Question

adding mixed numbers
with different denominators
step 1: find the least common denominator (lcd)
\\(\

$$\begin{array}{r}3\\frac{1}{2}\\\\ + 2\\frac{3}{8}\\\\ \\hline\\end{array}$$

\\) lcd = 8
step 2: using the lcd, find equivalent fractions
\\(\

$$\begin{array}{r}3\\frac{1}{2}= 3\\frac{4}{8}\\\\ + 2\\frac{3}{8}= + 2\\frac{3}{8}\\\\ \\hline\\end{array}$$

\\)
step 3: add the fractions
\\(\

$$\begin{array}{r}3\\frac{4}{8}\\\\ + 2\\frac{3}{8}\\\\ \\hline\\frac{7}{8}\\end{array}$$

\\)
step 4: add the whole numbers
\\(\

$$\begin{array}{r}3\\frac{4}{8}\\\\ + 2\\frac{3}{8}\\\\ \\hline5\\frac{7}{8}\\end{array}$$

\\)
solve and simplify your answer.
a. \\(\

$$\begin{array}{r}5\\frac{3}{4}\\\\ + 3\\frac{1}{12}\\\\ \\hline\\end{array}$$

\\) b. \\(\

$$\begin{array}{r}9\\frac{3}{5}\\\\ + 6\\frac{4}{15}\\\\ \\hline\\end{array}$$

\\) c. \\(\

$$\begin{array}{r}4\\frac{4}{9}\\\\ + 4\\frac{1}{3}\\\\ \\hline\\end{array}$$

\\) d. \\(\

$$\begin{array}{r}6\\frac{3}{10}\\\\ + 1\\frac{2}{5}\\\\ \\hline\\end{array}$$

\\)
e. \\(\

$$\begin{array}{r}8\\frac{3}{7}\\\\ + 4\\frac{1}{3}\\\\ \\hline\\end{array}$$

\\) f. \\(\

$$\begin{array}{r}1\\frac{5}{6}\\\\ + \\frac{1}{12}\\\\ \\hline\\end{array}$$

\\) g. \\(\

$$\begin{array}{r}4\\frac{3}{8}\\\\ + \\frac{3}{8}\\\\ \\hline\\end{array}$$

\\) h. \\(\

$$\begin{array}{r}7\\frac{3}{5}\\\\ + 5\\frac{1}{8}\\\\ \\hline\\end{array}$$

\\)
i. \\(\

$$\begin{array}{r}6\\frac{1}{2}\\\\ + 4\\frac{3}{16}\\\\ \\hline\\end{array}$$

\\) j. \\(\

$$\begin{array}{r}7\\frac{1}{6}\\\\ + 2\\frac{1}{3}\\\\ \\hline\\end{array}$$

\\) k. \\(\

$$\begin{array}{r}3\\frac{1}{2}\\\\ + 3\\frac{5}{11}\\\\ \\hline\\end{array}$$

\\) l. \\(\

$$\begin{array}{r}5\\frac{1}{9}\\\\ + \\frac{3}{18}\\\\ \\hline\\end{array}$$

\\)
m. \\(\

$$\begin{array}{r}8\\frac{3}{8}\\\\ + \\frac{1}{8}\\\\ \\hline\\end{array}$$

\\) n. \\(\

$$\begin{array}{r}5\\frac{5}{12}\\\\ + 5\\frac{7}{24}\\\\ \\hline\\end{array}$$

\\) o. \\(\

$$\begin{array}{r}9\\frac{1}{5}\\\\ + 3\\frac{7}{10}\\\\ \\hline\\end{array}$$

\\) p. \\(\

$$\begin{array}{r}7\\frac{3}{5}\\\\ + 6\\frac{1}{4}\\\\ \\hline\\end{array}$$

\\)

Explanation:

Parte a:

Step 1: Encontrar el MCD de 4 y 12

El mínimo común denominador (LCD) de 4 y 12 es 12.

Step 2: Convertir a fracciones equivalentes

\(5\frac{3}{4} = 5\frac{9}{12}\) (ya que \(3\times3 = 9\) y \(4\times3 = 12\))
\(3\frac{1}{12}\) permanece igual.

Step 3: Sumar las fracciones

\(\frac{9}{12} + \frac{1}{12} = \frac{10}{12} = \frac{5}{6}\)

Step 4: Sumar los números enteros

\(5 + 3 = 8\)

Step 5: Combinar

\(8 + \frac{5}{6} = 8\frac{5}{6}\)

Step 1: Encontrar el LCD de 5 y 15

El LCD de 5 y 15 es 15.

Step 2: Convertir a fracciones equivalentes

\(9\frac{3}{5} = 9\frac{9}{15}\) (ya que \(3\times3 = 9\) y \(5\times3 = 15\))
\(6\frac{4}{15}\) permanece igual.

Step 3: Sumar las fracciones

\(\frac{9}{15} + \frac{4}{15} = \frac{13}{15}\)

Step 4: Sumar los números enteros

\(9 + 6 = 15\)

Step 5: Combinar

\(15 + \frac{13}{15} = 15\frac{13}{15}\)

Step 1: Encontrar el LCD de 9 y 3

El LCD de 9 y 3 es 9.

Step 2: Convertir a fracciones equivalentes

\(4\frac{4}{9}\) permanece igual.
\(4\frac{1}{3} = 4\frac{3}{9}\) (ya que \(1\times3 = 3\) y \(3\times3 = 9\))

Step 3: Sumar las fracciones

\(\frac{4}{9} + \frac{3}{9} = \frac{7}{9}\)

Step 4: Sumar los números enteros

\(4 + 4 = 8\)

Step 5: Combinar

\(8 + \frac{7}{9} = 8\frac{7}{9}\)

Answer:

\(8\frac{5}{6}\)

Parte b: