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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.
How can you use addition of integers to subtract integers?
Subtracting an integer is the same as adding the additive inverse. In symbols: a - b = a + (-b), where "-b" is the additive inverse (the opposite) of b.
What is the opposite of an improper fraction?
The answer depends on what you mean by "opposite". Many users mean additive inverse - in which case it is a negative improper fraction. Some use the term to refer to the multiplicative inverse, in which case it is a proper fraction.
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.
How do you use real numbers in real world situations?
Unless you are an electrical engineer or a math teacher, every number you will ever use in a real world situation will be a real number.
