Question

What is $\dfrac{2}{3}$ divided by half?

Answer 1

Hint: First convert the given statement into a mathematical expression by replacing the term ‘half’ with the fraction $\dfrac{1}{2}$ and assume the value of this expression as x. Now, to divide the fraction $\dfrac{2}{3}$ with $\dfrac{1}{2}$ consider the first fraction as the dividend and the second as the divisor, take the reciprocal of $\dfrac{1}{2}$ and multiply it with $\dfrac{2}{3}$ and simplify to get the answer.

Complete step by step answer:
Here we have been asked to find the value of the expression $\dfrac{2}{3}$ divided by half. Let us the value of this expression as x, so in mathematical form we can write the expression as:
\[\Rightarrow x=\dfrac{2}{3}\div \dfrac{1}{2}\]
Here we can consider $\dfrac{2}{3}$ as the dividend while $\dfrac{1}{2}$ is the divisor. So, to divide a given number/fraction by another number/fraction means, we have to multiply the first number (dividend) with the reciprocal of the second number (divisor). Reciprocal of a number is obtained by simply inter-changing its numerator and denominator. Therefore, the reciprocal of $\dfrac{1}{2}$ is $\dfrac{2}{1}$ or we can simply say 2. Therefore, multiplying $\dfrac{2}{3}$ with 2 we get,
\[\begin{align}
  & \Rightarrow x=\dfrac{2}{3}\times 2 \\
 & \therefore x=\dfrac{4}{3} \\
\end{align}\]

Hence, $\dfrac{2}{3}$ divided by half is \[\dfrac{4}{3}\].

Note: You must remember the meaning of the term reciprocal and how to find the reciprocal of a fraction. The product of a number and its reciprocal is always 1. If you want you may write the obtained fraction as a mixed number as you may see that $\dfrac{4}{3}$ is an improper fraction. When you will divide 4 with 3 (c) you will get 1(a) as the quotient and 1 (b) as the remainder so it can be written as $a\dfrac{b}{c}=1\dfrac{1}{3}$.