Question

There are \[\dfrac{1}{{15}}\] stores that sell shoes. There are 180 stores in the mall. How many of the stores sell shoes?

Answer 1

Hint: In this question, we are asked to find the number of stores that sell shoes, for this first consider the required number of shoes be \[x\], now \[x\] will be the \[\dfrac{1}{{15}}\] part of the total number of stores i.e., 180, further calculation will give us the required number of stores that sell the shoes.

Complete step-by-step solution:
Given there are \[\dfrac{1}{{15}}\] stores that sell shoes. There are 180 stores in the mall and we have to find the number of stores that sell shoes.
Total number of stores= 180,
Out of which \[\dfrac{1}{{15}}\] stores sell shoes,
So, \[\dfrac{1}{{15}}\]th part of the total number of stores sell shoes,
Let \[x\] be the number of stores that sell shoes,
So, from the above data, we can say that,
\[ \Rightarrow \dfrac{x}{{180}} = \dfrac{1}{{15}}\],
Now multiplying 180 to both sides, we get,
\[ \Rightarrow \dfrac{x}{{180}} \times 180 = \dfrac{1}{{15}} \times 180\],
Now simplifying we get,
\[ \Rightarrow x = \dfrac{1}{{15}} \times 180\],
Now simplifying we get,
\[ \Rightarrow x = \dfrac{1}{{15}} \times 15 \times 12\],
Now eliminating like terms in the numerator and denominator we get,
\[ \Rightarrow x = 12\],
So the total number of stores that sell shoes are 12.

\[\therefore \] If there are \[\dfrac{1}{{15}}\] of the stores that sell shoes and there are 180 stores in the mall, then the number of the stores that sell shoes are equal to 12.

Note: In these type of question students can make mistake in calculations so, students should be careful in writing the equations and equating them , and this question can be solved directly by dividing 180 into 15 equal parts i.e., dividing 180 by 15 this can be written as \[\dfrac{{180}}{{15}}\],will give us the same answer.