Chapter 1: Q56. (page 16)

Simplify each expression
56. $7 (0.2 p + 0.3 q) + 5 (0.6 p - q)$

Short Answer

Expert verified

$7 (0.2 p + 0.3 q) + 5 (0.6 p - q)$ is simplified to $4.4 p - 0.9 q$

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	$a (b + c) = a b + a c and (b + c) a = b a + c a$ .

- Simplify by grouping same variables

To simplify given equation, first use distributive property then commutative property of addition then distributive property to group coefficients of same variable as shown below

$\begin{matrix} 7 (0.2 p + 0.3 q) + 5 (0.6 p - q) = 1.4 p + 2.1 q + 3 p - 5 q \\ = 1.4 p + 3 p + 2.1 q - 3 q \\ = (1.4 + 3) p + (2.1 - 3) q \end{matrix}$

- Simplify further

To simplify, evaluate parentheses as shown below

$(1.4 + 3) p + (2.1 - 3) q = 4.4 p - 0.9 q$

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Simplify each expression
56. $7 (0.2 p + 0.3 q) + 5 (0.6 p - q)$

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify further

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Simplify each expression56. 70.2p+0.3q+50.6p-q

Short Answer

Step by step solution

- Write properties of real numbers

- Simplify by grouping same variables

- Simplify further

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Logic and Functions

Applied Mathematics

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Statistics

Study anywhere. Anytime. Across all devices.

Simplify each expression
56. $7 (0.2 p + 0.3 q) + 5 (0.6 p - q)$