Question

What is 1/6 divided by 1/3?

Answer 1

Hint: To find value when 1/6 is divided by 1/3, we have to represent it in the form $${\displaystyle \frac{1}{6}}÷{\displaystyle \frac{1}{3}}$$ . Then, we have to change the division sign into a multiplication sign. Meanwhile, we have to take the reciprocal of the divisor. Then, we have to simplify.

Complete step-by-step solution:
We have to find the value when 1/6 is divided by 1/3. We can represent this division as
$${\displaystyle \frac{1}{6}}÷{\displaystyle \frac{1}{3}}$$ . Now, to divide , we have to change the division sign ( $÷$ ) into multiplication sign (x). Along with this, we have to take the reciprocal of the divisor. Let us consider a number in fractional form ${\displaystyle \frac{a}{b}}$. Reciprocal is obtained by exchanging the numerator and denominator, that is, ${\displaystyle \frac{b}{a}}$ . Hence, we can write
$$\begin{array}{rl}& {\displaystyle \frac{1}{6}}÷{\displaystyle \frac{1}{3}}\\ & ={\displaystyle \frac{1}{6}}\times 3\end{array}$$
Now, we can cancel the common factor 3.
$\Rightarrow {\displaystyle \frac{1}{2}}$
Hence, 1/6 divided by 1/3 is 1/2.

Note: Students must never forget to take the reciprocal of the divisor after changing the division sign. Reciprocal of a number is actually 1 divided by the number. In the given problem, reciprocal of 1/3 is actually found by dividing 1 by 1/3.
$\Rightarrow {\displaystyle \frac{1}{{\displaystyle \frac{1}{3}}}}=1\times 3=3$
Reciprocal can also be shown as a power of -1. Let us consider 1/3. Reciprocal of 1/3 can also be denoted as
 ${\left({\displaystyle \frac{1}{3}}\right)}^{-1}={\displaystyle \frac{1}{{\displaystyle \frac{1}{3}}}}=3$
Reciprocal is also known as the multiplicative inverse.
We can also find 1/6 divided by 1/3 by writing it in the form
${\displaystyle \frac{{\displaystyle \frac{1}{6}}}{{\displaystyle \frac{1}{3}}}}$
We have to take the fractional denominator to the numerator by multiplying the reciprocal of the denominator with the numerator.
$\Rightarrow {\displaystyle \frac{1}{6}}\times 3={\displaystyle \frac{1}{2}}$