Chapter 1: Q44. (page 16)

Identify the additive inverse and multiplicative inverse for each number
44. $2.5$

Short Answer

Expert verified

Additive inverse of $2.5$ is $- 2.5$ and multiplicative inverse of $2.5$ is $0.4$

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 2.5

Substitute $2.5$ for a

$a = 2.5$

Multiply both sides by $- 1$

$\begin{matrix} (- 1) \times a = (- 1) \times (2.5) \\ - a = - 2.5 \end{matrix}$

Thus additive inverse of $2.5$ is $- 2.5$

- 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 2.5

Substitute $2.5$ for a

$a = 2.5$

Convert decimal form of rational number to fraction form

$a = \frac{5}{2}$

Take reciprocal on both sides

$\begin{matrix} \frac{1}{a} = \frac{1}{\frac{5}{2}} \\ \frac{1}{a} = \frac{2}{5} \end{matrix}$

Convert fraction form again into decimal form

$\frac{1}{a} = 0.4$

Thus multiplicative inverse of $2.5$ is $0.4$

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Identify the additive inverse and multiplicative inverse for each number
44. $2.5$

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of 2.5

- Define multiplicative inverse

- Multiplicative inverse of 2.5

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Identify the additive inverse and multiplicative inverse for each number44. 2.5

Short Answer

Step by step solution

- Define additive inverse

- Additive inverse of 2.5

- Define multiplicative inverse

- Multiplicative inverse of 2.5

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Applied Mathematics

Pure Maths

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Identify the additive inverse and multiplicative inverse for each number
44. $2.5$