Multiplicative Inverse

🏆Practice special cases (0 and 1, inverse, fraction line)

Two numbers are multiplicative inverses 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 ${\Large a\cdot{1 \over a} = 1}$

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: $\frac{a}{\frac{1}{b}}=a⋅b$

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

$$0+0.2+0.6=$$

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

For example:

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

More examples:

The multiplicative inverse of $5$ is ${\Large {1 \over 5}}$
${\Large 5 \cdot {1 \over 5}=1}$

The multiplicative inverse of $3$ is ${\Large {1 \over 3}}$
${\Large 3 \cdot {1 \over 3}=1}$

The multiplicative inverse of ${\Large {5 \over 7}}$ is ${\Large {7 \over 5}}$
${\Large {7 \over 5} \cdot {5 \over 7}=1}$

The multiplicative inverse of ${\Large {9 \over 23}}$ is ${\Large {23 \over 9}}$
${\Large {23 \over 9} \cdot {9 \over 23}=1}$

The multiplicative inverse of $0.5$ is $2$

${\Large 2 \cdot 0.5=1}$

The multiplicative inverse of $0.25$ is $4$

${\Large 4 \cdot 0.25=1}$

Formulation of the Rule for Multiplicative Inverse Numbers:

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

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Multiplication and Division of Multiplicative Inverses

Division is equivalent to multiplication by the multiplicative inverse,

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

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

In general:  ${\Large a /{1 \over b} = a \cdot b}$

Exercises on Multiplicative Inverses

Solve the following exercises

• ${\Large {5+{{4 \over 7} \over 2} =}}$
• ${\Large {{6 \over 0.75} - 2 \cdot 3 =}}$
• ${\Large {{3{1 \over 2}-{{1 \over 3} \over {1 \over 6}}}=}}$
• ${\Large {{{{10 \over 7} \over 2 } + {2 \over {7 \over 8} }}=}}$
• ${\Large {{{3 \over 5} \over {9 \over 10}} + {{7 \over 9} \over {1 \over 3}}=}}$

Examples and Exercises with Solutions for Multiplicative Inverse

Exercise #1

$0+0.2+0.6=$

Step-by-Step Solution

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

$0+0.2=0.2$

$0.2+0.6=0.8$

0.8

Exercise #2

$12+3\times0=$

Step-by-Step Solution

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

$3\times0=0$

$12+0=12$

12

Exercise #3

$12+1+0=$

Step-by-Step Solution

According to the order of operations rules, since the exercise only involves addition operations, we will solve the problem from left to right:

$12+1=13$

$13+0=13$

13

Exercise #4

$8\times(5\times1)=$

Step-by-Step Solution

According to the order of operations, we first solve the expression in parentheses:

$5\times1=5$

Now we multiply:

$8\times5=40$

40

Exercise #5

$9-0+0.5=$

Step-by-Step Solution

According to the order of operations rules, since the exercise only involves addition and subtraction, we will solve the problem from left to right:

$9-0=9$

$9+0.5=9.5$