Question

What is the product of \[{{\left( \dfrac{3}{5} \right)}^{2}}\]?

Answer 1

Hint: This type of question depends on the multiplication of fractions. We know that a fraction has two parts a numerator (the number that appears above the line) and a denominator (the number that appears below the line) so when we perform multiplication of a fraction at that time we have to perform multiplication of the numerators and multiplication of the denominators. So that for example if we have two fractions say \[\dfrac{a}{b}\And \dfrac{c}{d}\] then their product can be defined as \[\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a\times c}{b\times d}\].

Complete step-by-step solution:
Now, we have to find the product of \[{{\left( \dfrac{3}{5} \right)}^{2}}\]. Here, the word product suggests that we have to perform multiplication of fractions.
Let us expand the given square of fraction:
\[\Rightarrow {{\left( \dfrac{3}{5} \right)}^{2}}=\left( \dfrac{3}{5} \right)\times \left( \dfrac{3}{5} \right)\]
We can observe that the above equation represents multiplication of fractions. We know that to perform multiplication of fractions we have to perform multiplication of the numerators and multiplication of the denominators.
\[\Rightarrow {{\left( \dfrac{3}{5} \right)}^{2}}=\left( \dfrac{3\times 3}{5\times 5} \right)\]
\[\Rightarrow {{\left( \dfrac{3}{5} \right)}^{2}}=\left( \dfrac{9}{25} \right)\]
Hence, the product of \[{{\left( \dfrac{3}{5} \right)}^{2}}\] is \[\left( \dfrac{9}{25} \right)\].

Note: In this type of question students may make mistakes in calculation of product. We have to note that our question is to find the product of \[{{\left( \dfrac{3}{5} \right)}^{2}}\] so we have to express it in the form of multiplication of fractions. Students may directly calculate the square of the numerator and the denominator and then express the final answer. Students have to take care in expansion of the product of \[{{\left( \dfrac{3}{5} \right)}^{2}}\] as multiplication of two fractions as per the question.