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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![**Question:** How many sets of \( \frac{3}{4} \) are in \( 2 \frac{1}{2} \)?
To find out how many sets of \( \frac{3}{4} \) are in \( 2 \frac{1}{2} \), you need to divide \( 2 \frac{1}{2} \) by \( \frac{3}{4} \).
1. **Convert Mixed Number to Improper Fraction:**
\( 2 \frac{1}{2} = \frac{5}{2} \)
2. **Division of Fractions:**
To divide by a fraction, multiply by its reciprocal.
\[
\frac{5}{2} \div \frac{3}{4} = \frac{5}{2} \times \frac{4}{3} = \frac{5 \times 4}{2 \times 3} = \frac{20}{6} = \frac{10}{3}
\]
3. **Simplify the Fraction:**
\( \frac{10}{3} \approx 3 \frac{1}{3} \)
So, there are \( 3 \frac{1}{3} \) sets of \( \frac{3}{4} \) in \( 2 \frac{1}{2} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75f4417d-fce2-44c5-a1da-2dd7ab7f33df%2F4020ee1e-ace5-4d6d-b583-cfc11a1a83c5%2Fvg59bds_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:** How many sets of \( \frac{3}{4} \) are in \( 2 \frac{1}{2} \)?
To find out how many sets of \( \frac{3}{4} \) are in \( 2 \frac{1}{2} \), you need to divide \( 2 \frac{1}{2} \) by \( \frac{3}{4} \).
1. **Convert Mixed Number to Improper Fraction:**
\( 2 \frac{1}{2} = \frac{5}{2} \)
2. **Division of Fractions:**
To divide by a fraction, multiply by its reciprocal.
\[
\frac{5}{2} \div \frac{3}{4} = \frac{5}{2} \times \frac{4}{3} = \frac{5 \times 4}{2 \times 3} = \frac{20}{6} = \frac{10}{3}
\]
3. **Simplify the Fraction:**
\( \frac{10}{3} \approx 3 \frac{1}{3} \)
So, there are \( 3 \frac{1}{3} \) sets of \( \frac{3}{4} \) in \( 2 \frac{1}{2} \).
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