Inverse Property Of Multiplication Example

What Is Multiplicative Inverse?

The meaning of the discussion "inverse" is something opposite in effect. The multiplicative inverse of a number is a number that, when multiplied by the given number, gives i as the product. By multiplicative inverse definition, it is the reciprocal of a number.

The multiplicative inverse of a number "a" is represented every bit a^-1or $\frac{1}{a}$.

Multiplicative Inverse Holding

The multiplicative inverse belongings states that if we multiply a number with its reciprocal, the product is always equal to 1. The image given beneath shows that $\frac{one}{a}$ is the reciprocal of the number "a".

A pair of numbers, when multiplied to give product 1, are said to be multiplicative inverses of each other. Here, a and $\frac{1}{a}$ are reciprocals of each other.

How to Find the Multiplicative Inverse?

Consider that we have seven apples. To brand them into groups of 1 each, we demand to divide them by 7. Since division is the reverse process of multiplication, dividing by a number is equivalent to multiplying by the reciprocal of the number.

Thus, 7 ÷ 7 = 7 × $\frac{i}{seven}$ = one

Hither, $\frac{1}{7}$ is called the multiplicative inverse of seven.

Allow united states of america understand the multiplicative inverse of dissimilar types of numbers like natural numbers, integers and fractions.

Natural Numbers

The numbers that are used for counting, such equally i, two, three, and so on, are known as natural numbers. The reciprocal of "a" is $\frac{1}{a}$.

For case, if we multiply vii past $\frac{1}{7}$, we go $seven\frac{1}{7}=1$. So, the multiplicative inverse of 7 is $\frac{1}{7}$.

Integers

The reciprocal of a positive integer "a" is $\frac{1}{a}$. Negative integers lie on the left side of zippo on a number line and their value is always less than 0. Negative integers have minus (-) sign in forepart of them. The product of any integer and its reciprocal must be ane. The reciprocal of a negative number will be a negative number. For example: If the number is -2, then its reciprocal volition be $-\frac{1}{2}$ not $\frac{i}{2}$, as $-2 \times \left[-\frac{1}{two}\right] = 1$

Fractions

To detect the reciprocal of a fraction nosotros can simply flip it over. The reciprocal of any fraction $\frac{a}{b}$ is $\frac{b}{a}$, considering $\frac{a}{b}\times\frac{b}{a}=1$.

Unit of measurement Fractions

Unit fraction is the fraction in which the numerator is 1 irrespective of the number in the denominator. The reciprocal of unit fraction $\frac{1}{x}$ is ten, a whole number. For case, reciprocal or multiplicative inverse of ¼ is 4.

Mixed Fraction

A mixed fraction is a combination of a whole number and a proper fraction. For case: $ii\frac{3}{7},five\frac{4}{five}$, etc.

In order to observe the reciprocal of a mixed fraction, nosotros convert information technology to an improper fraction and then find its reciprocal.

For example, to observe the reciprocal of $2\frac{three}{vii}$, we catechumen $2\frac{3}{7}$ to improper fraction, that is $\frac{17}{7}$.

Since the reciprocal of $2\frac{3}{seven}$ or $\frac{17}{7}$ is $\frac{7}{17}$.

Fun Facts

The discussion "reciprocal" comes from the Latin word "reciprocus", which means back and forth.
The multiplicative inverse of a proper fraction is an improper fraction.

Conclusion

In this article, we learned about the reciprocal of different types of numbers. To read more such informative manufactures on other concepts, do visit our website. We, at SplashLearn, are on a mission to make learning fun and interactive for all students.

Solved Examples

Example 1: What is the multiplicative inverse of -100?

Solution: The multiplicative inverse of -100 is -$\frac{ane}{100}$.

Case two: The reciprocal of a number is $two\frac{3}{5}$. Find the number.

Solution: A pair of numbers when multiplied to give production as one, they are said to be reciprocals of each other.

So, the reciprocal of $2\frac{3}{five}$ or $\frac{13}{v}$ is the original number. Since the reciprocal of $\frac{thirteen}{5}$ is $\frac{five}{thirteen}$, the original number is $\frac{5}{thirteen}$.

Instance iii: What is the multiplicative inverse of $\frac{2}{3} + \frac{iii}{two}$?

Solution: To detect the reciprocal, we need to simplify the expression start.

$\frac{ii}{three} + \frac{iii}{2} = \frac{thirteen}{6}$The reciprocal of $\frac{13}{6}$ is $\frac{6}{thirteen}$.

Practice Bug

Multiplicative Changed - Definition with Examples

Nourish this quiz & Test your knowledge.

-10

$-\frac{1}{ten}$

None of these

Correct respond is: 10
The reciprocal of $\frac{i}{10}$ is 10.

improper fraction

proper fraction

mixed fraction

None of these

Correct respond is: proper fraction
Mixed fractions can be converted into improper fractions. Since the reciprocal of an improper fraction is a proper fraction, the multiplicative changed of a mixed fraction is a proper fraction.

- iii

Right respond is: 0
The multiplicative inverse of 0 is $\frac{one}{0}$, which is not divers.

Frequently Asked Questions

What is the difference between multiplicative and additive inverse?

Condiment changed of a number is the number that, when added to the original number, gives 0 every bit the upshot. For instance: Additive inverse of 5 is -5. On the other hand, the multiplicative changed of a number is the number that, when multiplied by the original number, gives ane every bit the result. For instance: Multiplicative changed of five is $\frac{1}{5}$.

What is the multiplicative inverse of 0?

As per the definition of multiplicative changed of a number is a number that, when multiplied past the given number, yields the production every bit 1. Since the product of any number with zippo is always zero. So we tin can say that zilch doesn't have a reciprocal.

Since division by zero is not defined, the reciprocal of null, which is 1/0, is undefined. And so, information technology does not exist.

What is multiplicative identity?

The multiplicative identity is a number, which when multiplied to any number "a", gives a product as "a". Multiplicative identity is a existent number is 1, because $a\times1=a$

What is the use of multiplicative inverse?

The multiplicative changed is used to simplify the expressions. One application of multiplicative inverse is when nosotros solve the sectionalization problems. While dividing two numbers, we multiply the reciprocal of the divisor to the dividend. For example, 5 ÷ x = 5 × $\frac{1}{10} = \frac{1}{2}$.