Q43. Identify the additive inverse an... [FREE SOLUTION]

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Chapter 1: Q43. (page 16)

Identify the additive inverse and multiplicative inverse for each number
$- 10$

Short Answer

Expert verified

Additive inverse of $- 10$ is 10 and multiplicative inverse of $- 10$ is $- \frac{1}{10}$

Step by step solution

- Define additive inverse

Let 鈥榓鈥� be a real number such that

$a + (- a) = 0 = (- a) + a$

Then 鈥� $- a$ 鈥� is the additive inverse of 鈥榓鈥�

- Additive inverse of -10

Substitute $- 10$ for a

$a = - 10$

Multiply both sides by $- 1$

$\begin{matrix} (鈭� 1) 脳 a = (鈭� 1) 脳 (鈭� 10) \\ 鈭� a = 10 \end{matrix}$

Thus additive inverse of $- 10$ is 10

- Define multiplicative inverse

Let 鈥榓鈥� be a real number with $a = 0$ such that

$a 路 \frac{1}{a} = 1 = \frac{1}{a} 路 a$

Then 鈥� $\frac{1}{a}$ 鈥� is the multiplicative inverse of 鈥榓鈥�

- Multiplicative inverse of -10

Substitute $- 10$ for a

$a = - 10$

Reciprocal on both sides

$\begin{matrix} \frac{1}{a} = \frac{1}{鈭� 10} \\ \frac{1}{a} = 鈭� \frac{1}{10} \end{matrix}$

Thus multiplicative inverse of $- 10$ is $- \frac{1}{10}$

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Year	Average CPI
1950	42.1
1960	29.6
1970	38.8
1980	82.4
1990	130.7
2000	174.0

91影视

Identify the additive inverse and multiplicative inverse for each number
$- 10$

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -10

- Define multiplicative inverse

- Multiplicative inverse of -10

One App. One Place for Learning.

Most popular questions from this chapter

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Theoretical and Mathematical Physics

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91影视

Identify the additive inverse and multiplicative inverse for each number-10

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of -10

- Define multiplicative inverse

- Multiplicative inverse of -10

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Geometry

Mechanics Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Identify the additive inverse and multiplicative inverse for each number
$- 10$