Question

On Monday, Andrea finished \(\frac{1}{4}\) of her homework assignment. On Tuesday, she completed \(\frac{1}{2}\) of the remaining work. What fraction of her assignment does Andrea still have left to complete? (A) \(\frac{1}{8}\) (B) \(\frac{1}{4}\) (C) \(\frac{3}{8}\) (D) \(\frac{5}{8}\)

Short answer

Andrea has \(\frac{3}{8}\) of her assignment left to complete.

Step-by-step solution

Calculate fraction completed on Monday

Andrea finished 1/4 of her homework assignment on Monday.

Calculate fraction remaining after Monday

To find the remaining work after Monday, subtract the portion completed on Monday from the total assignment: Remaining fraction = Total fraction - Fraction completed on Monday Remaining fraction = \(1 - \frac{1}{4}=\frac{3}{4}\)

Calculate completed fraction on Tuesday

On Tuesday, Andrea completed 1/2 of the remaining work: Fraction completed on Tuesday = \(\frac{1}{2}(\frac{3}{4}) = \frac{3}{8}\)

Calculate total fraction completed

Add the fractions completed on Monday and Tuesday to find the total fraction completed: Total completed fraction = \(\frac{1}{4}+\frac{3}{8}=\frac{1}{4}+\frac{3}{8}\) To add these fractions, we need a common denominator, which is 8 in this case. Convert the fraction \(\frac{1}{4}\) to have the new denominator: \(\frac{1}{4}*\frac{2}{2}=\frac{2}{8}\) Now, add the fractions: Total fraction completed = \(\frac{2}{8}+\frac{3}{8}=\frac{5}{8}\)

Calculate fraction remaining

Subtract the total completed fraction from the total assignment to find the remaining fraction: Remaining fraction = Total fraction - Total completed fraction Remaining fraction = \(1-\frac{5}{8}=\frac{8}{8}-\frac{5}{8}=\frac{3}{8}\) So, Andrea has \(\frac{3}{8}\) of her assignment left to complete, which is answer (C).

Key concepts

Fractions Addition

Understanding how to add fractions is essential for solving many types of math problems. When adding fractions, the key is to have a common denominator, which is a shared multiple of the denominators of the fractions involved. For instance, consider the fractions \(\frac{1}{4}\) and \(\frac{3}{8}\). Here, the common denominator is 8.

To add \(\frac{1}{4}\) to \(\frac{3}{8}\), first, convert \(\frac{1}{4}\) so it has the same denominator as \(\frac{3}{8}\): \(\frac{1}{4} * \frac{2}{2} = \frac{2}{8}\). Now, with a common denominator, simply add the numerators: \(\frac{2}{8} + \frac{3}{8} = \frac{5}{8}\). This process allows you to combine fractions to find the cumulative effect, as in the case when solving the assigned textbook problem.

Fraction Subtraction

Subtracting fractions follows a similar rationale to addition. A common denominator between the two fractions is necessary for the operation to be valid. To illustrate, let's take the total fraction of homework 1, or \(\frac{8}{8}\), and subtract the fraction of homework Andrea has completed, \(\frac{5}{8}\). With the same denominators, the subtraction is straightforward: \(\frac{8}{8} - \frac{5}{8} = \frac{3}{8}\). This calculation reveals the fraction of homework Andrea has yet to finish.

In cases where the denominators are not the same, they must be manipulated to find a common denominator. Only then can the respective numerators be subtracted. This understanding of fraction subtraction helps one to determine the remaining value after a portion has been taken away, which is an integral part of solving fraction word problems.

GED Math Practice

Successfully navigating fraction problems is a key component of GED math practice. The GED test often includes questions that require a clear understanding of fractions and the ability to perform operations like addition and subtraction.

When preparing for the GED, it's important to practice with real-world scenarios like the exercise given, where you need to calculate portions completed and remaining. Step-by-step problem solving, as shown in the example, helps lay the foundation for the skills needed to tackle GED questions confidently. Remember to always simplify your answers and, where possible, convert improper fractions to mixed numbers if that's the expected format for the test.