Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter9: Roots And Radicals
Section9.3: Add And Subtract Square Roots
Problem 232E: Explain the process for determining whether two radicals are like or unlike. Make sure your answer...
Related questions
Question
![**Simplifying Fractions**
**Problem:**
Simplify the expression \( \frac{4}{5} - \frac{5}{4} \)
**Solution Steps:**
1. **Find the common denominator:** To subtract fractions, they must have a common denominator. The denominators of \( \frac{4}{5} \) and \( \frac{5}{4} \) are 5 and 4, respectively. The least common denominator (LCD) for these fractions is 20.
2. **Convert each fraction to the common denominator:**
- For \( \frac{4}{5} \):
- Numerator \( = 4 \times 4 = 16 \)
- Denominator \( = 5 \times 4 = 20 \)
- So, \( \frac{4}{5} = \frac{16}{20} \)
- For \( \frac{5}{4} \):
- Numerator \( = 5 \times 5 = 25 \)
- Denominator \( = 4 \times 5 = 20 \)
- So, \( \frac{5}{4} = \frac{25}{20} \)
3. **Subtract the converted fractions:**
- \( \frac{16}{20} - \frac{25}{20} \)
- Since the denominators are now the same, subtract the numerators:
- \( 16 - 25 \)
- Result: \( \frac{-9}{20} \)
Therefore, the simplified form of \( \frac{4}{5} - \frac{5}{4} \) is:
\[ \frac{-9}{20} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa2bd4a1-658a-407d-88ce-b68f7d21ec93%2F14bc5006-be20-4385-99d5-8422885f57e7%2Fpwpiy9h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Simplifying Fractions**
**Problem:**
Simplify the expression \( \frac{4}{5} - \frac{5}{4} \)
**Solution Steps:**
1. **Find the common denominator:** To subtract fractions, they must have a common denominator. The denominators of \( \frac{4}{5} \) and \( \frac{5}{4} \) are 5 and 4, respectively. The least common denominator (LCD) for these fractions is 20.
2. **Convert each fraction to the common denominator:**
- For \( \frac{4}{5} \):
- Numerator \( = 4 \times 4 = 16 \)
- Denominator \( = 5 \times 4 = 20 \)
- So, \( \frac{4}{5} = \frac{16}{20} \)
- For \( \frac{5}{4} \):
- Numerator \( = 5 \times 5 = 25 \)
- Denominator \( = 4 \times 5 = 20 \)
- So, \( \frac{5}{4} = \frac{25}{20} \)
3. **Subtract the converted fractions:**
- \( \frac{16}{20} - \frac{25}{20} \)
- Since the denominators are now the same, subtract the numerators:
- \( 16 - 25 \)
- Result: \( \frac{-9}{20} \)
Therefore, the simplified form of \( \frac{4}{5} - \frac{5}{4} \) is:
\[ \frac{-9}{20} \]
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