Question

How do you simplify \[\dfrac{3}{5} \times \dfrac{{10}}{{12}}\]?

Answer 1

Hint: In the given question, we have been given an expression which has two fractions separated by a multiplication sign. We have to simplify them. We can easily do that by first dividing the common factors among the two fractions, simplify them and then simply multiplying them.

Complete step-by-step answer:
The given expression is \[p = \dfrac{3}{5} \times \dfrac{{10}}{{12}}\].
\[p = \dfrac{3}{5} \times \dfrac{{10}}{{12}}\]
Cancelling \[12\] by \[3\] to get \[4\], and \[10\] by \[5\] to get \[2\], so we have,
\[p = \dfrac{2}{4}\]
Now, cancelling \[4\] by \[2\] to get \[2\], we have,
\[p = \dfrac{1}{2}\]
Hence,
\[p = \dfrac{1}{2}\]

Additional Information:
The answer that we got in this question is \[\dfrac{1}{2}\].
But, if we want to have it in decimal form, we are going to have to divide it,
\[2\mathop{\left){\vphantom{1\begin{array}{l}{\rm{ }}1\\\dfrac{{ - 0}}{\begin{array}{l}{\rm{ }}10\\\dfrac{{{\rm{ }} - 10}}{{{\rm{ }}0}}\end{array}}\end{array}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}{\rm{ }}1\\\dfrac{{ - 0}}{\begin{array}{l}{\rm{ }}10\\\dfrac{{{\rm{ }} - 10}}{{{\rm{ }}0}}\end{array}}\end{array}}}}
\limits^{\displaystyle\,\,\, {0.5}}\]
Hence, \[\dfrac{1}{2} = 0.5\]

Note: In the given question, we had to multiply two fractions. To do that, we change the fractions into their lowest form by dividing the common factors of the two fractions among each other and themselves too. Then we solve the two fractions by multiplying them, simplify them into lowest form, change the mixed fraction into improper fraction, and that gives us the answer.