Question
Answer
$$4\cdot\dfrac{\sqrt{12}}{4\sqrt{75}}=\dfrac{2}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4 \cdot \frac{\sqrt{12}}{4\sqrt{75}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4\cdot\frac{30}{300} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4 \cdot \frac{ 30 : \color{orangered}{ 30 } }{ 300 : \color{orangered}{ 30 }} \xlongequal{ } \\[1 em] & \xlongequal{ }4\cdot\frac{1}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2}{5}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{12} } \cdot \sqrt{75} = 30 $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{75} } \cdot \sqrt{75} = 300 $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 30 } $. |
| ③ | Multiply $4$ by $ \dfrac{1}{10} $ to get $ \dfrac{2}{5} $. Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Cancel down by $ \color{blue}{2} $ $$ \begin{aligned} 4 \cdot \frac{1}{10} & = \frac{4}{\color{red}{1}} \cdot \frac{1}{10} = \frac{4 : \color{blue}{2}}{10 : \color{blue}{2}} = \\[1ex] &= \frac{2}{5} \end{aligned} $$ |
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