Error Analysis  Your friend says that the quotient three eighths divided by three sixteenths
 is one half
. What is the correct​ quotient? What mistake did your friend likely​ make? 

Let's solve the problem step by step.

### Step 1: Understanding the Problem
The problem asks us to find the quotient of \(\frac{3}{8}\) divided by \(\frac{3}{16}\).

### Step 2: Divide the Fractions
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

\[
\frac{3}{8} \div \frac{3}{16} = \frac{3}{8} \times \frac{16}{3}
\]

### Step 3: Simplify the Expression
Now, multiply the fractions:

\[
\frac{3 \times 16}{8 \times 3} = \frac{48}{24} = 2
\]

### Step 4: Correct Quotient
The correct quotient is **2**.

### Identifying the Mistake
Your friend likely made a mistake by either:
1. Incorrectly simplifying the division of fractions.
2. Misinterpreting the operation as \(\frac{3}{16} \div \frac{3}{8}\) instead of \(\frac{3}{8} \div \frac{3}{16}\).

### Summary
- **Correct Quotient:** 2
- **Friend's Mistake:** Misinterpreting the division operation or incorrectly simplifying the division.

Would you like more details, or do you have any questions? Here are some related questions to explore:

1. What is the reciprocal of a fraction, and how is it used in division?
2. How do you simplify fractions after multiplication?
3. What is the difference between multiplying and dividing fractions?
4. How can common mistakes in fraction division be avoided?
5. How does understanding division of fractions help in real-world applications?

**Tip:** Always double-check your operations when dealing with fractions, especially when dividing or multiplying, to avoid common errors.

Explore how to solve the division of fractions problem: 3/8 divided by 3/16. Learn step-by-step with detailed explanations and identify common mistakes. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation