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With lowest term, and explanations, make it clear

Let's solve the first few problems from each section of the worksheet and explain the steps involved. I will cover the first problem from "Adding and Subtracting using Fractions," "Multiplying Fractions," and "Dividing Fractions."

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### **Adding and Subtracting using Fractions**
#### Problem a) \( \frac{1}{6} + \frac{1}{6} \)
1. **Step 1**: Since both fractions have the same denominator, we can simply add the numerators:
   \[
   \frac{1 + 1}{6} = \frac{2}{6}
   \]
   
2. **Step 2**: Simplify the result by dividing both the numerator and denominator by 2:
   \[
   \frac{2}{6} = \frac{1}{3}
   \]

**Answer**: \( \frac{1}{3} \)

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### **Multiplying Fractions**
#### Problem a) \( \frac{1}{3} \times \frac{1}{2} \)
1. **Step 1**: Multiply the numerators:
   \[
   1 \times 1 = 1
   \]
   
2. **Step 2**: Multiply the denominators:
   \[
   3 \times 2 = 6
   \]
   
3. **Step 3**: The resulting fraction is:
   \[
   \frac{1}{6}
   \]
   
**Answer**: \( \frac{1}{6} \)

---

### **Dividing Fractions**
#### Problem a) \( 2 \div \frac{1}{2} \)
1. **Step 1**: To divide by a fraction, we multiply by its reciprocal. The reciprocal of \( \frac{1}{2} \) is \( 2 \). Thus, we perform:
   \[
   2 \times 2 = 4
   \]
   
**Answer**: \( 4 \)

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### Summary of solutions:
- Adding and Subtracting: \( \frac{1}{3} \)
- Multiplying Fractions: \( \frac{1}{6} \)
- Dividing Fractions: \( 4 \)

Would you like me to go over more problems or go deeper into the explanations? Feel free to ask any questions!

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**Related Questions**:
1. How do you subtract fractions with different denominators?
2. What are the steps to simplify a fraction after multiplying?
3. How do you find the reciprocal of a fraction?
4. How can you multiply more than two fractions?
5. What is the rule for dividing mixed numbers?

**Tip**: When working with fractions, always simplify the final answer to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD).

Solve problems related to adding, subtracting, multiplying, and dividing fractions. Simplify to the lowest terms and explain each step clearly.

Solve fraction problems involving addition, subtraction, multiplication, and division. Simplify each fraction to its lowest term with clear explanations for each step. Suitable for Grades 6-8 math students.

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