Addition to dissimilar fraction 3/14 + 5/18 + 6/15=

To add the dissimilar fractions \( \frac{3}{14} + \frac{5}{18} + \frac{6}{15} \), follow these steps:

### Step 1: Find the Least Common Denominator (LCD)
- **Denominators:** 14, 18, and 15
- **LCD Calculation:** The least common denominator is the smallest number that all the denominators can divide into.
  - **Prime Factorizations:**
    - 14 = \( 2 \times 7 \)
    - 18 = \( 2 \times 3^2 \)
    - 15 = \( 3 \times 5 \)
  - **LCD:** Multiply the highest powers of all prime factors:
    - \( 2 \times 3^2 \times 5 \times 7 = 1260 \)
  - So, the LCD is 1260.

### Step 2: Convert Each Fraction to Have the LCD as the Denominator
- \( \frac{3}{14} = \frac{3 \times 90}{14 \times 90} = \frac{270}{1260} \)
- \( \frac{5}{18} = \frac{5 \times 70}{18 \times 70} = \frac{350}{1260} \)
- \( \frac{6}{15} = \frac{6 \times 84}{15 \times 84} = \frac{504}{1260} \)

### Step 3: Add the Fractions
\[
\frac{270}{1260} + \frac{350}{1260} + \frac{504}{1260} = \frac{270 + 350 + 504}{1260} = \frac{1124}{1260}
\]

### Step 4: Simplify the Fraction
- Find the greatest common divisor (GCD) of 1124 and 1260, which is 4.
- Simplify:
\[
\frac{1124}{1260} = \frac{1124 \div 4}{1260 \div 4} = \frac{281}{315}
\]

So, \( \frac{3}{14} + \frac{5}{18} + \frac{6}{15} = \frac{281}{315} \).

Would you like more details or have any questions?

Here are some related questions:
1. How do you subtract dissimilar fractions?
2. How do you multiply fractions with different denominators?
3. How can you simplify a fraction to its lowest terms?
4. What is the method for dividing fractions?
5. How do you find the LCD for more than two fractions?

**Tip:** Always simplify fractions to their lowest terms after performing operations.

Learn how to add dissimilar fractions 3/14 + 5/18 + 6/15 step-by-step with detailed explanations. This problem covers adding fractions with different denominators, finding the least common denominator (LCD), and simplifying fractions. Suitable for students in Grades 6-8.

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