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Chapter 5: Problem 612

In the following exercises, solve. $$ 0.6 p=13.2 $$

Short Answer

Expert verified
p = 22

Step by step solution

01

- Isolate the Variable

To solve for the variable \( p \), we need to isolate it on one side of the equation. The equation given is \(0.6p = 13.2\).
02

- Divide by the Coefficient

To isolate \( p \), divide both sides of the equation by the coefficient of \( p \), which is 0.6. \[ p = \frac{13.2}{0.6} \]
03

- Simplify the Division

Perform the division to find the value of \( p \). \[ p = \frac{13.2}{0.6} = 22 \]

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Key Concepts

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

Isolate the Variable
To solve a linear equation, the goal is to find the value of the variable. In this case, the variable is p. Our given equation is:
\( 0.6p = 13.2 \)

The first step is to isolate the variable, meaning we want p to be alone on one side of the equation. When the variable is isolated, it becomes easier to see its value. To isolate p, you need to look at what is being done to it. Here, p is being multiplied by 0.6. Our job is to undo this multiplication in the next steps.

Divide by the Coefficient
Now that we know p is being multiplied by 0.6, we need to reverse this operation to isolate p. We do this by dividing both sides of the equation by the coefficient of p, which is 0.6. This looks like this:
\[ p = \frac{13.2}{0.6} \]

Dividing by the coefficient effectively cancels out the multiplication on the left side, leaving p as:
\( p = \frac{13.2}{0.6} \)

Now, we have isolated the variable, and the equation becomes simpler to work with. The isolated variable is now ready for the final step 鈥� simplifying the division.

Simplify the Division
In the last step, we need to perform the division to find the value of p. Our simplified equation is:
\[ p = \frac{13.2}{0.6} \]

To make it simpler, remember these small division tips:
  • Both the numerator (top number) and the denominator (bottom number) can be multiplied or divided by the same number without changing the value of the fraction.

  • You can convert both the numerator and denominator to whole numbers. For instance, multiply both by 10:

  • \( \frac{13.2 \times 10}{0.6 \times 10} = \frac{132}{6} \)

  • Now, this fraction \( \frac{132}{6} \) is much easier to divide.


So, performing this division:
\[ p = \frac{132}{6} = 22 \]

Congratulations! You have now solved for p. The value of \( p \) is 22.

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