Multiplicative Inverse

πŸ†Practice special cases (0 and 1, inverse, fraction line)

Two numbers are multiplicative inverses when their product results in 1 1 .

For example:

12{\Large {1 \over 2}} and 2 2 are multiplicative inverses because 2β‹…12=1{\Large 2 \cdot {1 \over 2}=1}

Formulation of the Rule for Multiplicative Inverse Numbers:

Whenever a is different from 00, it follows that aβ‹…1a=1{\Large a\cdot{1 \over a} = 1}

Multiplication and Division of Multiplicative Inverses

Division is equivalent to multiplication by its multiplicative inverse,

That is: Β 213=2β‹…3=6{\Large {{2 \over {1 \over 3}} = 2 \cdot 3 = 6}}

Because 3 3 is the multiplicative inverse of Β 13{\Large {1 \over 3}}

Generally: a1b=aβ‹…b \frac{a}{\frac{1}{b}}=aβ‹…b

Start practice

Test yourself on special cases (0 and 1, inverse, fraction line)!

einstein

\( 12+3\times0= \)

Practice more now

Two numbers are multiplicative inverses when their multiplication results in 1 1 .

For example:

12{\Large {1 \over 2}} and 2 2 are multiplicative inverses because 2β‹…12=1{\Large 2 \cdot {1 \over 2}=1}

More examples:

The multiplicative inverse of 5 5 is 15{\Large {1 \over 5}}
5β‹…15=1{\Large 5 \cdot {1 \over 5}=1}


The multiplicative inverse of 3 3 is 13{\Large {1 \over 3}}
3β‹…13=1{\Large 3 \cdot {1 \over 3}=1}


The multiplicative inverse of 57{\Large {5 \over 7}} is 75{\Large {7 \over 5}}
75β‹…57=1{\Large {7 \over 5} \cdot {5 \over 7}=1}


The multiplicative inverse of 923{\Large {9 \over 23}} is 239{\Large {23 \over 9}}
239β‹…923=1{\Large {23 \over 9} \cdot {9 \over 23}=1}


The multiplicative inverse of 0.5 0.5 is 2 2

2β‹…0.5=1{\Large 2 \cdot 0.5=1}


The multiplicative inverse of 0.25 0.25 is 4 4

4β‹…0.25=1{\Large 4 \cdot 0.25=1}


Formulation of the Rule for Multiplicative Inverse Numbers:

Whenever a is different from 0 0 , it happens that aβ‹…1a=1{\Large a\cdot{1 \over a} = 1}


Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge

Multiplication and Division of Multiplicative Inverses

Division is equivalent to multiplication by the multiplicative inverse,

that is: Β 213=2β‹…3=6{\Large {{2 \over {1 \over 3}} = 2 \cdot 3 = 6}}

This is because 3 3 is the multiplicative inverse of Β 13{\Large {1 \over 3}}

In general: Β a/1b=aβ‹…b{\Large a /{1 \over b} = a \cdot b}


Exercises on Multiplicative Inverses

Solve the following exercises

  • 5+472={\Large {5+{{4 \over 7} \over 2} =}}
  • 60.75βˆ’2β‹…3={\Large {{6 \over 0.75} - 2 \cdot 3 =}}
  • 312βˆ’1316={\Large {{3{1 \over 2}-{{1 \over 3} \over {1 \over 6}}}=}}
  • 1072+278={\Large {{{{10 \over 7} \over 2 } + {2 \over {7 \over 8} }}=}}
  • 35910+7913={\Large {{{3 \over 5} \over {9 \over 10}} + {{7 \over 9} \over {1 \over 3}}=}}
```html

If you are interested in this article, you might also be interested in the following articles:

Positive, Negative Numbers and Zero

The Real Number Line

Opposite Numbers

Absolute Value

Elimination of Parentheses in Real Numbers

Multiplication and Division of Real Numbers

Abbreviated Multiplication Formulas

On the Tutorela blog, you will find a variety of articles about mathematics.


```
Do you know what the answer is?
Start practice