- Topics At a Glance
- Different Types of Numbers
- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
**Comparing Fractions**- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
**Multiplicative Inverses**- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
- Things to Do with Real Numbers
- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

Every fraction with a nonzero numerator has a **multiplicative inverse**, which is simply the number we can multiply our fraction by to get 1. You'll find that we are very often striving to get back to one or to "achieve oneness." *Om*...

**Sample Problem**

The multiplicative inverse of is -4, since () × (-4) = 1

**Sample Problem**

The multiplicative inverse of is , since × = 1.

The multiplicative inverse of a fraction is called the reciprocal, and is the upside-down version of that fraction. Don't take us too literally here—you won't be converting to a fraction on its head. Instead, you're just pulling the old switcheroo on the numerator and denominator.

To find the multiplicative inverse of an integer or mixed number, write the integer or mixed number as a fraction first, and then make the switch. It's like one of those bad movies on ABC Family where someone wakes up in someone else's place and has to figure out how to get back. Or a really good movie, like *The Change-Up*.

Why can't the fraction have a multiplicative inverse? , so There's no way to multiply by something and get 1 as an answer. It has no multiplicative identity. It's like it has a case of multiplicative amnesia. It should probably go to a multiplicative hospital. Okay, we've officially beaten that word to death. We'll get it to a multiplicative morgue stat.

Example 1

Find the multiplicative inverse of . |

Example 2

Find the multiplicative inverse of -4. |

Exercise 1

Find the multiplicative inverse of the given value.

Exercise 2

Find the multiplicative inverse of the given value.

Exercise 3

First find the product and then find the multiplicative inverse of the product.

4/5 x (reciprocal of 3/2)

Exercise 4

Find the multiplicative inverse of the given value.

-2

Exercise 5

Find the multiplicative inverse of the final answer: