Write a how-many-units-in-1-group word problem for 2+ ==?. Use the situation of the problem to help you explain why you can 4 3 solve the division problem by multiplying 2 by the reciprocal of
Write a how-many-units-in-1-group word problem for 2+ ==?. Use the situation of the problem to help you explain why you can 4 3 solve the division problem by multiplying 2 by the reciprocal of
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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![### Division of Fractions: How-Many-Units-In-1-Group Word Problem
**Problem Statement:**
Write a how-many-units-in-1-group word problem for \( 2 \div \frac{3}{4} = ? \). Use the situation of the problem to help you explain why you can solve the division problem by multiplying 2 by the reciprocal of \( \frac{3}{4} \).
**Solution Explanation:**
To solve \( 2 \div \frac{3}{4} \), we can follow these steps:
1. **Understand the Reciprocal:** The reciprocal of a fraction is obtained by flipping the numerator and the denominator. For \( \frac{3}{4} \), the reciprocal is \( \frac{4}{3} \).
2. **Convert Division to Multiplication:** Dividing by a fraction is equivalent to multiplying by its reciprocal. Hence, \( 2 \div \frac{3}{4} \) can be rewritten as \( 2 \times \frac{4}{3} \).
3. **Perform the Multiplication:**
\[ 2 \times \frac{4}{3} = \frac{2 \times 4}{3} = \frac{8}{3} \]
4. **Interpret the Result:** The result \( \frac{8}{3} \) or \( 2 \div \frac{3}{4} \), means there are \( \frac{8}{3} \) (or approximately 2.67) groups of \( \frac{3}{4} \) in the number 2.
### Word Problem Example:
*Imagine you have 2 liters of juice, and you need to fill containers that each hold \( \frac{3}{4} \) of a liter. How many full containers can you fill with 2 liters of juice?*
By calculating \( 2 \div \frac{3}{4} \), you determine that you can fill \( \frac{8}{3} \) containers, meaning you can completely fill 2 containers and have some juice left over for a little more than half of another container.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e4d9a92-7f6d-41e2-a11d-6abc746a28c0%2Fdd43c396-c498-4401-be31-7235fd65f8ea%2F0qlf82_processed.png&w=3840&q=75)
Transcribed Image Text:### Division of Fractions: How-Many-Units-In-1-Group Word Problem
**Problem Statement:**
Write a how-many-units-in-1-group word problem for \( 2 \div \frac{3}{4} = ? \). Use the situation of the problem to help you explain why you can solve the division problem by multiplying 2 by the reciprocal of \( \frac{3}{4} \).
**Solution Explanation:**
To solve \( 2 \div \frac{3}{4} \), we can follow these steps:
1. **Understand the Reciprocal:** The reciprocal of a fraction is obtained by flipping the numerator and the denominator. For \( \frac{3}{4} \), the reciprocal is \( \frac{4}{3} \).
2. **Convert Division to Multiplication:** Dividing by a fraction is equivalent to multiplying by its reciprocal. Hence, \( 2 \div \frac{3}{4} \) can be rewritten as \( 2 \times \frac{4}{3} \).
3. **Perform the Multiplication:**
\[ 2 \times \frac{4}{3} = \frac{2 \times 4}{3} = \frac{8}{3} \]
4. **Interpret the Result:** The result \( \frac{8}{3} \) or \( 2 \div \frac{3}{4} \), means there are \( \frac{8}{3} \) (or approximately 2.67) groups of \( \frac{3}{4} \) in the number 2.
### Word Problem Example:
*Imagine you have 2 liters of juice, and you need to fill containers that each hold \( \frac{3}{4} \) of a liter. How many full containers can you fill with 2 liters of juice?*
By calculating \( 2 \div \frac{3}{4} \), you determine that you can fill \( \frac{8}{3} \) containers, meaning you can completely fill 2 containers and have some juice left over for a little more than half of another container.
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