Chapter 1: Q8. (page 18)

8. Name the property illustrated by $b c + (- b c) = 0$

Short Answer

Expert verified

Name of the property illustrated isAdditive Inverse.

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	$a \cdot b = b \cdot a$
Associative	$(a + b) + c = a + (b + c)$	$(a \cdot b) \cdot c = a \cdot (b \cdot c)$
Identity	a+0=a=0+a	$a \cdot 1 = a = 1 \cdot a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a \neq 0$ , then $a \cdot \frac{1}{a} = 1 = \frac{1}{a} \cdot a$
Distributive	$a (b + c) = a b + a c and (b + c) a = b a + c a$

- Substitution in given values

Substitute a for bc in given equation.

For a=bc

Multiply both sides by $- 1$

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

Now equation becomes $a + (- a) = 0$

- Identify the property

From the table of properties of real numbers, $a + (- a) = 0$ is the property of inverse in addition

Thus, additive inverse is illustrated by given equation.

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8. Name the property illustrated by $b c + (- b c) = 0$

Short Answer

Step by step solution

- Write properties of real numbers

- Substitution in given values

- Identify the property

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8. Name the property illustrated by bc+-bc=0

Short Answer

Step by step solution

- Write properties of real numbers

- Substitution in given values

- Identify the property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Pure Maths

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

8. Name the property illustrated by $b c + (- b c) = 0$