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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![### Evaluation of Mixed Numbers
This section aims to help you evaluate mixed numbers. Work through the following example to understand the process better.
#### Problem Statement:
Evaluate \( 2 \dfrac{1}{4} + \dfrac{5}{6} \).
#### Multiple Choice Answers:
- \( \boxed{2 \dfrac{3}{5}} \)
- \( \dfrac{37}{12} \)
- \( 3 \)
### Steps to Solve
1. **Convert the Mixed Number to an Improper Fraction:**
First, convert \( 2 \dfrac{1}{4} \) to an improper fraction.
\[
2 \dfrac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\]
2. **Find a Common Denominator:**
The given fractions now are \( \frac{9}{4} \) and \( \frac{5}{6} \). To add these fractions, you need a common denominator. The least common multiple of 4 and 6 is 12.
Convert the fractions:
\[
\frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12}
\]
\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\]
3. **Add the Fractions:**
\[
\frac{27}{12} + \frac{10}{12} = \frac{37}{12}
\]
4. **Convert the Improper Fraction to a Mixed Number:**
\[
\frac{37}{12} = 3 \dfrac{1}{12}
\]
### Conclusion:
Converting \( 2 \dfrac{1}{4} + \dfrac{5}{6} \) results in \( 3 \dfrac{1}{12} \). The correct answer is not listed in the multiple-choice options provided.
There is an apparent error in the choices given. The selected choice \( \boxed{2 \dfrac{3}{5}} \) is not the correct answer](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3bd0cd3-f3a0-44e9-8e1d-fdfa6268f022%2F9ccdb870-ccba-49c3-93b9-5f65be200c03%2Fjj7q4nf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluation of Mixed Numbers
This section aims to help you evaluate mixed numbers. Work through the following example to understand the process better.
#### Problem Statement:
Evaluate \( 2 \dfrac{1}{4} + \dfrac{5}{6} \).
#### Multiple Choice Answers:
- \( \boxed{2 \dfrac{3}{5}} \)
- \( \dfrac{37}{12} \)
- \( 3 \)
### Steps to Solve
1. **Convert the Mixed Number to an Improper Fraction:**
First, convert \( 2 \dfrac{1}{4} \) to an improper fraction.
\[
2 \dfrac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\]
2. **Find a Common Denominator:**
The given fractions now are \( \frac{9}{4} \) and \( \frac{5}{6} \). To add these fractions, you need a common denominator. The least common multiple of 4 and 6 is 12.
Convert the fractions:
\[
\frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12}
\]
\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\]
3. **Add the Fractions:**
\[
\frac{27}{12} + \frac{10}{12} = \frac{37}{12}
\]
4. **Convert the Improper Fraction to a Mixed Number:**
\[
\frac{37}{12} = 3 \dfrac{1}{12}
\]
### Conclusion:
Converting \( 2 \dfrac{1}{4} + \dfrac{5}{6} \) results in \( 3 \dfrac{1}{12} \). The correct answer is not listed in the multiple-choice options provided.
There is an apparent error in the choices given. The selected choice \( \boxed{2 \dfrac{3}{5}} \) is not the correct answer
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