Problem 63 Solve the equations. $$-p=-\fr... [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 63

Solve the equations. $$-p=-\frac{7}{10}$$

Short Answer

Expert verified

p = \frac{7}{10}

Step by step solution

Isolate the Variable

To isolate the variable $p$, notice that it is being multiplied by -1. Therefore, we need to divide both sides of the equation by -1 to solve for $p$.

Perform the Division

Divide both sides of the equation $ -p = -\frac{7}{10} $ by -1 to get: \[ -p \div -1 = -\frac{7}{10} \div -1 \]

Simplify the Equation

The division results in: \[ p = \frac{7}{10} \] Simplifying the right side of the equation, we find that $ p = \frac{7}{10} $

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Key Concepts

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

isolating variables

Isolating the variable is an essential skill in solving equations. When we talk about isolating a variable, we're referring to the process of getting the variable by itself on one side of the equation.
This often involves undoing operations that have been applied to the variable. In our example exercise, the variable is 'p', and it's currently being multiplied by -1 which we see as $-p = -\frac{7}{10}$.
To undo this, we need to divide both sides of the equation by -1. The key idea is to perform the opposite operation to isolate the variable.

division in equations

Division in equations is a method used to simplify problems and isolate variables. Here, we needed to divide both sides by -1 because the variable 'p' was multiplied by -1.
When dividing, remember to apply the division to each term individually.
Thus, from $-p = -\frac{7}{10}$, dividing by -1 on both sides results in: $-p \div -1 = -\frac{7}{10} \div -1$.
This operation cancels out the negative signs, making the equation simpler to solve.

simplifying fractions

Simplifying fractions is a common step when dividing fractions in equations. Simplification often means reducing the fraction to its simplest form.
In our solved problem, after dividing both sides by -1, we got: $-\frac{7}{10} \div -1 = \frac{7}{10} $.
Since a negative divided by a negative gives a positive, the fraction $\frac{7}{10}$ is already in its simplest form. Always check to ensure the fraction is in its simplest state by looking for common factors in the numerator and denominator.
In this case, we find that the fraction doesn't contain any further common factors and is thus fully simplified.

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91影视

Solve the equations. $$-p=-\frac{7}{10}$$

Short Answer

Step by step solution

Isolate the Variable

Perform the Division

Simplify the Equation

Key Concepts

isolating variables

division in equations

simplifying fractions

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