Multiplicative Inverse Practice Problems & Exercises

Master multiplicative inverses with step-by-step practice problems. Learn reciprocals, fraction division, and special cases involving 0 and 1.

📚What You'll Master in This Practice Session

Find multiplicative inverses of whole numbers, fractions, and decimals
Apply the rule a × (1/a) = 1 to solve complex problems
Convert division by fractions into multiplication by reciprocals
Solve multi-step problems involving multiplicative inverses and mixed operations
Understand why zero has no multiplicative inverse and special properties of 1
Work with fraction line notation and complex fraction expressions

Understanding Multiplicative Inverse

Complete explanation with examples

Two numbers are multiplicative inverses (also called reciprocals) when their product results in $1$ .

For example:

${\Large {1 \over 2}}$ and $2$ are multiplicative inverses because ${\Large 2 \cdot {1 \over 2}=1}$

Formulation of the Rule for Multiplicative Inverse Numbers:

Whenever $a$ is different from $0$ , it follows that ${\Large a\cdot{1 \over a} = 1}$

Note: Zero $0$ does not have a multiplicative inverse because division by zero is undefined.

Multiplication and Division of Multiplicative Inverses

Division is equivalent to multiplication by its multiplicative inverse,

That is: ${\Large {{2 \over {1 \over 3}} = 2 \cdot 3 = 6}}$

Because $3$ is the multiplicative inverse of ${\Large {1 \over 3}}$

Generally: $\frac{a}{\frac{1}{b}}=a⋅b$

Detailed explanation

Practice Multiplicative Inverse

Test your knowledge with 21 quizzes

$12+3\times0=$

Examples with solutions for Multiplicative Inverse

Step-by-step solutions included

Exercise #1

$\frac{6}{3}\times1=\text{ ?}$

Step-by-Step Solution

According to the order of operations, we will solve the exercise from left to right since it only contains multiplication and division operations:

$\frac{6}{3}=2$

$2\times1=2$

Answer:

$2$

Video Solution

Exercise #2

Solve the following exercise:

$12+3\cdot0=$

Step-by-Step Solution

According to the order of operations, we first multiply and then add:

$12+(3\cdot0)=$

$3\times0=0$

$12+0=12$

Answer:

$12$

Exercise #3

Solve the following exercise:

$2+0:3=$

Step-by-Step Solution

According to the order of operations rules, we first divide and then add:

$2+(0:3)=$

$0:3=0$

$2+0=2$

Answer:

$2$

Exercise #4

$9 \times (2 \times 1) =$

Step-by-Step Solution

First, calculate the expression within the parentheses:

$2 \times 1 = 2$

Now, multiply the result by 9:

$9 \times 2 = 18$

Thus, the final answer is $18$ .

Answer:

Exercise #5

$0+0.2+0.6=$ ?

Step-by-Step Solution

According to the order of operations, the exercise is solved from left to right as it contains only an addition operation:

$0+0.2=0.2$

$0.2+0.6=0.8$

Answer:

0.8

Video Solution

Frequently Asked Questions

Everything you need to know about Multiplicative Inverse

What is a multiplicative inverse and how do I find it?

A multiplicative inverse (or reciprocal) is a number that when multiplied by the original number equals 1. To find it: for whole numbers like 5, the inverse is 1/5; for fractions like 3/7, flip it to get 7/3; for decimals like 0.25, convert to fraction (1/4) then flip to get 4.

Why doesn't zero have a multiplicative inverse?

Zero has no multiplicative inverse because there's no number that when multiplied by 0 gives 1. Since 0 × any number = 0 (never 1), division by zero is undefined in mathematics.

How do I divide by a fraction using multiplicative inverses?

To divide by a fraction, multiply by its multiplicative inverse instead. For example: 2 ÷ (1/3) = 2 × 3 = 6, because 3 is the multiplicative inverse of 1/3.

What are common mistakes when working with multiplicative inverses?

Common errors include: 1) Confusing additive inverse (-a) with multiplicative inverse (1/a), 2) Forgetting that 1 is its own multiplicative inverse, 3) Trying to find the inverse of zero, 4) Not simplifying fractions before finding inverses.

How do multiplicative inverses help with complex fractions?

Complex fractions like (a)/(1/b) become simple multiplication: a × b. This works because dividing by 1/b is the same as multiplying by b (the multiplicative inverse of 1/b).

What's the difference between reciprocal and multiplicative inverse?

Reciprocal and multiplicative inverse mean exactly the same thing - they're interchangeable terms. Both refer to the number that when multiplied by the original gives a product of 1.

How do I check if two numbers are multiplicative inverses?

Simply multiply them together. If the product equals 1, they are multiplicative inverses. For example: 2/5 × 5/2 = 10/10 = 1, so 2/5 and 5/2 are multiplicative inverses.

Can negative numbers have multiplicative inverses?

Yes, negative numbers have multiplicative inverses. For -3, the multiplicative inverse is -1/3 because (-3) × (-1/3) = 1. The inverse of a negative number is also negative.

Continue Your Math Journey

Master Multiplicative Inverse first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Division and Fraction Bars (Vinculum)The Numbers 0 and 1 in Operations Neutral Element (Identity Element)Order or Hierarchy of Operations with Fractions Special cases (0 and 1, reciprocals, fraction line)The Order of Operations

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Complete the missing number Decimal numbers Exercises with fractions Identify the greater value Is the equality correct? Parentheses within parentheses Two Pairs of Parentheses Using 0 Using 1 Using fractions Using negative numbers Using parentheses

Multiplicative Inverse Practice Problems & Exercises

Understanding Multiplicative Inverse

Formulation of the Rule for Multiplicative Inverse Numbers:

Multiplication and Division of Multiplicative Inverses

Practice Multiplicative Inverse

Examples with solutions for Multiplicative Inverse

Frequently Asked Questions

What is a multiplicative inverse and how do I find it?

Why doesn't zero have a multiplicative inverse?

How do I divide by a fraction using multiplicative inverses?

What are common mistakes when working with multiplicative inverses?

How do multiplicative inverses help with complex fractions?

What's the difference between reciprocal and multiplicative inverse?

How do I check if two numbers are multiplicative inverses?

Can negative numbers have multiplicative inverses?

More Multiplicative Inverse Questions

Special Cases (0 and 1, Inverse, Fraction Line)

Continue Your Math Journey

Suggested Topics to Practice in Advance

Topics Learned in Later Sections

Practice by Question Type