Q38. Use the properties of real to an... [FREE SOLUTION]

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Chapter 1: Q38. (page 15)

Use the properties of real to answer each question
If $m n = 1$ , what is the value of $n$ ? What is $n$ called with respect to $m$ ?

Short Answer

Expert verified

Value of n is $\frac{1}{m}$ . n is multiplicative inverse of m

Step by step solution

- Write properties of real numbers

Properties of real numbers are written in following table:

For any real numbers $a, b,$ and $c :$
Property	Addition	Multiplication
Commutative	$a + b = b + a$	$a 路 b = b 路 a$
Associative	$(a + b) + c = a + (b + c)$	$(a 路 b) 路 c = a 路 (b 路 c)$
Identity	$a + 0 = a = 0 + a$	$a 路 1 = a = 1 路 a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a 鈮� 0$ , then $a 路 \frac{1}{a} = 1 = \frac{1}{a} 路 a$
Distributive	$a (b + c) = a b + a c and (b + c) a = b a + c a$

- Compare with given equation

Compare inverse property of multiplication with given equation to find required value as shown below

$\begin{matrix} a 鈰� \frac{1}{a} = 1 \\ m n = 1 \end{matrix}$

Thus, on substituting $\frac{1}{m}$ for $n$ , given equation is satisfied.

- relation between n and m

Substitute $\frac{1}{m}$ for n in given equation

$\begin{matrix} m n = 1 \\ m \frac{1}{m} = 1 \\ 1 = 1 \end{matrix}$

Thus, n is multiplicative inverse of m

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91影视

Use the properties of real to answer each question
If $m n = 1$ , what is the value of $n$ ? What is $n$ called with respect to $m$ ?

Short Answer

Step by step solution

- Write properties of real numbers

- Compare with given equation

- relation between n and m

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

Use the properties of real to answer each questionIf mn=1, what is the value of n? What is ncalled with respect to m?

Short Answer

Step by step solution

- Write properties of real numbers

- Compare with given equation

- relation between n and m

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Discrete Mathematics

Statistics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Use the properties of real to answer each question
If $m n = 1$ , what is the value of $n$ ? What is $n$ called with respect to $m$ ?