Answer
To represent \( \frac{6}{10} \), draw a rectangle divided into 10 equal parts and shade 6. Two equivalent fractions are \( \frac{3}{5} \) and \( \frac{12}{20} \).
Solution
Sure! Let's work through **Part A** together.
### **Part A: Drawing a Model for \( \frac{6}{10} \) and Two Equivalent Fractions**
#### **1. Drawing a Fraction Bar Model for \( \frac{6}{10} \):**
A **fraction bar model** visually represents a fraction by dividing a bar into equal parts.
- **Step 1:** Draw a rectangle (this is your whole).
- **Step 2:** Divide the rectangle into **10 equal parts** since the denominator is 10.
- **Step 3:** Shade **6 out of the 10 parts** to represent \( \frac{6}{10} \).
*If you're drawing this, visualize a rectangle split into 10 equal sections with 6 of them shaded.*
#### **2. Identifying Two Equivalent Fractions:**
Equivalent fractions are different fractions that represent the same value.
- **First Equivalent Fraction:** \( \frac{3}{5} \)
- **Explanation:** Simplify \( \frac{6}{10} \) by dividing both numerator and denominator by 2.
\[
\frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\]
- **Second Equivalent Fraction:** \( \frac{12}{20} \)
- **Explanation:** Multiply both numerator and denominator of \( \frac{6}{10} \) by 2.
\[
\frac{6 \times 2}{10 \times 2} = \frac{12}{20}
\]
#### **3. Drawing Fraction Bar Models for the Equivalent Fractions:**
- **For \( \frac{3}{5} \):**
- **Step 1:** Draw a rectangle.
- **Step 2:** Divide it into **5 equal parts**.
- **Step 3:** Shade **3 out of the 5 parts**.
- **For \( \frac{12}{20} \):**
- **Step 1:** Draw a rectangle.
- **Step 2:** Divide it into **20 equal parts**.
- **Step 3:** Shade **12 out of the 20 parts**.
*If you're drawing these, ensure the divisions are equal and accurately represent the shaded portions.*
#### **Visual Summary:**
| Fraction | Model Description |
|----------|--------------------------------------------------------|
| \( \frac{6}{10} \) | Rectangle divided into 10 parts, 6 shaded |
| \( \frac{3}{5} \) | Rectangle divided into 5 parts, 3 shaded |
| \( \frac{12}{20} \)| Rectangle divided into 20 parts, 12 shaded |
These models help visualize that \( \frac{6}{10} \), \( \frac{3}{5} \), and \( \frac{12}{20} \) all represent the same portion of a whole.
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**Feel free to draw these models on paper using the steps provided to get a clear visual understanding!**
Reviewed and approved by the UpStudy tutoring team
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