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What are Multiplicative Inverses?

What are multiplicative inverses?

Summary

  1. If the product of two numbers is equal to 1, then those numbers are multiplicative inverses!
  2. Remember, "product" just means multiplication
  3. The numbers 5/3 and 3/5 are multiplicative inverses!
  4. If we didn't know the multiplicative inverse of 5/3, how would we find it?
  5. We can take the reciprocal of 5/3 to find it's multiplicative inverse
  6. To find a reciprocal of a fraction, you just have to flip the top and bottom of that fraction!

Notes

    1. Remember, "product" just means multiplication
    1. For example, 2 and 1/2 are multiplicative inverses because 2•(1/2)=1
    1. The reciprocal of a number is just that number as a fraction, but flipped over
    1. The numbers 5/3 and 3/5 are multiplicative inverses!
    2. That means their product is equal to 1
    1. (5/3)•(3/5)=1
    2. The 3's and 5's cancel out, and we're left with 1 as our answer
    1. Since the product of 5/3 and 3/5 is equal to 1, they must be multiplicative inverses
    2. Remember, "product" just means multiplication
    1. Since the product of 5/3 and 3/5 is equal to 1, they must be multiplicative inverses
    1. How would we figure out any number's multiplicative inverse?
    1. Multiplicative inverses have a product that equals 1
    2. Remember, "product" means multiplication
    1. Multiplying a number by it's reciprocal will always be equal to 1
    2. So a number and it's reciprocal MUST be multiplicative inverses!
    3. The reciprocal of a fraction is a number that you get from switching the top and bottom of the original fraction
    1. If you want to find the reciprocal of a whole number just turn it into a fraction by putting it over 1
    2. For example, the fraction form of 4 is 4/1
    3. Then you can just flip the fraction!
    4. So the reciprocal of 4 (or 4/1) is 1/4
    1. You just have to flip the fraction to find a reciprocal
    1. To find 3/5, we just found the reciprocal of 5/3
    2. To find a reciprocal of a fraction, we just have to flip the fraction and make the top the bottom, and the bottom the top
    1. Remember, "product" just means multiplication
    2. Multiplicative inverses have a product equal to 1
    1. Multiplicative inverses have a product equal to 1
    2. Remember, "product" just means multiplication
    3. (5/3)•(3/5)=1 because the 3's and 5's cancel out leaving just the 1