Question

If \(\frac{1}{5}\) of \(x=15\), what is \(\frac{4}{3}\) of \(x\) ? A. 4 B. 25 C. 75 D. 100

Short answer

D. 100

Step-by-step solution

Determine the value of x

Given that \(\frac{1}{5}\) of \(x=15\), we can write the equation as: \[\frac{1}{5}x = 15\] To find the value of \(x\), we need to isolate it by multiplying both sides by 5: \[x=15 \times 5\] Now, calculate the value of \(x\): \[x=75\]

Find the value of \(\frac{4}{3}\) of x

Now that we have the value of \(x\), we can find the value of \(\frac{4}{3}\) of \(x\) using the equation: \[\frac{4}{3}x = \frac{4}{3} \times 75\] Now, calculate the value of \(\frac{4}{3}\) of \(x\): \[\frac{4}{3}x = 100\]

Compare the result with the answer choices

Now we can compare our result with the given answer choices: A. 4 B. 25 C. 75 D. 100 Our calculated value of \(\frac{4}{3}\) of \(x\) is 100, which matches answer choice D. Therefore, the correct answer is: D. 100

Key concepts

Algebra

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols; it is a language through which we describe patterns and relationships among quantities. In the GED math problems, algebraic concepts are fundamental and are often represented in the form of equations.

To solve algebraic equations, one must understand the properties of equality and the operations that can be used to isolate the variable, which represents an unknown quantity in the problem. For instance, if you want to solve \( \frac{1}{5}x = 15 \), you'll need to perform operations that will 'undo' what's been done to the variable, \(x\).

In this particular example, multiplication is used to isolate \(x\). Multiplying both sides of the equation by 5 negates the division by 5 on the left side, leaving \(x\) by itself. Always keep in mind that whatever operation you do to one side of the equation, you must do the same to the other side, maintaining the balance that is central to equation solving.

Fractions in Equations

When dealing with fractions in equations, as often seen in GED math problems, the principle remains the same: isolate the variable to solve for it. However, fractions add an extra layer of complexity. The key here is understanding how to remove fractions to simplify the equation.

For instance, an equation like \( \frac{4}{3}x = 100 \) may look intimidating at first glance with fractions. But, once \(x\) is already known (from previous parts of the problem, like \(x=75\)), you can directly substitute the value of \(x\) in the equation and solve it.

If you need to get rid of the fraction before knowing the value of \(x\), you could multiply both sides by the denominator to make the equation easier to solve. Techniques like finding a common denominator or cross-multiplying can be valuable tools when working with complex fractions in equations. Understanding and practicing these methods are crucial for improving proficiency in algebra and performing well on the math portion of the GED.

GED Test Preparation

Preparing for the GED (General Educational Development) test requires a strategic approach, especially for the math section, which includes algebra among other topics. To excel at the GED math problems, it's important to have a good foundation in algebra and the ability to solve equations with fractions, as seen in the exercise provided.

Practice is a critical part of GED test preparation. Work through various algebra problems, ensuring that you can apply the correct methodologies in equations, whether they involve fractions, variables, or other algebraic expressions. Useful study tips include:

• Taking timed practice tests to simulate the actual exam conditions.
• Reviewing concepts and practicing problems in areas where you find difficulty.
• Seeking additional resources, such as videos or tutoring, for difficult topics.
• Using flashcards for quick review of algebra terms and rules.

Preparation also involves familiarizing yourself with the test format and improving your test-taking strategies, like the process of elimination used in the example exercise. By covering all these bases, you'll increase your chances of achieving a score that accurately reflects your mathematical ability.