Chapter 1: Q11. (page 15)

Identify the additive inverse and multiplicative inverse for each number
11. $\frac{1}{3}$

Short Answer

Expert verified

Additive inverse of $\frac{1}{3}$ is $- \frac{1}{3}$ and multiplicative inverse of $\frac{1}{3}$ is 3

Step by step solution

- Define additive inverse

Let ‘a’ be a real number such that

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

Then $‘ - a ’$ is the additive inverse of ‘a’

- Additive inverse of 13

Substitute $\frac{1}{3}$ for $a$

$a = \frac{1}{3}$

Multiply both sides by $- 1$

$\begin{matrix} (- 1) \times a = (- 1) \times (\frac{1}{3}) \\ - a = - \frac{1}{3} \end{matrix}$

Thus additive inverse of $\frac{1}{3}$ is $- \frac{1}{3}$

- Define multiplicative inverse

Let ‘a’ be a real number with $a = 0$ such that

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

Then ' $\frac{1}{a}$ ' is the multiplicative inverse of ‘a’

- Multiplicative inverse of 13

Substitute $\frac{1}{3}$ for $a$

$a = \frac{1}{3}$

Reciprocal on both sides

$\begin{matrix} \frac{1}{a} = \frac{1}{\frac{1}{3}} \\ \frac{1}{a} = 3 \end{matrix}$

Thus multiplicative inverse of $\frac{1}{3}$ is 3

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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

Identify the additive inverse and multiplicative inverse for each number
11. $\frac{1}{3}$

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of 13

- Define multiplicative inverse

- Multiplicative inverse of 13

One App. One Place for Learning.

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Identify the additive inverse and multiplicative inverse for each number11. 13

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of 13

- Define multiplicative inverse

- Multiplicative inverse of 13

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Decision Maths

Geometry

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Identify the additive inverse and multiplicative inverse for each number
11. $\frac{1}{3}$