Q37. NUMBER THEORYUse the properties ... [FREE SOLUTION]

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Chapter 1: Q37. (page 15)

NUMBER THEORY
Use the properties of real to answer each question
37. If $m + n = 0$ , what is the value of $n$ ? What is $n$ called with respect to $m$ ?

Short Answer

Expert verified

Value of $n$ is $(- m)$ . $n$ is additive 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 addition with given equation to find required value as shown below

$\begin{matrix} a + (鈭� a) = 0 \\ m + n = 0 \end{matrix}$

Thus, on substituting $(- m)$ for $n$ , given equation is satisfied.

- relation between n and m

Substitute $(- m)$ for $n$ in given equation

$\begin{matrix} m + n = 0 \\ m + (鈭� m) = 0 \\ 0 = 0 \end{matrix}$

Thus, n is additive inverse of m

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Year	Average CPI
1950	42.1
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2000	174.0

91影视

NUMBER THEORY
Use the properties of real to answer each question
37. If $m + n = 0$ , 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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Probability and Statistics

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91影视

NUMBER THEORYUse the properties of real to answer each question37. Ifm+n=0, 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

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

NUMBER THEORY
Use the properties of real to answer each question
37. If $m + n = 0$ , what is the value of $n$ ? What is $n$ called with respect to $m$ ?