Problem 62 Find each product or quotient. ... [FREE SOLUTION]

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Chapter 1: Problem 62

Find each product or quotient. $$ \frac{-8 x^{2}}{4} $$

Short Answer

Expert verified

-2x^2

Step by step solution

- Simplify the Coefficients

Divide the coefficients: \[ \frac{-8}{4} = -2 \] This simplifies the expression to: \[ -2 \frac{x^{2}}{1} \]

- Simplify the Variable Part

Since there is no variable part left to simplify, the expression remains the same. The final expression is: \[ -2x^2 \]

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Key Concepts

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

Simplifying Coefficients

When simplifying algebraic expressions, the first step is usually to handle the coefficients. Coefficients are the numerical parts of terms that include variables. For example, in the expression $ -8x^2 $, the coefficient is $-8$.
Let's see how to simplify coefficients in an algebraic fraction:

Consider the exercise, where we need to find the quotient:
\[ \frac{-8x^2}{4} \]

Start by dividing the coefficients:
\[ \frac{-8}{4} = -2 \]
So, now the expression simplifies to:
\[ -2 \frac{x^2}{1} \]

Note: Simplified coefficients make it easier to handle and simplify the entire algebraic expression.

Understanding the Variable Part

The variable part of an algebraic expression consists of letters that represent numbers. In our example, the variable part is $x^2$. Variables can have exponents that show how many times the variable is multiplied by itself.

After simplifying the coefficients, it's important to check the variable part. For our expression:
\[ -2 \frac{x^2}{1} \]

We observe that $ \frac{x^2}{1} $ stays the same because this fraction is already in its simplest form. But sometimes you may need to simplify the variable part by dividing or combining like terms.

Understanding how to handle the variable parts will help in manipulating and simplifying complex algebraic expressions.

Simplifying Algebraic Fractions

Algebraic fractions are fractions where the numerator, the denominator, or both contain algebraic expressions (involving variables). Simplifying these fractions involves breaking down both the numerical coefficients and the variable parts.

Let's simplify the given algebraic fraction:
\[ \frac{-8x^2}{4} \]

First, divide the coefficients:
\[ \frac{-8}{4} = -2 \]

Next, look at the variable part. In this case, $\frac {x^2}{1}$ remains $x^2$ as it is already simplified. Bringing them together, we get:
\[ -2x^2 \]

This is the simplified form of the given algebraic fraction. Handling both coefficients and variables properly ensures accuracy in solving algebraic fractions.

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91影视

Find each product or quotient. $$ \frac{-8 x^{2}}{4} $$

Short Answer

Step by step solution

- Simplify the Coefficients

- Simplify the Variable Part

Key Concepts

Simplifying Coefficients

Understanding the Variable Part

Simplifying Algebraic Fractions

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