How many groups of 7 1/3 are there in 2 3/4?

To determine how many groups of \( 7 \frac{1}{3} \) are in \( 2 \frac{3}{4} \), we need to divide these two mixed numbers.

### Step-by-step process:

1. **Convert the mixed numbers to improper fractions:**
   \[
   7 \frac{1}{3} = \frac{22}{3}, \quad 2 \frac{3}{4} = \frac{11}{4}
   \]

2. **Set up the division:**
   \[
   \frac{11}{4} \div \frac{22}{3}
   \]

3. **Rewrite the division as multiplication by the reciprocal:**
   \[
   \frac{11}{4} \times \frac{3}{22}
   \]

4. **Multiply the fractions:**
   \[
   \frac{11 \times 3}{4 \times 22} = \frac{33}{88}
   \]

5. **Simplify the fraction:**
   \[
   \frac{33}{88} = \frac{3}{8}
   \]

So, there are **\( \frac{3}{8} \)** groups of \( 7 \frac{1}{3} \) in \( 2 \frac{3}{4} \).

Would you like more details on any step? Here are 5 related questions:

1. How do you convert improper fractions back to mixed numbers?
2. What are some common mistakes when dividing mixed numbers?
3. Can we visualize this division on a number line?
4. How do you handle word problems involving division of mixed numbers?
5. How can dividing fractions be applied in real-life situations?

**Tip:** When dividing fractions, always remember to multiply by the reciprocal of the second fraction.

Discover how to divide mixed numbers like 7 1/3 and 2 3/4 through an easy-to-follow step-by-step guide. Learn key concepts like converting mixed numbers to improper fractions and multiplying by reciprocals. Perfect for students in 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