narrate an incident when you landed yourself in trouble due to a misunderstanding describe in detail what happened and how it ended
-when, where, your feeling
-what was the misunderstanding, people involved, your feelings
-what troubles you got into
-describe the misunderstanding,why
-how did it ending
Answers
Answer:
Multiplicative inverse is used to simplify mathematical expressions. The word 'inverse' implies something opposite/contrary in effect, order, position, or direction. A number that nullifies the impact of a number to identity 1 is called a multiplicative inverse.
What is Multiplicative Inverse?
The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1. The multiplicative inverse of 'a' is denoted by a-1 or 1/a. In other words, when the product of two numbers is 1, they are said to be multiplicative inverses of each other. The multiplicative inverse of a number is defined as the division of 1 by that number. It is also called the reciprocal of the number. The multiplicative inverse property says that the product of a number and its multiplicative inverse is 1.
Multiplicative Inverse Property
For example, let us consider 5 apples. Now, divide the apples into five groups of 1 each. To make them into groups of 1 each, we need to divide them by 5. Dividing a number by itself is equivalent to multiplying it by its multiplicative inverse . Hence, 5 ÷ 5 = 5 × 1/5 = 1. Here, 1/5 is the multiplicative inverse of 5.
Multiplicative Inverse of a Natural Number
Natural numbers are counting numbers starting from 1. The multiplicative inverse of a natural number a is 1/a.
Examples
3 is a natural number. If we multiply 3 by 1/3, the product is 1. Therefore, the multiplicative inverse of 3 is 1/3.
Similarly, the multiplicative inverse of 110 is 1/110.
Multiplicative Inverse of a Negative Number
Just as for any positive number, the product of a negative number and its reciprocal must be equal to 1. Thus, the multiplicative inverse of any negative number is its reciprocal. For example, (-6) × (-1/6) = 1, therefore, the multiplicative inverse of -6 is -1/6.
Let us consider a few more examples for a better understanding.
Multiplicative Inverse of a Unit Fraction
A unit fraction is a fraction with the numerator 1. If we multiply a unit fraction 1/x by x, the product is 1. The multiplicative inverse of a unit fraction 1/x is x.
Examples:
The multiplicative inverse of the unit fraction 1/7 is 7. If we multiply 1/7 by 7, the product is 1. (1/7 × 7 = 1)
The multiplicative inverse of the unit fraction 1/50 is 50. If we multiply 1/50 by 50, the product is 1. (1/50 × 50 = 1)
Multiplicative Inverse of a Fraction
The multiplicative inverse of a fraction a/b is b/a because a/b × b/a = 1 when (a,b ≠ 0)
Examples
×
√
2
−1
√
2
−1
Step 2: Solve.
3
√
2
+1
2⋅1
Step 3: Simplify to the lowest form. 3(√2+1)
Modular Multiplicative Inverse
The modular multiplicative inverse of an integer p is another integer x such that the product px is congruent to 1 with respect to the modulus m. It can be represented as: px ≡ 1 (mod m). In other words, m divides px - 1 completely. Also, the modular multiplicative inverse of an integer p can exist with respect to the modulus m only if gcd(p, m) = 1
In a nutshell, the multiplicative inverses are as follows:
Type Multiplicative Inverse Example
Natural Number
x
1/x Multiplicative Inverse of 4 is 1/4
Integer
x, x ≠ 0
1/x Multiplicative Inverse of -4 is -1/4
Fraction
x/y; x,y ≠ 0
y/x Multiplicative Inverse of 2/7 is 7/2
Unit Fraction
1/x, x ≠ 0
x Multiplicative Inverse of 1/20 is 20
Tips on Multiplicative Inverse
The multiplicative inverse of a fraction can be obtained by interchanging the numerator and denominator.
The multiplicative inverse of 1 is 1.
The multiplicative inverse of 0 is not defined.
The multiplicative inverse of a number x is written as 1/x or x-1.
The multiplicative inverse of a mixed fraction can be obtained by converting the mixed fraction into an improper fraction and determining its reciprocal.
Important Notes on Multiplicative Inverse
The multiplicative inverse of a number is also called its reciprocal.
The product of a number and its multiplicative inverse is equal to 1.
Related Topics
Explanation: