To solve this, we need to add the two fractions: $\frac{5}{6} + \frac{9}{14}$.

Step 1: Find the Least Common Denominator (LCD)

The denominators are 6 and 14. The least common denominator is the least common multiple (LCM) of these two numbers.

• The prime factorization of 6 is $2 \times 3$.
• The prime factorization of 14 is $2 \times 7$.

The LCM is $2 \times 3 \times 7 = 42$.

Step 2: Convert the fractions to have the LCD

Now, we convert both fractions to have the denominator 42.

• For $\frac{5}{6}$, multiply both the numerator and denominator by 7 to get: $\frac{5}{6} = \frac{5 \times 7}{6 \times 7} = \frac{35}{42}$

• For $\frac{9}{14}$, multiply both the numerator and denominator by 3 to get: $\frac{9}{14} = \frac{9 \times 3}{14 \times 3} = \frac{27}{42}$

Step 3: Add the fractions

Now, add the fractions: $\frac{35}{42} + \frac{27}{42} = \frac{35 + 27}{42} = \frac{62}{42}$

Step 4: Simplify the fraction

Simplify $\frac{62}{42}$ by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2: $\frac{62}{42} = \frac{62 \div 2}{42 \div 2} = \frac{31}{21}$

Step 5: Write as a mixed number

Since $31 \div 21 = 1$ remainder 10, we can write it as a mixed number: $\frac{31}{21} = 1 \frac{10}{21}$

So, $\frac{5}{6} + \frac{9}{14} = 1 \frac{10}{21}$.

Let me know if you would like further details or clarifications.

Related Questions:

1. How do you find the least common denominator of two fractions?
2. What are the steps to convert an improper fraction to a mixed number?
3. Can you explain how to simplify a fraction?
4. What is the prime factorization method used to find the LCM?
5. How do you convert a mixed number back to an improper fraction?

Tip:

When adding fractions, always check if you can simplify the final answer by dividing the numerator and denominator by their greatest common divisor (GCD).