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Chapter 1: Problem 13

Write an equation that represents the statement. The quotient of \(r\) and 2 is 9 .

Short Answer

Expert verified
The equation is \(\frac{r}{2} = 9\).

Step by step solution

01

Understand the statement

The statement says 'The quotient of r and 2 is 9'. This means r divided by 2 equals 9.
02

Formulate the equation

Based on the understanding from Step 1, the equation can be written as \(\frac{r}{2} = 9\).

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Key Concepts

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

Quotient
When tackling algebraic equations, understanding the word "quotient" is essential. A quotient is the result of dividing one number by another. For example, in our exercise, the term "quotient" tells us that the problem involves division. Specifically, we are dividing a variable, denoted by \(r\), by the number 2.
  • In mathematical terms, if you divide a number \(a\) by another number \(b\), the result is \(\frac{a}{b}\), which is the quotient.
  • A clear understanding of this concept translates directly to setting up correct equations, which is crucial in algebra.
Remember, when you see the word "quotient," think about the division operation. In our problem, it specifically means that \(\frac{r}{2}\) is the expression needed for further calculations.
Equation Formulation
Equation formulation is the process of translating a word problem into a mathematical statement. In our case, we transformed "The quotient of \(r\) and 2 is 9" into an equation. It is crucial to correctly interpret the language. Here鈥檚 how to break it down:
  • First, identify the components involved: the variable \(r\), the constant 2, and the result 9.
  • Translate the word "quotient" into the corresponding mathematical operation, which is division in this context.
  • Structure this understanding into the equation \(\frac{r}{2} = 9\).
Start by identifying keywords in the problem like "quotient" or "equals"鈥攖hese guide you in constructing the equation effectively. Formulating equations correctly is essential for problem-solving in algebra. It provides a clear model to follow and solve.
Problem Solving
Problem solving involves using the formulated equation to find the value of the unknown variable. With the equation \(\frac{r}{2} = 9\), you need to isolate \(r\). This process requires operations that maintain the equation's balance.
  • In this case, multiply both sides of the equation by 2 to undo the division. This gives us \(r = 18\).
  • It's important to ensure every operation applied to one side of the equation is also applied to the other side to keep it equal.
  • Once \(r\) is isolated, you've solved the equation!
Effective problem solving in algebra is about taking systematic steps to find solutions. Be methodical: carefully manipulate the equation until the variable is isolated. This builds confidence and competence in handling algebraic equations.

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Most popular questions from this chapter

You buy six T-bone steaks that cost \(\$ 7.99\) per pound. The weight listed on the package is \(5.72\) pounds. The scale that weighed the package is accurate to within \(\frac{1}{2}\) ounce. How much money might you have been undercharged or overcharged?

Solve the inequality. Then graph the solution set on the real number line. \(x^{2}+4 x+4 \geq 9\)

Solve the inequality. Then graph the solution set on the real number line. \(x^{2}+2 x-3<0\)

A projectile is fired straight upward from ground level with an initial velocity of 160 feet per second. During what time period will its height be less than 384 feet?

Solve the inequality. Then graph the solution set on the real number line. \(\frac{2}{5} x>7\)
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