Problem 40 - 1,001 GED Practice Questions For Dummies

Question

If \(\frac{2}{7} x=31\), what does \(\frac{4}{7} x\) equal? (A) \(15.5\) (B) 62 (C) \(108.5\) (D) 217

Step-by-Step Solution

Answer

(B) 62

Step 1: Find the value of x

To find the value of x, we need to solve the given equation \(\frac{2}{7} x = 31\). To do this, multiply both sides by \(\frac{7}{2}\) to isolate x: \(x = 31 \times \frac{7}{2}\)

Step 2: Calculate x

Calculate the value of x by multiplying 31 with \(\frac{7}{2}\): \(x = 31 \times \frac{7}{2} = \frac{31 \times 7}{2} = \frac{217}{2}\)

Step 3: Calculate \(\frac{4}{7}x\)

Now that we have the value of x, we can calculate the value of \(\frac{4}{7}x\), by multiplying \(\frac{4}{7}\) with \(\frac{217}{2}\): \(\frac{4}{7}x = \frac{4}{7} \times \frac{217}{2}\)

Step 4: Simplify the expression

Simplify the expression by multiplying the fractions: \(\frac{4}{7}x = \frac{4 \times 217}{7 \times 2} = \frac{868}{14}\)

Step 5: Reduce the fraction

Reduce the fraction by dividing both the numerator and denominator by 2: \(\frac{4}{7}x = \frac{868 \div 2}{14 \div 2} = \frac{434}{7}\) Now comparing the final result \(\frac{434}{7}\) with the provided options: (A) 15.5, the decimal representation of this option is \(\frac{31}{2}\) which is not equal to \(\frac{434}{7}\) (B) 62, the fraction representation of this option is \(\frac{434}{7}\), which is the correct answer. (C) 108.5, the decimal representation of this option is \(\frac{217}{2}\) which is not equal to \(\frac{434}{7}\) (D) 217, the fraction representation of this option is \(\frac{868}{4}\) which is not equal to \(\frac{434}{7}\) So the correct answer is (B) 62.

Key Concepts

Solving Linear Equations

Solving linear equations is a fundamental skill in algebra. A linear equation is an equation for a straight line and can be as simple as a one-step process or as complex as a multistep computation. In the exercise, you are given a linear equation where the variable is part of a fraction. The primary objective here is to isolate the variable, making x the subject of the equation.

To achieve this, we use the property of equality that states if you perform the same operation on both sides of an equation, the equation remains balanced. The equation given is \(\frac{2}{7} x = 31\), and to solve for x, we multiply both sides by the reciprocal of \(\frac{2}{7}\), which is \(\frac{7}{2}\). By doing so, we effectively cancel out the fraction on the left and are left with x on one side of the equation. This process is essential for maintaining the balance of the equation while isolating the variable.

Common Mistakes to Avoid

• Always remember to perform the same operation on both sides of the equation.
• Be cautious not to confuse the reciprocal of a fraction with its opposite.
• After finding the value of x, apply it back to other parts of the problem carefully to ensure accuracy.

Fractions in Algebra

Fractions appear frequently in algebra, and understanding how to manage them is crucial. In our exercise, fractions are used to indicate a portion of x. Key operations with fractions include simplification, addition, subtraction, multiplication, and division.

Multiplying fractions, as shown in the solution steps, involves multiplying the numerators together and the denominators together. The step that might cause students trouble is simplifying the fraction, which involves finding a common factor in both the numerator and denominator and dividing them by it.

Operational Tips:

• Multiplication of fractions does not require a common denominator.
• Always simplify fractions to their lowest terms to make comparison and further calculations easier.
• Remember that dividing by a fraction is equivalent to multiplying by its reciprocal.

In the given problem, after solving for x, the fraction \(\frac{4}{7} x\) was simplified, leading us to the correct answer.

GED Math Test Prep

Preparing for the GED Math test involves mastering a variety of topics, including algebra, geometry, and data analysis. When preparing for algebra questions, like the one presented in the exercise, practice is key. Familiarizing yourself with the basic operations and concepts helps mitigate errors and build confidence.

Strategies for effective GED Math preparation:

Understand The Concepts

• Grasp the core concepts of algebra, like solving equations and working with fractions, as they form the basis for more complicated problems.

Practice Regularly

• Consistent practice with a variety of problems increases speed and accuracy.
• Use practice tests to identify weak areas and focus your study on those topics.

Review Mistakes

• Analyze your mistakes to understand where your reasoning might have gone wrong and to prevent similar errors in the future.

Approaching your GED Math test prep with a disciplined schedule, clear understanding of algebraic principles, and relentless practice will greatly improve your chances of scoring well on the test.