Last summer we introduced reciprocals in our Reciprocal post, and then we showed how to add a fraction and its reciprocal (AddFracRecip). Today we will turn things upside down a bit and maybe even backwards. This concept has appeared 5 times so far this year on high school tests, with a median placement at question # 22.
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Number Dojo Level: 116
These questions require careful attention and careful manipulation. They are not necessarily difficult, but they can be a little confusing as to what is being asked. For example, the opposite of a number is its negative equivalent. Also, multiplicative inverse is just a fancy way to say reciprocal.
Example 1: The reciprocal of the opposite of 2.5 is ___
- The opposite of 2.5 is -2.5.
- To find the reciprocal of -2.5, I like to think of it as -25/10 (instead of thinking of -2 1/2 or converting it to an improper fraction the traditional way).
- The reciprocal is -10/25, which reduces to -2/5.
Example 2: The reciprocal of the opposite of 4.2 is ___
- The opposite of 4.2 is -4.2.
- Think of this as -42/10, which reduces to -22/5.
- The reciprocal is -5/22.
Example 3: The multiplicative inverse of the opposite of -7.2 is ___
- The opposite of -7.2 is 7.2.
- Think of this as 72/10, which reduces to 36/5.
- The reciprocal is 5/36.
- |-7| = 7.
- The reciprocal of 7 is 1/7.
Example 6: The negative reciprocal of 2.5 is ___
- 2.5 is 25/10 or 5/2.
- Its reciprocal is 2/5.
- The negative is -2/5.