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,...
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![### Educational Website: Mathematics Section
#### Example Problem: Subtracting Fractions
**Problem Statement:**
Subtract the fractions and show all work:
\[ \frac{1}{2} - \frac{3}{4} = \]
**Solution Steps:**
1. **Identify the Lowest Common Denominator (LCD):**
- First, list the multiples of each denominator to find the LCD.
Multiples of 2: \( 2, 4, 6, 8, 10, 12, 16 \)
Multiples of 4: \( 4, 8, 12, 16 \)
- The smallest common multiple between the denominators 2 and 4 is 4. Therefore, 4 is the LCD.
2. **Adjust Fractions to Have the Same Denominator:**
- Convert \(\frac{1}{2}\) to a fraction with denominator 4:
\[ \frac{1}{2} = \frac{2}{4} \]
- \(\frac{3}{4}\) already has the denominator 4, so it remains the same:
\[ \frac{3}{4} \]
3. **Subtract the Fractions:**
- Now perform the subtraction with like denominators:
\[ \frac{2}{4} - \frac{3}{4} = \frac{2 - 3}{4} = \frac{-1}{4} \]
Thus, the result is:
\[ \frac{1}{2} - \frac{3}{4} = -\frac{1}{4} \]
#### Work Shown:
- Multiples of 2: `2, 4, 6, 8, 10, 12, 16`
- Multiples of 4: `4, 8, 12, 16`
- Calculation: \(\frac{2}{4} - \frac{3}{4} = \frac{-1}{4} \)
This detailed breakdown illustrates the process of subtracting fractions by finding a common denominator, converting both fractions, and then performing the subtraction operation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb614cecd-2dbc-4e7c-af5f-0f6b495ec878%2Fbeb2fe51-7406-4a59-8012-20e8bee674fc%2Fmhm89fa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Website: Mathematics Section
#### Example Problem: Subtracting Fractions
**Problem Statement:**
Subtract the fractions and show all work:
\[ \frac{1}{2} - \frac{3}{4} = \]
**Solution Steps:**
1. **Identify the Lowest Common Denominator (LCD):**
- First, list the multiples of each denominator to find the LCD.
Multiples of 2: \( 2, 4, 6, 8, 10, 12, 16 \)
Multiples of 4: \( 4, 8, 12, 16 \)
- The smallest common multiple between the denominators 2 and 4 is 4. Therefore, 4 is the LCD.
2. **Adjust Fractions to Have the Same Denominator:**
- Convert \(\frac{1}{2}\) to a fraction with denominator 4:
\[ \frac{1}{2} = \frac{2}{4} \]
- \(\frac{3}{4}\) already has the denominator 4, so it remains the same:
\[ \frac{3}{4} \]
3. **Subtract the Fractions:**
- Now perform the subtraction with like denominators:
\[ \frac{2}{4} - \frac{3}{4} = \frac{2 - 3}{4} = \frac{-1}{4} \]
Thus, the result is:
\[ \frac{1}{2} - \frac{3}{4} = -\frac{1}{4} \]
#### Work Shown:
- Multiples of 2: `2, 4, 6, 8, 10, 12, 16`
- Multiples of 4: `4, 8, 12, 16`
- Calculation: \(\frac{2}{4} - \frac{3}{4} = \frac{-1}{4} \)
This detailed breakdown illustrates the process of subtracting fractions by finding a common denominator, converting both fractions, and then performing the subtraction operation.
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