Problem 108 Simplify. $$ \frac{4 w y t}{... [FREE SOLUTION]

Chapter 1: Problem 108

Simplify. $$ \frac{4 w y t}{4}+\frac{-8 w y t}{2}-\frac{-2 w y}{2} $$

Short Answer

Expert verified

-3 w y t - w y

Step by step solution

- Simplify Individual Fractions

Simplify each term separately.\[ \frac{4 w y t}{4} = w y t \] and \[ \frac{-8 w y t}{2} = -4 w y t \] and \[ \frac{-2 w y}{2} = -w y \].

- Combine Like Terms

Add and subtract the simplified terms. Now the expression is: \[ w y t - 4 w y t - w y \].

- Perform Operations

Combine the like terms by performing the operations: \[ (1w y t - 4 w y t) - w y = -3 w y t - w y \].

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Key Concepts

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

Simplifying Fractions

When simplifying fractions, our goal is to make each fraction as simple as possible. In the given exercise, each term needs to be simplified individually. Let's break it down:

The first part $ \frac{4 w y t}{4} $ simplifies to $ w y t $. This is because the 4 in the numerator and the denominator cancel each other out.
In the second term, $ \frac{-8 w y t}{2} $, we divide -8 by 2 to get -4. So the term simplifies to $ -4 w y t $.
For the third term, $ \frac{-2 w y}{2} $, dividing -2 by 2 gives us -1. Therefore, the term becomes $ -w y $.

Simplifying fractions helps to make algebraic expressions easier to manage in subsequent steps. Always remember to look for common factors in the numerator and denominator that can cancel each other out.

Combining Like Terms

After simplifying each fraction individually, the next step is to combine like terms. Like terms are terms that have the same variables raised to the same powers. In our simplified expression $ w y t - 4 w y t - w y $, we can see:

$ w y t $ and $ -4 w y t $ are like terms because they both contain $ w y t $.
$ -w y $ is a different term because it lacks the $ t $ variable.

To combine like terms, we perform addition and subtraction on their coefficients (the numerical part). For instance, $ w y t - 4 w y t $ combines to $ -3 w y t $. Afterward, we then include $ -w y $, which is not like any other terms in the expression.

Algebraic Expressions

Finally, let's talk about algebraic expressions. An algebraic expression includes numbers, variables, and arithmetic operations (addition, subtraction, multiplication, and division). In this exercise, our expression $ \frac{4 w y t}{4} + \frac{-8 w y t}{2} - \frac{-2 w y}{2} $ contains multiple components.

Variables (\

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91影视

Simplify. $$ \frac{4 w y t}{4}+\frac{-8 w y t}{2}-\frac{-2 w y}{2} $$

Short Answer

Step by step solution

- Simplify Individual Fractions

- Combine Like Terms

- Perform Operations

Key Concepts

Simplifying Fractions

Combining Like Terms

Algebraic Expressions

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