# RATL 2 | Lesson 2 | Solutions (Adding Fractions)

If needed, here is an example of using factoring to add the fractions in a):

$$\dfrac{3}{2\cdot{2}\cdot{2}}+\dfrac{1}{2\cdot{3}}=\dfrac{3\cdot{3}}{2\cdot{2}\cdot{2}\cdot{3}}+\dfrac{1\cdot{2}\cdot{2}}{2\cdot{3}\cdot{2}\cdot{2}}=\dfrac{9+4}{2\cdot{2}\cdot{2}\cdot{3}}=\dfrac{13}{24}$$

It may be helpful to explain in writing how to add the fractions for each of the problems. Below are a set of procedures for problem a) to get you started:

1. Factor each of the two denominators: 6 and 8.
2. Rewrite the denominators with the prime factorizations.
3. Find the LCM of the denominators by looking at which number has the greatest number of each factor. In this case, three 2’s and one 3.
4. Multiply the numerator and denominator of each fraction by the missing factors of the LCM. The first fraction is multiplied by $$\dfrac{3}{3}$$. The second fraction is multiplied by $$\dfrac{2\cdot{2}}{2\cdot{2}}$$.
5. Multiply the factors of each numerator and take their sum. Multiply the factor of the denominator (LCM). Result is the sum of the two fractions.

Solutions:

a) $$\dfrac{13}{24}$$  b) $$\dfrac{7}{8}$$  c) $$\dfrac{127}{336}$$   d) $$\dfrac{8}{15}$$