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Chapter 4: Problem 293

In the following exercises, find the difference. $$-\frac{7}{c}-\frac{7}{c}$$

Short Answer

Expert verified
-\frac{14}{c}

Step by step solution

01

Identify the Initial Expression

The initial expression to simplify is \[-\frac{7}{c} - \frac{7}{c}\].
02

Combine the Like Terms

Since both terms are like terms (they have the same denominator), they can be combined directly. Add the numerators together, keeping the denominator the same.\[-\frac{7}{c} - \frac{7}{c} = -\frac{7 + 7}{c} = -\frac{14}{c}\].

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Key Concepts

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

like terms
In this exercise, we are working with terms that have the same variable in the denominator. These are known as 'like terms'.
Like terms are essential in algebra because they can be simplified or combined.
For example, \(-\frac{7}{c}\) and \(-\frac{7}{c}\) have the exact same variable and denominator value.
This makes them like terms, which means we can combine them by adding or subtracting their numerators.
Combining like terms makes algebraic expressions simpler and easier to work with.
common denominator
To subtract fractions, they must have a common denominator.
The denominator is the bottom number of the fraction that tells us how many equal parts the whole is divided into.
In this exercise, both fractions \(-\frac{7}{c}\) and \(-\frac{7}{c}\) have the same denominator.
This makes it easier to combine them into a single fraction.
If the denominators were different, we would first need to convert them to a common denominator before subtracting.
simplifying fractions
After combining the fractions, the next step is simplifying.
Simplifying fractions involves reducing them to their simplest form.
For the example in the exercise, after combining \(-\frac{7}{c}\) and \(-\frac{7}{c}\), we get \(-\frac{14}{c}\).
To simplify, we check if we can further reduce the fraction by finding the greatest common divisor (GCD) of the numerator and denominator.
In this case, \(-\frac{14}{c}\) is already in its simplest form if \c\ is a variable and not a number that shares factors with 14.
Always check if a fraction can be simplified to make your final answer as clear as possible.

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Most popular questions from this chapter

In the following exercises, simplify. $$ -\frac{22}{25}+\frac{9}{40} $$

In the following exercises, simplify. $$\frac{\frac{1}{6}+\frac{3}{10}}{\frac{14}{30}}$$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x-\frac{1}{3}\) when (a) \(x=\frac{2}{3} \quad\) (b) \(x=-\frac{2}{3}\)

In the following exercises, subtract. $$\frac{11}{12}-\frac{5}{12}$$

In the following exercises, perform the indicated operation. $$ 8 \frac{6}{11}-2 \frac{9}{11} $$
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