How to multiply fractions (Basic)

Let's calculate $\dfrac{ 2 }{ 3 } \times \dfrac{ 5 }{ 7 }$. You can take 3 steps:

  1. Multiply the numerators.
  2. Multiply the denominators.
  3. Write a slash.

\begin{eqnarray*} && \frac{ 2 }{ 3 } \times \frac{ 5 }{ 7 } \\ &=& \frac{ 2 \times 5 }{ 3 \times 7 } \\ &=& \frac{ 10 }{ 21 } \end{eqnarray*}

Questions

  1. $\dfrac{ 1 }{ 2 } \times \dfrac{ 1 }{ 3 }$

  2. $\dfrac{ 5 }{ 6 } \times \dfrac{ 3 }{ 5 }$

Answers

1.

\begin{eqnarray*} && \frac{ 1 }{ 2 } \times \frac{ 1 }{ 3 } \\ &=& \frac{ 1 \times 1 }{ 2 \times 3 } \\ &=& \frac{ 1 }{ 6 } \end{eqnarray*}

2.

\begin{eqnarray*} && \frac{ 5 }{ 6 } \times \frac{ 3 }{ 5 } \\ &=& \frac{ 5 \times 3 }{ 6 \times 5 } \\ &=& \frac{ 15 }{ 30 } \end{eqnarray*}

Oh, 15 is a divisor of 30, then $\dfrac{ 15 }{ 30 } = \dfrac{ 1 }{ 2 }$.

\begin{eqnarray*} && \frac{ 5 }{ 6 } \times \frac{ 3 }{ 5 } \\ &=& \frac{ 5 \times 3 }{ 6 \times 5 } \\ &=& \frac{ 15 }{ 30 } \\ &=& \frac{ 1 }{ 2 } \end{eqnarray*}

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