How to multiply fractions (Basic)

Let’s calculate $\frac{2}{3}\times \frac{5}{7}$. 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. $\frac{1}{2}\times \frac{1}{3}$

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

Answers

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

\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 $\frac{15}{30}=\frac{1}{2}$.

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