Problem 61 Solve the equations. $$4 c=-\f... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 4: Problem 61

Solve the equations. $$4 c=-\frac{1}{3}$$

Short Answer

Expert verified

c = -\frac{1}{12}

Step by step solution

Isolate the Variable

To solve the equation, first isolate the variable, which is denoted as $ c $. The given equation is $ 4c = -\frac{1}{3} $.

Divide Both Sides by 4

Divide both sides of the equation by 4 to solve for $ c $. This gives:\[ c = \frac{-\frac{1}{3}}{4} \]

Simplify the Fraction

Simplify the fraction $ \frac{-\frac{1}{3}}{4} $. This can be rewritten as:\[ c = -\frac{1}{3} \times \frac{1}{4} = -\frac{1}{12} \]

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Key Concepts

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

Isolating the Variable

Isolating the variable is the fundamental step in solving linear equations. Here, the variable is denoted as $ c $. To isolate $ c $, we need to get it by itself on one side of the equation. In the given problem, we start with the equation \[ 4c = -\frac{1}{3} \].

Isolating the variable involves performing operations that undo any operations applied to the variable.

In this case, $ c $ is multiplied by 4. To isolate $ c $, we need to undo this multiplication by dividing both sides of the equation by 4.

So, the operation we perform is dividing both sides by 4:
\[ c = \frac{-\frac{1}{3}}{4} \]
The goal in this step is to have the variable $ c $ appear by itself with a coefficient of 1.

Dividing Fractions

When dividing fractions, it's crucial to understand how fraction division works. Dividing by a number is the same as multiplying by its reciprocal.

Let鈥檚 take the fraction equation from isolating the variable step:
\[c = \frac{-\frac{1}{3}}{4} \]
Here we are dividing by 4.

This can be thought of as multiplying by the reciprocal of 4, which is \frac{1}{4}.

So, this fraction division problem can be rewritten as a multiplication problem:
\[ c = -\frac{1}{3} \times \frac{1}{4} \]
This approach simplifies handling fractions and makes the arithmetic more intuitive.

Simplifying Fractions

Simplifying fractions involves reducing a fraction to its simplest form, where the numerator and denominator have no common factors other than 1.

From the dividing fractions step, we obtained:

\[ c = -\frac{1}{3} \times \frac{1}{4} \]

To simplify, multiply the numerators together and the denominators together:
\[ c = -\frac{1 \times 1}{3 \times 4} = -\frac{1}{12} \]
Here, $ -\frac{1}{12} $ is already in its simplest form as the numerator 1 and the denominator 12 have no common factors other than 1.

Simplifying fractions ensures that we present the result in the most reduced, cleanest form.

So, the final value of $ c $ is $ -\frac{1}{12} $.

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91影视

Solve the equations. $$4 c=-\frac{1}{3}$$

Short Answer

Step by step solution

Isolate the Variable

Divide Both Sides by 4

Simplify the Fraction

Key Concepts

Isolating the Variable

Dividing Fractions

Simplifying Fractions

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