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

**For example:**

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

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

**For example:**

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

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

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:** **$\frac{a}{\frac{1}{b}}=a⋅b$**

\( 0+0.2+0.6= \)

**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 $4$

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

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

Test your knowledge

Question 1

\( 12+3\times0= \)

Question 2

\( 12+1+0= \)

Question 3

\( 8\times(5\times1)= \)

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

**Solve the following exercises**

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

$0+0.2+0.6=$

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

$12+3\times0=$

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

$3\times0=0$

$12+0=12$

12

$12+1+0=$

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

$8\times(5\times1)=$

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

$5\times1=5$

Now we multiply:

$8\times5=40$

40

$9-0+0.5=$

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

$9-0=9$

$9+0.5=9.5$

9.5

Do you know what the answer is?

Question 1

\( 9-0+0.5= \)

Question 2

Solve the following exercise:

\( 12+3\cdot0= \)

Question 3

\( 0:7+1= \)

Related Subjects

- Order of Operations: Exponents
- Order of Operations: Roots
- Order of Operations with Parentheses
- Advanced Arithmetic Operations
- The commutative property
- The Commutative Property of Addition
- The Commutative Property of Multiplication
- The Associative Property
- The Associative Property of Addition
- The Associative Property of Multiplication
- The Distributive Property
- The Distributive Property for Seventh Graders
- The Distributive Property of Division
- The Distributive Property in the Case of Multiplication
- Subtracting Whole Numbers with Addition in Parentheses
- Division of Whole Numbers Within Parentheses Involving Division
- Subtracting Whole Numbers with Subtraction in Parentheses
- Division of Whole Numbers with Multiplication in Parentheses
- The commutative properties of addition and multiplication, and the distributive property
- Exponents and Roots - Basic
- What is a square root?
- Square Root of a Negative Number
- Exponents and Exponent rules
- Basis of a power
- The exponent of a power
- Powers