Question

Find the equivalent fraction by multiplication and division method:
\[\begin{align}
  & \left( i \right)\text{ }\dfrac{1}{3}=\dfrac{\left( 1 \right)\times \left( 3 \right)}{\left( 3 \right)\times \left( 3 \right)}=\dfrac{\left( {} \right)}{\left( {} \right)} \\
 & \left( ii \right)\text{ }\dfrac{3}{4}=\dfrac{\left( {} \right)\times \left( {} \right)}{\left( {} \right)\times \left( {} \right)}=\dfrac{\left( {} \right)}{\left( {} \right)} \\
 & \left( iii \right)\text{ }\dfrac{3}{9}=\dfrac{\left( {} \right)\div \left( {} \right)}{\left( {} \right)\div \left( {} \right)}=\dfrac{\left( {} \right)}{\left( {} \right)} \\
\end{align}\]

Answer 1

Hint: We should know that the definition of equivalent fraction. Equivalent fractions are different fractions that represent the same fraction. The numerator and the denominator of a fraction must be multiplied or divided by the same nonzero whole number in order to have equivalent fractions. From the question, it is clear that we have to find the equivalent fraction by multiplication and division method. In each and every case, we should find the equivalent fraction with the help of a suitable method.

Complete step-by-step answer:
From the question, it is clear that we have to find the equivalent fraction by multiplication and division method.
Before solving the question, we should know the definition of equivalent fraction. Equivalent fractions are different fractions that represent the same fraction. The numerator and the denominator of a fraction must be multiplied or divided by the same nonzero whole number in order to have equivalent fractions.
From the question, let us consider
\[\left( i \right)\text{ }\dfrac{1}{3}=\dfrac{\left( 1 \right)\times \left( 3 \right)}{\left( 3 \right)\times \left( 3 \right)}=\dfrac{\left( {} \right)}{\left( {} \right)}\]
From this it is clear that we have to fill the blank given. From the question, it is also clear that the numerator and denominator are multiplied by 3. Then, we get
\[\dfrac{1}{3}=\dfrac{\left( 1 \right)\times \left( 3 \right)}{\left( 3 \right)\times \left( 3 \right)}=\dfrac{3}{9}\]
So, it is clear that \[\dfrac{3}{9}\] is the equivalent fraction of \[\dfrac{1}{3}\].
From the question, let us consider
\[\left( ii \right)\text{ }\dfrac{3}{4}=\dfrac{\left( {} \right)\times \left( {} \right)}{\left( {} \right)\times \left( {} \right)}=\dfrac{\left( {} \right)}{\left( {} \right)}\]
From this it is clear that we have to fill the blank given. From the question, it is clear that we should find the equivalent fraction.
Let us multiply the numerator and denominator with 4.
\[\dfrac{3}{4}=\dfrac{\left( 3 \right)\times \left( 4 \right)}{\left( 4 \right)\times \left( 4 \right)}=\dfrac{12}{16}\]
So, it is clear that \[\dfrac{3}{4}\] is the equivalent fraction of \[\dfrac{12}{16}\].
From the question, let us consider
\[\left( iii \right)\text{ }\dfrac{3}{9}=\dfrac{\left( {} \right)\div \left( {} \right)}{\left( {} \right)\div \left( {} \right)}=\dfrac{\left( {} \right)}{\left( {} \right)}\]
From this it is clear that we have to fill the blanks given. From the question, it is clear that we should find the equivalent fraction.
Let us divide the numerator and denominator by 3.
\[\left( iii \right)\text{ }\dfrac{3}{9}=\dfrac{\left( 3 \right)\div \left( 3 \right)}{\left( 9 \right)\div \left( 3 \right)}=\dfrac{1}{3}\]
So, it is clear that \[\dfrac{3}{9}\]is the equivalent fraction of \[\dfrac{1}{3}\].

Note: Students may have a misconception that to find an equivalent fraction we can multiply (or) divide the numerator and denominator of the fraction with different numbers. But we know that we should multiply or divide the numerator and denominator with the same number. So, this type of misconception should be avoided. Otherwise, it may result in wrong answers.