Question: Whats $\frac{5}{14}$ + $\frac{6}{9}$
1. **State the problem:** We need to find the sum of the fractions $\frac{5}{14}$ and $\frac{6}{9}$.
2. **Formula and rules:** To add fractions, they must have a common denominator. The formula is:
$$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$
3. **Find the least common denominator (LCD):**
The denominators are $14$ and $9$. The prime factors are:
- $14 = 2 \times 7$
- $9 = 3^2$
The LCD is $2 \times 7 \times 3^2 = 126$.
4. **Rewrite each fraction with the LCD:**
$$\frac{5}{14} = \frac{5 \times 9}{14 \times 9} = \frac{45}{126}$$
$$\frac{6}{9} = \frac{6 \times 14}{9 \times 14} = \frac{84}{126}$$
5. **Add the fractions:**
$$\frac{45}{126} + \frac{84}{126} = \frac{45 + 84}{126} = \frac{129}{126}$$
6. **Simplify the fraction:**
Both numerator and denominator share a common factor of $3$:
$$\frac{\cancel{3} \times 43}{\cancel{3} \times 42} = \frac{43}{42}$$
7. **Final answer:**
$$\frac{43}{42}$$ which is an improper fraction and can also be written as $1 \frac{1}{42}$.