To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

In this question, we can make a common denominator of $8.$

To put $\dfrac 1 4$ over a denominator of $8,$ we multiply the numerator and denominator by $2$:

\[ \dfrac{1}{4} = \dfrac{1\times 2}{4\times 2} = \dfrac{2}{8} \]

We can now add the fractions. We keep the denominator the same and we add the numerators.

\begin{align*} \dfrac{3}{8} + \dfrac{2}{8} = \dfrac{5}{8} \end{align*}

To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

In this question, we can make a common denominator of $8.$

To put $\dfrac 1 2$ over a denominator of $8,$ we multiply the numerator and denominator by $4$:

\[ \dfrac{1}{2} = \dfrac{1\times 4}{2\times 4} = \dfrac{4}{8} \]

We can now add the fractions. We keep the denominator the same and we add the numerators.

\begin{align*} \dfrac{1}{8} + \dfrac{4}{8} = \dfrac{5}{8} \end{align*}

To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

In this question, we can make a common denominator of $10.$

To put $\dfrac 12$ over a denominator of $10,$ we multiply the numerator and denominator by $5$:

\[ \dfrac{1}{2} = \dfrac{1\times 5}{2\times 5} = \dfrac{5}{10} \]

We can now add the fractions. We keep the denominator the same, and we add the numerators.

\begin{align*} \dfrac{5}{10} + \dfrac{3}{10} = \dfrac{8}{10} \end{align*}

We can simplify this fraction by dividing the numerator and denominator by $2$:

\[ \dfrac{8\div 2}{10\div 2} =\bbox[3pt,Gainsboro]{\color{blue}\dfrac{4}{5}} \]

To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

Let's look at the denominators:

\[ \dfrac{1}{\color{red}3} + \dfrac{1}{\color{blue}4} \]

In this question, we can make a common denominator of ${\color{red}3} \times {\color{blue}4} = 12.$

To put $\dfrac 1 {3} $ over a denominator of $12,$ we multiply the numerator and denominator by ${4} $:

\[ \dfrac{1}{{3} } = \dfrac{1\times {4} }{{3} \times {4} } = \dfrac{4}{12} \]

To put $\dfrac 1 {4} $ over a denominator of $12,$ we multiply the numerator and denominator by ${3} $:

\[ \dfrac{1}{{4} } = \dfrac{1\times {3} }{{4} \times {3} } = \dfrac{3}{12} \]

We can now add the fractions. We keep the denominator the same and we add the numerators.

\[ \dfrac{4}{12} + \dfrac{3}{12} = \dfrac{7}{12} \]

To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

Let's look at the denominators:

\[ \dfrac{1}{\color{red}9} + \dfrac{1}{\color{blue}2} \]

In this question, we can make a common denominator of ${\color{red}2} \times {\color{blue}9} = 18.$

To put $\dfrac 1 {9} $ over a denominator of $18,$ we multiply the numerator and denominator by ${2} $:

\[ \dfrac{1}{{9} } = \dfrac{1\times {2} }{{9} \times {2} } = \dfrac{2}{18} \]

To put $\dfrac 1 {2} $ over a denominator of $18,$ we multiply the numerator and denominator by ${9} $:

\[ \dfrac{1}{{2} } = \dfrac{1\times {9} }{{2} \times {9} } = \dfrac{9}{18} \]

We can now add the fractions. We keep the denominator the same, and we add the numerators.

\[ \dfrac{2}{18} + \dfrac{9}{18} = \bbox[3pt,Gainsboro]{\color{blue}\dfrac{11}{18}} \]

To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

Let's look at the denominators:

\[ \dfrac{2}{\color{red}3} + \dfrac{1}{\color{blue}2} \]

In this question, we can make a common denominator of ${\color{red}2} \times {\color{blue}3} = 6.$

To put $\dfrac 2 {3} $ over a denominator of $6,$ we multiply the numerator and denominator by ${2} $:

\[ \dfrac{2}{{3} } = \dfrac{2\times {2} }{{3} \times {2} } = \dfrac{4}{6} \]

To put $\dfrac 3 {2} $ over a denominator of $6,$ we multiply the numerator and denominator by ${3} $:

\[ \dfrac{3}{{2} } = \dfrac{3\times {3} }{{2} \times {3} } = \dfrac{9}{6} \]

We can now add the fractions. We keep the denominator the same, and we add the numerators.

\[ \dfrac{4}{6} + \dfrac{9}{6} = \bbox[3pt,Gainsboro]{\color{blue}\dfrac{13}{6}} \]

To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

Let's look at the denominators: \[ \dfrac{1}{\color{red}12} + \dfrac{1}{\color{blue}10} \]

The least common denominator of $\color{red}12$ and $\color{blue}10$ is $60.$

To put $\dfrac{1}{12}$ over a denominator of $60,$ we multiply the numerator and denominator by $5{:}$ \[ \dfrac{1}{12} = \dfrac{1 \times 5}{12 \times 5} = \dfrac{5}{60} \]

To put $\dfrac{1}{10}$ over a denominator of $60,$ we multiply the numerator and denominator by $6{:}$ \[ \dfrac{1}{10} = \dfrac{1 \times 6}{10 \times 6} = \dfrac{6}{60} \]

We can now add the fractions. We keep the denominator the same, and we add the numerators. \begin{align*} \dfrac{5}{60} + \dfrac{6}{60} = \bbox[3pt,Gainsboro]{\color{blue}\dfrac{11}{60}} \end{align*}

To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

Let's look at the denominators:

\[ \dfrac{5}{\color{red}12} + \dfrac{3}{\color{blue}8} \]

The least common denominator of $\color{red}12$ and $\color{blue}8$ is $24.$

To put $\dfrac 5 {12} $ over a denominator of $24,$ we multiply the numerator and denominator by ${2} $:

\[ \dfrac{5}{12 } = \dfrac{5\times 2 }{12 \times 2 } = \dfrac{10}{24} \]

To put $\dfrac 3 {8} $ over a denominator of $24,$ we multiply the numerator and denominator by $3 $:

\[ \dfrac{3}{8} = \dfrac{3\times 3}{8 \times 3} = \dfrac{9}{24} \]

We can now add the fractions. We keep the denominator the same and we add the numerators.

\begin{align*} \dfrac{10}{24} + \dfrac{9}{24} = \dfrac{19}{24} \end{align*}

To add two fractions with unlike denominators, we need to express each fraction as an equivalent fraction with a common denominator.

Let's look at the denominators: \[ \dfrac{1}{\color{red}6} + \dfrac{2}{\color{blue}15} \]

The least common denominator of $\color{red}6$ and $\color{blue}15$ is $30.$

To put $\dfrac{1}{6}$ over a denominator of $30,$ we multiply the numerator and denominator by $5{:}$ \[ \dfrac{1}{6} = \dfrac{1 \times 5}{6 \times 5} = \dfrac{5}{30} \]

To put $\dfrac{2}{15}$ over a denominator of $30,$ we multiply the numerator and denominator by $2{:}$ \[ \dfrac{2}{15} = \dfrac{2 \times 2}{15 \times 2} = \dfrac{4}{30} \]

We can now add the fractions. We keep the denominator the same, and we add the numerators. \begin{align*} \dfrac{5}{30} + \dfrac{4}{30} = \dfrac{9}{30} \end{align*}

We can simplify this fraction by dividing the numerator and denominator by $3{:}$ \[ \dfrac{9 \div 3}{30 \div 3} = \bbox[3pt,Gainsboro]{\color{blue}\dfrac{3}{10}} \]