Chapter 1: Q12. (page 15)

Identify the additive inverse and multiplicative inverse for each number
$1.5$

Short Answer

Expert verified

Additive inverse of $1.5$ is $- 1.5$ and multiplicative inverse of 1.5 is $\frac{2}{3}$

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 1.5

Substitute $1.5$ for a

$a = 1.5$

Multiply both sides by $- 1$

$\begin{matrix} (- 1) \times a = (- 1) \times (1.5) \\ - a = - 1.5 \end{matrix}$

Thus additive inverse of 1.5 is -1.5

- 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 1.5

Substitute $1.5$ for $a$

Convert it from decimal form to fraction

$\begin{matrix} a = 1.5 \\ = \frac{15}{10} \\ = \frac{3}{2} \end{matrix}$

Reciprocal on both sides

$\begin{matrix} \frac{1}{a} = \frac{1}{\frac{3}{2}} \\ \frac{1}{a} = \frac{2}{3} \end{matrix}$

Thus multiplicative inverse of $\frac{3}{2}$ is $\frac{2}{3}$

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Identify the additive inverse and multiplicative inverse for each number
$1.5$

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of 1.5

- Define multiplicative inverse

- Multiplicative inverse of 1.5

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Identify the additive inverse and multiplicative inverse for each number1.5

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of 1.5

- Define multiplicative inverse

- Multiplicative inverse of 1.5

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Calculus

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Identify the additive inverse and multiplicative inverse for each number
$1.5$