Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![To solve the problem and reduce the result to the lowest fractional terms, follow these steps:
Given problem:
\[
\left( \frac{4}{7} - \frac{1}{8} \right) \times \left( \frac{1}{4} + \frac{5}{10} \right)
\]
**Step 1: Solve inside the brackets.**
- **Subtraction inside the first bracket:**
\[
\frac{4}{7} - \frac{1}{8}
\]
Find a common denominator (56), then:
\[
\frac{4}{7} = \frac{32}{56}, \quad \frac{1}{8} = \frac{7}{56}
\]
\[
\frac{32}{56} - \frac{7}{56} = \frac{25}{56}
\]
- **Addition inside the second bracket:**
\[
\frac{1}{4} + \frac{5}{10}
\]
Simplify \(\frac{5}{10}\) to \(\frac{1}{2}\), then find a common denominator (4):
\[
\frac{1}{4} = \frac{1}{4}, \quad \frac{1}{2} = \frac{2}{4}
\]
\[
\frac{1}{4} + \frac{2}{4} = \frac{3}{4}
\]
**Step 2: Multiply the results from within the brackets.**
\[
\frac{25}{56} \times \frac{3}{4} = \frac{75}{224}
\]
**Step 3: Reduce the fraction to its lowest terms.**
Since 75 and 224 have no common factors other than 1, \(\frac{75}{224}\) is already in its simplest form.
Therefore, the final answer is:
\[
\frac{75}{224}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9163f72-9cb9-47ec-9932-aa32cb69a25b%2Fb480f865-1de6-48e9-8abe-52be6eafeafd%2Fnb9evav_processed.png&w=3840&q=75)
Transcribed Image Text:To solve the problem and reduce the result to the lowest fractional terms, follow these steps:
Given problem:
\[
\left( \frac{4}{7} - \frac{1}{8} \right) \times \left( \frac{1}{4} + \frac{5}{10} \right)
\]
**Step 1: Solve inside the brackets.**
- **Subtraction inside the first bracket:**
\[
\frac{4}{7} - \frac{1}{8}
\]
Find a common denominator (56), then:
\[
\frac{4}{7} = \frac{32}{56}, \quad \frac{1}{8} = \frac{7}{56}
\]
\[
\frac{32}{56} - \frac{7}{56} = \frac{25}{56}
\]
- **Addition inside the second bracket:**
\[
\frac{1}{4} + \frac{5}{10}
\]
Simplify \(\frac{5}{10}\) to \(\frac{1}{2}\), then find a common denominator (4):
\[
\frac{1}{4} = \frac{1}{4}, \quad \frac{1}{2} = \frac{2}{4}
\]
\[
\frac{1}{4} + \frac{2}{4} = \frac{3}{4}
\]
**Step 2: Multiply the results from within the brackets.**
\[
\frac{25}{56} \times \frac{3}{4} = \frac{75}{224}
\]
**Step 3: Reduce the fraction to its lowest terms.**
Since 75 and 224 have no common factors other than 1, \(\frac{75}{224}\) is already in its simplest form.
Therefore, the final answer is:
\[
\frac{75}{224}
\]
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