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High School Trigonometry: Help and Review31 chapters | 240 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Karin Gonzalez*

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, we will cover the definition of the multiplicative inverse, as well as its property. We will review some examples of the property so that we can gain a better understanding of the material. Following the lesson will be a brief quiz.

A **multiplicative inverse** is a reciprocal. What is a reciprocal? A **reciprocal** is one of a pair of numbers that when multiplied with another number equals the number 1. For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1!

Let's look at a couple examples before proceeding with the lesson.

**Example 1:**

What is the multiplicative inverse of 15? In other words, which number when multiplied with 15 would give us the number 1 as a result? Let's solve this in an algebraic way, with *x* being the unknown multiplicative inverse.

15 * *x* = 1*x* = 1/15

That's it! It was really that simple! The multiplicative inverse of a number is that number as the denominator and 1 as the numerator. When we multiply 15 and 1/15, we get 1.

**Example 2:**

What is the multiplicative inverse of 1/4? Now this example is a little different because we are beginning with a fraction. Let's again solve this algebraically, with *x* being the unknown multiplicative inverse of 1/4.

1/4 * *x* = 1*x* = 1 / (1/4)

(1/1) / (1/4) = (1/1) * (4/1) = 4

Remember that when you divide fractions, you must flip the numerator and denominator of the second fraction and then multiply. We got 4 as the multiplicative inverse of 1/4. Makes sense, right?

So, the conclusion that we can draw from these two examples is that when you have a whole number, the multiplicative inverse of that number will be that number in fraction form with the whole number as the denominator and 1 as the numerator. When you have a fraction with 1 as the numerator, the multiplicative inverse of that fraction will simply be the denominator of the fraction.

You may be thinking, that's just way too easy! What about when we have a fraction like 4/5? What would be the multiplicative inverse of that? Well, let's solve it algebraically, with *x* being the unknown multiplicative inverse.

4/5 * *x* = 1

1 / (4/5) = *x*

(1/1) * (5/4) = *x*

5/4= *x*

Wow! If we look at the answer, 5/4, there is something strangely similar to its multiplicative inverse, 4/5. Oh, yes. The multiplicative inverse of the fraction, 4/5, is actually just the fraction flipped. Does that work for other fractions, too? Yes, it most certainly does!

The **multiplicative inverse property** states that for every number that is not zero, *x* multiplied with 1/*x* will equal 1.

You may be saying now, well isn't that what we have been covering in this lesson so far? Yes, it is. The multiplicative inverse and multiplicative inverse property are really that simple.

A **multiplicative inverse** is a reciprocal. A **reciprocal** is one of a pair of numbers that when multiplied with another number equals the number 1. When we ask what the multiplicative inverse of a number *n* is, we are asking what number when multiplied with *n* will give us 1.

If we have a whole number, the multiplicative inverse will be that number as the denominator and 1 as the numerator. When we have a fraction with 1 as the numerator, the multiplicative inverse of that fraction will be the denominator. When we have a fraction, the multiplicative inverse is just the fraction flipped.

The **multiplicative inverse property** states that for every number that is not zero, *x* multiplied with 1/*x* will equal 1.

After watching this lesson, you should be able to:

- Define multiplicative inverse and reciprocal
- Be able to find the multiplicative inverse of both whole numbers and fractions
- Explain the multiplicative inverse property

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High School Trigonometry: Help and Review31 chapters | 240 lessons | 1 flashcard set

- What are the Different Types of Numbers? 6:56
- Graphing Rational Numbers on a Number Line 5:02
- Notation for Rational Numbers, Fractions & Decimals 6:16
- The Order of Real Numbers: Inequalities 4:36
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- Identity Property of Addition: Definition & Example 4:02
- Identity Property of Multiplication: Definition & Example 3:12
- Identity Property: Definition & Examples 5:59
- Multiplicative Identity Property: Definition & Example 3:36
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