Question

What is $\dfrac{1}{2}\div \dfrac{3}{4}$ ?

Answer 1

Hint: To divide $\dfrac{1}{2}$ by $\dfrac{3}{4}$ , we have to change the division sign ( $\div $ ) to multiplication sign ( $\times $ ). Along with this step, we have to take the reciprocal of the divisor. Then, we have to multiply the resultant fractions and simplify by cancelling the common factors.

Complete step by step solution:
We have to divide $\dfrac{1}{2}$ by $\dfrac{3}{4}$ . To divide fractional numbers, we have to follow certain steps.
Firstly, we have to change the division sign ( $\div $ ) to the multiplication sign ( $\times $ ). Along with this step, we have to take the reciprocal of the divisor. We know that reciprocal of a fraction, say $\dfrac{a}{b}$ will be $\dfrac{b}{a}$ . Hence, we can write $\dfrac{1}{2}\div \dfrac{3}{4}$ as
$\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{1}{2}\times \dfrac{4}{3}$
We have to check whether the two fractions have common terms. If not, we will multiply the fractions. We can see that the numerator of the second fraction and the denominator of the first fraction have common factor 2. Hence, we can eliminate it.
$\Rightarrow 1\times \dfrac{2}{3}=\dfrac{2}{3}$
Hence, the answer is $\dfrac{2}{3}$ .

Note: Students can also multiply the fractions after step 1 and then simplify instead of simplifying the fractions first.
$\dfrac{1}{2}\div \dfrac{3}{4}=\dfrac{1}{2}\times \dfrac{4}{3}=\dfrac{4}{6}$
Now, we can simplify the fractions by cancelling the common factors.
$\dfrac{4}{6}=\dfrac{2}{3}$
We can also represent the resultant fraction in decimal notation. For this, we will divide 2 by 3. We can see that the numerator is less than the denominator. Hence, we will write the numerator as 2.00.
$3\overset{0.66}{\overline{\left){\begin{align}
  & 2.00 \\
 & -0 \\
 & \_\_\_ \\
 & 20 \\
 & -18 \\
 & \_\_\_\_ \\
 & \text{ }20 \\
 & \text{ }-18 \\
 & \_\_\_\_\_\_ \\
 & \text{ }2 \\
\end{align}}\right.}}$
Hence, the decimal notation of $\dfrac{2}{3}$ is 0.66.