Choose The Best Answer. If $p = -7$ And $r = \frac{1}{2}$, What Does $p \cdot R - R$ Equal?A. -4 B. -3 C. 3 D. 4

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Understanding the Problem

In this problem, we are given two variables, pp and rr, with specific values. We need to find the value of the expression p⋅r−rp \cdot r - r when p=−7p = -7 and r=12r = \frac{1}{2}. To solve this problem, we will follow the order of operations (PEMDAS) and use basic algebraic properties.

Step 1: Substitute the Given Values

The first step is to substitute the given values of pp and rr into the expression. We have:

p=−7p = -7 r=12r = \frac{1}{2}

So, the expression becomes:

(−7)⋅(12)−(12)(-7) \cdot \left(\frac{1}{2}\right) - \left(\frac{1}{2}\right)

Step 2: Multiply the Numbers

Next, we need to multiply the numbers in the expression. We have:

(−7)⋅(12)=−72(-7) \cdot \left(\frac{1}{2}\right) = -\frac{7}{2}

So, the expression becomes:

−72−(12)-\frac{7}{2} - \left(\frac{1}{2}\right)

Step 3: Subtract the Fractions

Now, we need to subtract the fractions in the expression. We have:

−72−(12)=−72−12-\frac{7}{2} - \left(\frac{1}{2}\right) = -\frac{7}{2} - \frac{1}{2}

To subtract fractions, we need to have the same denominator. In this case, the denominator is 2. So, we can subtract the numerators:

−72−12=−82-\frac{7}{2} - \frac{1}{2} = -\frac{8}{2}

Step 4: Simplify the Expression

Finally, we can simplify the expression by dividing the numerator by the denominator:

−82=−4-\frac{8}{2} = -4

Conclusion

Therefore, the value of the expression p⋅r−rp \cdot r - r when p=−7p = -7 and r=12r = \frac{1}{2} is:

-4

This is the correct answer.

Why Choose -4?

We chose -4 as the correct answer because it is the result of the expression p⋅r−rp \cdot r - r when p=−7p = -7 and r=12r = \frac{1}{2}. We followed the order of operations (PEMDAS) and used basic algebraic properties to simplify the expression.

Common Mistakes

One common mistake is to forget to follow the order of operations (PEMDAS). Another mistake is to not simplify the expression correctly.

Tips and Tricks

To solve this problem, you need to follow the order of operations (PEMDAS) and use basic algebraic properties. You also need to simplify the expression correctly.

Real-World Applications

This problem is relevant to real-world applications in mathematics, such as solving algebraic expressions and equations.

Conclusion

In conclusion, the value of the expression p⋅r−rp \cdot r - r when p=−7p = -7 and r=12r = \frac{1}{2} is:

-4

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to follow these steps:

  1. Find the least common denominator (LCD) of the fractions.
  2. Convert each fraction to have the LCD as the denominator.
  3. Add or subtract the fractions as needed.
  4. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. For example, x, y, and z are variables. A constant is a value that does not change. For example, 2, 5, and 10 are constants.

Q: How do I solve an equation with variables on both sides?

A: To solve an equation with variables on both sides, you need to follow these steps:

  1. Add or subtract the same value to both sides of the equation to get all the variables on one side.
  2. Multiply or divide both sides of the equation by the same value to get all the variables on one side.
  3. Simplify the resulting equation to find the value of the variable.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable is 1. For example, 2x + 3 = 5 is a linear equation. A quadratic equation is an equation in which the highest power of the variable is 2. For example, x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to follow these steps:

  1. Find the x-intercept and y-intercept of the equation.
  2. Plot the x-intercept and y-intercept on a coordinate plane.
  3. Draw a line through the two points to graph the equation.

Q: What is the difference between a function and a relation?

A: A function is a relation in which each input value corresponds to exactly one output value. For example, f(x) = 2x + 1 is a function. A relation is a set of ordered pairs that do not necessarily have a one-to-one correspondence between the input and output values.

Conclusion

In conclusion, we have covered some common questions and answers related to algebra and mathematics. We hope this article has been helpful in clarifying any doubts you may have had. If you have any further questions, please don't hesitate to ask.