Chapter 1: Q39. (page 15)

Use the properties of real to answer each question
If $m n = m$ , what is the value of $n$ ?

Short Answer

Expert verified

Value of n is1.

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	$a + b = b + a$	$a \cdot b = b \cdot a$
Associative	$(a + b) + c = a + (b + c)$	$(a \cdot b) \cdot c = a \cdot (b \cdot c)$
Identity	$a + 0 = a = 0 + a$	$a \cdot 1 = a = 1 \cdot a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a \neq 0$ , then $a \cdot \frac{1}{a} = 1 = \frac{1}{a} \cdot a$
Distributive	$a (b + c) = a b + a c and (b + c) a = b a + c a$

- Compare with given equation

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

$\begin{matrix} a \cdot 1 = a \\ m n = m \end{matrix}$

Thus, on substituting 1 for n, given equation is satisfied.

- Verification

Substitute 1 for n in given equation

$\begin{matrix} m n = m \\ m \cdot 1 = m \\ m = m (True) \end{matrix}$

Thus, n is multiplicative identity of m

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use the properties of real to answer each question
If $m n = m$ , what is the value of $n$ ?

Short Answer

Step by step solution

- Write properties of real numbers

- Compare with given equation

- Verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Calculus

Pure Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Use the properties of real to answer each question If mn=m, what is the value of n?

Short Answer

Step by step solution

- Write properties of real numbers

- Compare with given equation

- Verification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Calculus

Pure Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Use the properties of real to answer each question
If $m n = m$ , what is the value of $n$ ?