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 212=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 a1a=1{\Large a\cdot{1 \over a} = 1}

Multiplicative Inverse

Multiplication and Division of Multiplicative Inverses

Division is equivalent to multiplication by its multiplicative inverse,

That is:  213=23=6{\Large {{2 \over {1 \over 3}} = 2 \cdot 3 = 6}}

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

Generally: a1b=ab \frac{a}{\frac{1}{b}}=a⋅b

Suggested Topics to Practice in Advance

  1. The Order of Basic Operations: Addition, Subtraction, and Multiplication
  2. Order of Operations: Exponents
  3. Order of Operations: Roots
  4. Order of Operations with Parentheses

Practice Multiplicative Inverse

Examples with solutions for Multiplicative Inverse

Exercise #1

Solve the following exercise:

12+30= 12+3\cdot0=

Step-by-Step Solution

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

12+(30)= 12+(3\cdot0)=

3×0=0 3\times0=0

12+0=12 12+0=12

Answer

12 12

Exercise #2

Solve the following exercise:

2+0:3= 2+0:3=

Step-by-Step Solution

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

2+(0:3)= 2+(0:3)=

0:3=0 0:3=0

2+0=2 2+0=2

Answer

2 2

Exercise #3

25+2510= \frac{25+25}{10}=

Video Solution

Step-by-Step Solution

Let's begin by multiplying the numerator:

25+25=50 25+25=50

We obtain the following fraction:

5010 \frac{50}{10}

Finally let's reduce the numerator and denominator by 10 and we are left with the following result:

51=5 \frac{5}{1}=5

Answer

5 5

Exercise #4

0:7+1= 0:7+1=

Video Solution

Step-by-Step Solution

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

0:7=0 0:7=0

0+1=1 0+1=1

Answer

1 1

Exercise #5

12+1+0= 12+1+0=

Video Solution

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 12+1=13

13+0=13 13+0=13

Answer

13

Exercise #6

0+0.2+0.6= 0+0.2+0.6=

Video Solution

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+0.2=0.2

0.2+0.6=0.8 0.2+0.6=0.8

Answer

0.8

Exercise #7

12+0+12= \frac{1}{2}+0+\frac{1}{2}=

Video Solution

Step-by-Step Solution

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

12+0=12 \frac{1}{2}+0=\frac{1}{2}

12+12=11=1 \frac{1}{2}+\frac{1}{2}=\frac{1}{1}=1

Answer

1 1

Exercise #8

90+0.5= 9-0+0.5=

Video Solution

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:

90=9 9-0=9

9+0.5=9.5 9+0.5=9.5

Answer

9.5

Exercise #9

19+10= 19+1-0=

Video Solution

Step-by-Step Solution

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

19+1=20 19+1=20

200=20 20-0=20

Answer

20 20

Exercise #10

2+0:3= 2+0:3=

Video Solution

Step-by-Step Solution

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

0:3=0 0:3=0

2+0=2 2+0=2

Answer

2 2

Exercise #11

12+3×0= 12+3\times0=

Video Solution

Step-by-Step Solution

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

3×0=0 3\times0=0

12+0=12 12+0=12

Answer

12

Exercise #12

8×(5×1)= 8\times(5\times1)=

Video Solution

Step-by-Step Solution

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

5×1=5 5\times1=5

Now we multiply:

8×5=40 8\times5=40

Answer

40

Exercise #13

7×1+12= 7\times1+\frac{1}{2}=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we first insert the multiplication exercise into parentheses:

(7×1)+12= (7\times1)+\frac{1}{2}=

Let's solve the exercise inside the parentheses:

7×1=7 7\times1=7

And now we get the exercise:

7+12=712 7+\frac{1}{2}=7\frac{1}{2}

Answer

712 7\frac{1}{2}

Exercise #14

63×1= \frac{6}{3}\times1=

Video Solution

Step-by-Step Solution

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

63=2 \frac{6}{3}=2

2×1=2 2\times1=2

Answer

2 2

Exercise #15

Solve the following exercise:

(180):3= (18-0):3=

Step-by-Step Solution

According to the order of operations rules, we must first solve the expression inside of the parentheses. Following this we will perform the division:

180=18 18-0=18

18:3=6 18:3=6

Answer

6 6

Topics learned in later sections

  1. Division and Fraction Bars (Vinculum)
  2. The Numbers 0 and 1 in Operations
  3. Neutral Element (Identiy Element)
  4. The Order of Operations
  5. Order or Hierarchy of Operations with Fractions