Question

Write five fractions equivalent to the following: \[\dfrac{2}{3}\] .

Answer 1

Hint: Here, we need to find the five equivalent of fraction. Equivalent fraction is the fraction in which the numerator and denominator can be different but the value is the same. Simplifying to get equivalent numbers is possible up to the point where both the numerator and denominator are still whole numbers.

Complete step by step solution:
In the given problem,
Let the fraction is \[\dfrac{2}{3}\] .
To find the five equivalent of the given fraction, we can get
By multiplying the numerator and denominator with \[2\] , we get
The first equivalent of the fraction is \[\dfrac{2}{3} \times \dfrac{2}{2} = \dfrac{4}{6}\]
Similarly, we can multiplying the numerator and denominator with \[3\] , we get
The second equivalent of the fraction is \[\dfrac{2}{3} \times \dfrac{3}{3} = \dfrac{6}{9}\]
Similarly, By multiplying the numerator and denominator with \[4\] , we get
The third equivalent of the fraction is \[\dfrac{2}{3} \times \dfrac{4}{4} = \dfrac{8}{{12}}\]
Similarly, By multiplying the numerator and denominator with \[5\] , we get
The fourth equivalent of the fraction is \[\dfrac{2}{3} \times \dfrac{5}{5} = \dfrac{{10}}{{15}}\]
Similarly, By multiplying the numerator and denominator with \[6\] , we get
The fifth equivalent of the fraction is \[\dfrac{2}{3} \times \dfrac{6}{6} = \dfrac{{12}}{{18}}\]
Therefore, the five equivalents of the fraction, \[\dfrac{2}{3}\] is \[\dfrac{4}{6},\dfrac{6}{9},\dfrac{8}{{12}},\dfrac{{10}}{{15}},\dfrac{{12}}{{18}}.\]
Thus the values of the fraction does not change when we perform multiplication.
So, the correct answer is \[\dfrac{4}{6},\dfrac{6}{9},\dfrac{8}{{12}},\dfrac{{10}}{{15}},\dfrac{{12}}{{18}}\] ”.

Note: We note that these fractions are actually the same because the value of the fraction does not change when we multiply or divide both the numerator and the denominator by the same number. As a result, when equivalent fractions are reduced to their simplified value, they all have the same value. It's important to remember that equivalent fractions can only be obtained by multiplying or dividing the same numbers, not by adding or subtracting. Simplifying to get equivalent numbers is possible up to the point where both the numerator and denominator are still whole numbers.