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Chapter 1: Problem 64

Find each product or quotient. $$ \frac{6 x y^{2}-8 w}{2} $$

Short Answer

Expert verified
3xy^{2} - 4w

Step by step solution

01

Identify the numerator and denominator

The given expression is a fraction where the numerator (top part) is \(6xy^{2} - 8w\) and the denominator (bottom part) is 2.
02

Split the numerator by the denominator

Separate the terms in the numerator, each divided by the denominator: \(\frac{6xy^{2}}{2} - \frac{8w}{2}\).
03

Simplify each fraction

Simplify \(\frac{6xy^{2}}{2}\) to get \(3xy^{2}\), and \(\frac{8w}{2}\) to get \(4w\).
04

Combine the simplified terms

Combine the results obtained from Step 3: \(3xy^{2} - 4w\).

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Key Concepts

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

Simplifying Fractions
Simplifying fractions involves making them easier to work with. When dealing with algebraic fractions, simplifying means reducing the fractions to their simplest form. This can involve factoring the numerator and the denominator, then canceling out common factors. In our example, \(\frac{6xy^{2} - 8w}{2}\), simplifying this fraction means dividing both terms in the numerator by the denominator. Dividing each part can make the entire fraction simpler and more manageable.
Numerator and Denominator
In any fraction, the numerator is the top part, and the denominator is the bottom part. Understanding their roles is important in fraction operations. For the given expression \(\frac{6xy^{2} - 8w}{2}\), the numerator is \(6xy^{2} - 8w\), and the denominator is 2. By splitting the numerator, we divide each term separately by the denominator. This step simplifies calculations: \(\frac{6xy^{2}}{2} - \frac{8w}{2}\). Always ensure to handle both parts correctly to simplify the fraction accurately.
Algebraic Expressions
Algebraic expressions consist of variables, coefficients, and constants combined using mathematical operations. For instance, in \(6xy^{2} - 8w\), \(x\) and \(y\) are variables, 6 and -8 are coefficients, and \(w\) is another variable. When simplifying algebraic fractions, each term of the expression needs attention. Dividing the numerator \(6xy^{2}\) by the denominator 2 yields \(3xy^{2}\), and \(\frac{-8w}{2}\) simplifies to \(-4w\). This leads to the final simplified expression: \(3xy^{2} - 4w\). Properly managing the parts of algebraic expressions ensures clear and accurate simplification.

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Most popular questions from this chapter

Use an operation with signed numbers to solve each problem and identify the operation used. Just before the recession, First Federal Homestead had \(\$ 15.6\) million in mortgage loans, had \(\$ 23.3\) million on deposit, and owned \(\$ 8.5\) million worth of real estate. After the recession started, the value of the real estate decreased to \(\$ 4.8\) million. What was the net worth of First Federal before the recession and after the recession started? (To a financial institution a loan is an asset and a deposit is a liability.)

Combine like terms. $$ -3 a+15 a $$

Simplify. $$ -3\left(a w^{2}+5 a^{2} w\right)-2\left(-a^{2} w-a^{2} w\right) $$

Simplify each expression. $$ 6+5\left(k^{3}-2\right)-k^{3}+5 $$

Perform these computations. $$28-0.01$$
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