**Middle School Number Sense Lesson 32: Finding the Reciprocal**

This question type showed up

**18 times**this year (on average

**once per test**). The average placement was at question # 34, with the median at

**question # 28**.

**Number Dojo Level: 79**

The

**reciprocal**of a number is also called its

**multiplicative inverse**. You can divide 1 by any number to find the number's reciprocal. Also, the product of any number and its reciprocal is

**always 1**. There are several types of questions that appear on number sense tests; I will demonstrate how to find the solution to each type.

To find the reciprocal of a:

**Whole number**(Integer): Write it as a fraction's denominator, with 1 as the numerator**Fraction**: Flip it over. In other words, switch its denominator and numerator.**Mixed Number**: Convert it to an improper fraction, and then flip it over.**Decimal**: Convert it to a fraction, and then flip it over.

Be sure to pay attention to what's after the answer blank. The test writers will often ask for a specific type of answer, such as

**decimal**,

**mixed number**, or

**fraction**.

**Example 1: The multiplicative inverse of 5 is ___**

- There is no specific type of answer required. Simply write a fraction with 5 on the bottom and 1 on the top. The answer is
**1/5**. (.2 would also be correct).

**Example 2: The reciprocal of 3/7 is ___**

- There is no specific type of answer required. Simply flip the fraction over and write
**7/3**. (2 1/3 would also be correct).

Example 3: The reciprocal of -5/8 is ___ (decimal)

Example 3: The reciprocal of -5/8 is ___ (decimal)

- Flip the fraction over to get
**-****8/5**. - Convert -8/5 to a decimal. (Review
**ConvFracDeci**if necessary). The answer is**-****1.6**.

**Example 4: The multiplicative inverse of 7/16 is ___ (mixed number)**

- Flip the fraction over to get
**16/7**. - Convert to a mixed number. The answer is
**2 2/7**.

**Example 5: The reciprocal of 1.3 is ___ (fraction)**

- Convert the decimal to a fraction. (Review
**ConvDeciFrac**if necessary). You get 13/10. - Flip the fraction over to get
**10/13**.

**Example 6: The reciprocal of -2.4 is ___ (fraction)**

- Convert the decimal to a fraction: -24/10 =
**-12/5**. - Flip the fraction over to get
**-5/12**.

**Example 7: The multiplicative inverse of 0.4 is ___ (mixed number)**

- Convert the decimal to a fraction: 4/10 =
**2/5**. - Flip the fraction over to get
**5/2**. - Convert it to a mixed number:
**2 1/2**.

**Here's a free worksheet to help you practice Reciprocal:**

reciprocal.pdf |

**Up Next for Middle School: PrimeFactor**