -(1/3) or negative one-third. The multiplicative inverse of a number is the number that you multiply it by to get a result of 1 (the multiplicative identity). So, since -3 times -(1/3) is 1, -(1/3) is the multiplicative inverse of -3. Similarly, +3 is the ADDITIVE inverse of -3. The additive inverse of a number is the number you add to it to get a result of 0 (the additive identity). So, since -3 + (+3) = 0, +3 is the additive inverse of -3. The original answer given here was that the multiplicative inverse of -3 is +3, which is flat incorrect.
What is the additive inverse of -2 over -3?
-5
What is the additive inverse of 1 over 4?
-1/4
What is the additive inverse of 1 over 2?
-1/2
What is the additive inverse of fraction -4 over 7?
4/7
What is the additive inverse of 3 over 4?
Oh, dude, the additive inverse of 3 over 4 is -3 over 4. It's like flipping the sign of the fraction, you know? So, if you owed someone 3/4 of a pizza, the additive inverse would mean you now have 3/4 of a pizza. Cool, right?
What is the additive inverse of negative seven over nine?
+7/9, positive seven over nine.
Whats the Multiplicative Inverse of negative fifteen and two thirds?
If the multiplicative inverse of a number is the number that you could multiply with the original number in order to obtain one, then the mulitplicative inverse of -15 and 2/3 is -3/47 negative three fourtysevenths, or negative three over fourtyseven.
What does inverse mean in mathematics?
It depends on the context. The additive inverse of a number, X, is the number -X such that their sum is 0. The multiplicative inverse of a (non-zero) number, Y, is the number -Y such that their product is 1. The inverse of a function f, is the function g (over appropriate domains and ranges) such that if f(X) = Y then g(Y) = X. So, for example, if f(X) = 2X then g(X) = X/2 or if f(X) = exp(X) then g(X) = ln(X), and so on.
Why when multiplying two negative numbers do you get a positive number?
The answer has to do with the fundamental properties of operations on numbers (the notions of "addition", "subtraction", "multiplication", and "division"). Each number has an "additive inverse" associated to it (a sort of "opposite" number), which when added to the original number gives zero. This is in fact the reason why the negative numbers were introduced: so that each positive number would have an additive inverse. For example, the inverse of 3 is -3, and the inverse of -3 is 3. Note that when you take the inverse of an inverse you get the same number back again: "-(-3)" means "the inverse of -3", which is 3 (because 3 is the number which, when added to -3, gives zero). To put it another way, if you change sign twice, you get back to the original sign. Now, any time you change the sign of one of the factors in a product, you change the sign of the product: (-something) × (something else) is the inverse of (something) × (something else), because when you add them (and use the fact that multiplication needs to distribute over addition), you get zero. For example, (-3) ´ (-4) is the inverse of (3) ´ (-4) because when you add them and use the distributive law, you get . (-3) ´ (-4) + (3) ´ (-4) = (-3 + 3) ´ (-4) = 0 ´ (-4) = 0 So (-3) ´ (-4) is the inverse of (3) ´ (-4) , which is itself (by similar reasoning) the inverse of 3 ´ 7. Therefore, (-3) ´ (-4) is the inverse of the inverse; in other words, the inverse of -12 in other words, 12. The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.
