Question

What is $16\dfrac{2}{3}\%$ as a fraction?

Answer 1

Hint: We need to find the value $16\dfrac{2}{3}\%$ as a fraction. Firstly, we divide the given fraction by the number hundred. Then, we simplify the derived expression to express the given percentage in the form of the fraction.

Complete step-by-step answer:
Fractions, in mathematics, are used to represent the portion or the part of the entire thing. They are generally represented as,
$\Rightarrow \dfrac{a}{b}$
Here,
$a$ is the numerator of the fraction
$b$ is the denominator of the fraction
For Example:
$\Rightarrow \dfrac{1}{2},\dfrac{2}{5}$
A percentage is a value expressed as a fraction of hundred or $\dfrac{1}{100}$ . It is denoted by the symbol ’$\%\;$’. The value expressed as a percentage does not have any dimension or unit of measurement.
For Example: we have $\Rightarrow 2\%,3\%$
Now, let us understand how to solve the given question with an example.
Example:
Express $4\%\;$ as the fraction.
The word percent means ‘per hundred’. Dividing the given percentage with hundred, we get,
$\Rightarrow 4\times \dfrac{1}{100}$
$\Rightarrow \dfrac{4}{100}$
Cancelling the common factors, we get,
$\Rightarrow \dfrac{1}{25}$
$\therefore 4\%=\dfrac{1}{25}$
According to our question,
$\Rightarrow 16\dfrac{2}{3}\%$
The above mixed fraction can be written as $\left( 16+\dfrac{2}{3} \right)$
Writing the same, we get,
$\Rightarrow \left( 16+\dfrac{2}{3} \right)\%$
Dividing the above expression with hundred, we get,
$\Rightarrow \dfrac{\left( 16+\dfrac{2}{3} \right)}{100}$
Simplifying the above expression,
$\Rightarrow \left( 16+\dfrac{2}{3} \right)\times \dfrac{1}{100}$
Multiplying each term of the expression with $\left( \dfrac{1}{100} \right)$ , we get,
$\Rightarrow \left( 16\times \dfrac{1}{100} \right)+\left( \dfrac{2}{3}\times \dfrac{1}{100} \right)$
Simplifying the above expression,
$\Rightarrow \left( \dfrac{16}{100} \right)+\left( \dfrac{2}{300} \right)$
Fractions can only be added if the denominator of the fractions is the same.
We need to make the denominators of the fractions the same using the concept of least common multiple.
Taking LCM for the two fractions,
$\Rightarrow \dfrac{\left( \left( 16\times 3 \right)+2 \right)}{300}$
$\Rightarrow \dfrac{\left( 48+2 \right)}{300}$
$\Rightarrow \dfrac{50}{300}$
Writing the above expression as the product of factors,
$\Rightarrow \dfrac{5\times 10}{5\times 10\times 6}$
Cancelling the common factors from the above expression, we get,
$\Rightarrow \dfrac{1}{6}$

Note: The value $16\dfrac{2}{3}$ is a mixed fraction and is usually mistaken as $\left( 16\times \dfrac{2}{3} \right)$ but it is equal to $\left( 16+\dfrac{2}{3} \right)$ . We can equalize the denominators of the fractions of unlike fractions as follows,
$\Rightarrow \dfrac{a}{b}+\dfrac{c}{d}=\dfrac{\left( a\times d \right)+\left( b\times c \right)}{\left( b\times d \right)}$ .