Question

What is the quotient of 4/7 divided by 3/7?

Answer 1

Hint: To find the quotient of 4/7 divided by 3/7, we have to express this in mathematical form as $\dfrac{4}{7}\div \dfrac{3}{7}$ . Now, we have to convert this in the multiplication form by changing the division sign to the multiplication sign and taking the reciprocal of the divisor. Then simplify the resultant form.

Complete step-by-step answer:
We have to find the quotient of 4/7 divided by 3/7. Firstly let us express this in mathematical form.
$\Rightarrow \dfrac{4}{7}\div \dfrac{3}{7}$
Now , we have to change the division sign ( $\div $ ) to the multiplication sign (x). When doing this, we must take the reciprocal of the divisor. Here, we can see that $\dfrac{3}{7}$ is the divisor. We know that reciprocal of a number, say, $\dfrac{a}{b}$ is $\dfrac{b}{a}$ , that is, we exchange the terms in the numerator and denominator. Therefore, the reciprocal of $\dfrac{3}{7}$ is $\dfrac{7}{3}$ . Now, we can write
$\Rightarrow \dfrac{4}{7}\times \dfrac{7}{3}$
We can cancel 7 from the denominator of $\dfrac{4}{7}$ and the numerator of $\dfrac{7}{3}$ .
$\begin{align}
  & \Rightarrow \dfrac{4}{\require{cancel}\cancel{7}}\times \dfrac{\require{cancel}\cancel{7}}{3} \\
 & \Rightarrow 4\times \dfrac{1}{3} \\
\end{align}$
Let us do the multiplication process.
$\Rightarrow \dfrac{4}{3}$
We can also write the above result in the decimal form.
$\Rightarrow \dfrac{4}{3}=1.333$
Hence, the quotient of 4/7 divided by 3/7 is 4/3 or 1.333.

Note: Students must know what a dividend, divisor, quotient and remainder is. Dividend is the number to be divided. Divisor is the number that is used to divide the dividend. Quotient is the result of the division. Remainder is the number left after division. We can also write $\dfrac{4}{3}$ in mixed fraction form.
$3\overset{1}{\overline{\left){\begin{align}
  & 4 \\
 & -3 \\
 & \_\_\_\_ \\
 & 1 \\
\end{align}}\right.}}$
Hence, we can write $\dfrac{4}{3}$ in the form $\text{Quotient}\dfrac{\text{Remainder}}{\text{Divisor}}$ , that is, $1\dfrac{1}{3}$ .
Students must also know how to multiply and simplify the fractions.