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Chapter 1: Problem 19

Fill in the blanks to make true statements. \(m n^{2}-0.2 m n^{2}=\) ______

Short Answer

Expert verified
0.8mn^{2}

Step by step solution

01

Identify the Like Terms

First, recognize that both terms in the expression contain the common factors: \(mn^{2}\). So the expression can be simplified by combining these like terms.
02

Factor Out the Common Term

Factor out \(mn^{2}\) from both terms of the expression: \[mn^{2} (1 - 0.2) \]
03

Simplify Inside the Parentheses

Simplify the expression inside the parentheses: \[1 - 0.2 = 0.8\]
04

Multiply the Simplified Factor

Multiply \(mn^{2}\) by the simplified factor: \[mn^{2} \times 0.8 = 0.8mn^{2} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

like terms
In algebra, like terms are terms that have the same variable raised to the same power. For example, in the expression from the exercise, both terms, \(mn^2\) and \(0.2mn^2\), are like terms because they both involve the variable \(mn^2\).

When combining like terms, you simply add or subtract the coefficients (the numerical part) in front of the variables. In our case, we subtracted the coefficient 0.2 from the coefficient 1, leading to a result of 0.8. This makes simplifying expressions easier and more straightforward!
factoring
Factoring in algebra involves breaking down an expression into simpler components that, when multiplied together, produce the original expression. In the given exercise, we factor out \(mn^2\) from both terms:

This helps us combine the terms more easily by focusing just on the coefficients. The factored form simplifies the expression and helps us clearly see how to further simplify: 1. Expression before factoring: \(mn^2 - 0.2mn^2\)
2. Factored expression: \(mn^2(1-0.2)\)
simplification
Simplification is the process of reducing an expression to its simplest form. It's like cleaning up an equation to make it neater and easier to work with.

In the given problem, we simplified \(1 - 0.2\) inside the parentheses to get 0.8. Then we multiplied this simplified result by \(mn^2\), giving us the final simplified form: \(0.8mn^2\).

This process ensures that we have a compact, easy-to-understand expression.
algebra
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

It is about finding the unknown or putting real-life variables into equations and then solving them.

In our exercise, we used basic algebraic principles to deal with variables and coefficients to arrive at a simplified form of the given expression.

Understanding these core concepts in algebra鈥攍ike terms, factoring, and simplification鈥攎akes solving complex expressions easier and more intuitive.

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Most popular questions from this chapter

Each table describes a linear relationship. For each relationship, find the slope of the line and the \(y\) -intercept. Then write an equation for the relationship in the form \(y=m x+b .\) $$\begin{array}{|c|c|c|c|c|c|}\hline x & {9} & {7} & {5} & {3} & {1} \\\ \hline y & {5} & {4} & {3} & {2} & {1} \\ \hline\end{array}$$

For each equation, identify the slope and the y-intercept. Graph the line to check your answer. $$ y=2 x+0.25 $$

Just as the \(y\) -intercept of a line is the \(y\) value at which the line crosses the \(y\) -axis, the \(x\) -intercept is the \(x\) value at which the line crosses the \(x\) -axis. In Exercises \(22-25,\) find an equation of a line with the given \(x\) -intercept and slope. \(x\) -intercept \(3,\) slope 2

Find an equation of the line passing through the given points. $$ (3,5) \text { and }(9,9) $$

Alejandro looked at the equations \(y=\frac{3}{2} x-1\) and \(y=-\frac{2}{3} x+2\) and said, These lines form a right angle. a. Graph both lines on two different grids, with the axes labeled as shown here. b. Compare the lines on each grid. Do both pairs of lines form a right angle? c. What kind of assumption must Alejandro have made when he said the lines form a right angle?
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