$$\dfrac{5}{3}+\dfrac{3}{4}u\cdot3v=\dfrac{27uv+20}{12}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{3}+\frac{3}{4}u\cdot3v& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{3}+\frac{3u}{4}\cdot3v \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5}{3}+\frac{9u}{4}v \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5}{3}+\frac{9uv}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{27uv+20}{12}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{3}{4} $ by $ u $ to get $ \dfrac{ 3u }{ 4 } $. Step 1: Write $ u $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3}{4} \cdot u & \xlongequal{\text{Step 1}} \frac{3}{4} \cdot \frac{u}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot u }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 3u }{ 4 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{3u}{4} $ by $ 3 $ to get $ \dfrac{ 9u }{ 4 } $. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3u}{4} \cdot 3 & \xlongequal{\text{Step 1}} \frac{3u}{4} \cdot \frac{3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3u \cdot 3 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9u }{ 4 } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{9u}{4} $ by $ v $ to get $ \dfrac{ 9uv }{ 4 } $. Step 1: Write $ v $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{9u}{4} \cdot v & \xlongequal{\text{Step 1}} \frac{9u}{4} \cdot \frac{v}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9u \cdot v }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9uv }{ 4 } \end{aligned} $$ |
| ④ | Add $ \dfrac{5}{3} $ and $ \dfrac{9uv}{4} $ to get $ \dfrac{ \color{purple}{ 27uv+20 } }{ 12 }$. To add raitonal expressions, both fractions must have the same denominator. |