**High School Number Sense Lesson 83: Finding the Reciprocal (2 or More Calculations)**

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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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**.

**Example 4:**

**The multiplicative inverse of 7**

^{-1}is ___1. 7

^{-1}=

**1/7**.

2. The reciprocal is

**7**.

**Example 5: The multiplicative inverse of |-7| is ___**

- |-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**.

**Up Next for High School: EstOrderOfOp**