Question

How do you change \[\dfrac{15}{25}\] to simplest form?

Answer 1

Hint: To change the given fraction that is \[\dfrac{15}{25}\] to simplest form, first we have to write the factors of the numerator which is 15 and then the factors of the denominator which is 25. Then we have to write their factors in place of the numbers respectively. Then try to cancel out the common terms in the fraction to get the fraction in its simplest form.

Complete step by step solution:
The given fraction for simplification is \[\dfrac{15}{25}\]
We know the factors of 15 are 5 and 3.
Similarly the factors of 25 are 5 and 5.
\[\dfrac{15}{25}\]
\[\Rightarrow \dfrac{5\times 3}{5\times 5}\]
Let’s cancel out the common factor i.e. 5 from both numerator and the denominator,
\[\Rightarrow \dfrac{3}{5}\]
So the simplest form of the \[\dfrac{15}{25}\] can be written as \[\dfrac{3}{5}\]
we can also be represented in decimal form by dividing 3 by 5 as,
\[5\overset{0.6}{\overline{\left){\begin{align}
  & 30 \\
 & \underline{\begin{align}
  & \underline{30} \\
 & 00 \\
\end{align}} \\
\end{align}}\right.}}\]
So, the simplest form of the \[\dfrac{15}{25}\] can also be written as 0.6 which is its decimal form of representation.

Note: The process of finding out the factors of the terms in numerator and denominator which is 15 and 25 is very important in this type of problems. Students can go wrong in substituting the terms with their factors and cancelling out the common terms as if any single term missed, it can end up in the wrong answer. We also can divide the numerator from the denominator to get the simplest form but it will be the form of a fraction.