Question

What is ${\displaystyle \frac{2}{3}}$ of 18?

Answer 1

Hint: In the given question, we are supposed to find ${\displaystyle \frac{2}{3}}$ of 18. We start to solve the given question by multiplying the fraction ${\displaystyle \frac{2}{3}}$ and a whole number 18. The product between the two will give us the required result.

Complete step by step solution:
We are asked to find ${\displaystyle \frac{2}{3}}$ of 18. We will be solving the given question by finding out the product between the two given numbers.
The whole numbers are the numbers that include all the positive integers and zero. It does not include negative integers and fractions. They are also called the basic counting numbers.
A fraction, in mathematics, represents a part of a whole thing. It consists of two parts namely,
numerator, denominator.
The number on the top is called the numerator.
The number on the bottom is called the denominator.
Let us understand the concept of the fraction with an example as follows,
Example:
$\Rightarrow {\displaystyle \frac{a}{b}}$
In the above fraction,
$a$ is the numerator of the fraction
$b$ is the denominator of the fraction
Example:
How do you reduce ${\displaystyle \frac{1}{4}}$ by 16?
We need to multiply ${\displaystyle \frac{1}{4}}$ and 16.
$\Rightarrow {\displaystyle \frac{1}{4}}\times 16$
Cancelling out the factors, we get,
$\Rightarrow 4$
Now, we need to multiply ${\displaystyle \frac{2}{3}}$ and 18.
$\Rightarrow {\displaystyle \frac{2}{3}}\times 18$
From the above, we know that 18 is a whole number and ${\displaystyle \frac{2}{3}}$ is a fraction
To multiply a whole number with a fraction, we need to convert the whole number into a fraction.
The whole number can be converted into a fraction with a denominator of one.
From the above, the whole number 18 can be written in fractional form as follows,
$\Rightarrow {\displaystyle \frac{18}{1}}$
Substituting the above value, we get,
$\Rightarrow {\displaystyle \frac{2}{3}}\times {\displaystyle \frac{18}{1}}$
According to the rules of fractions,
The multiplication of fractions is done by multiplying the numerators and denominators of the fraction, respectively.
Applying the same, we get,
$\Rightarrow {\displaystyle \frac{2\times 18}{3\times 1}}$
Simplifying the above fraction, we get,
$\Rightarrow 6\times 2$
$\Rightarrow 12$

$\therefore$ The value of ${\displaystyle \frac{2}{3}}$ of 18 is 12.

Note: The result obtained in the given question can be cross-checked as follows,
The division of the result obtained and ${\displaystyle \frac{2}{3}}$ must result in $18$
From the above, the result obtained is $12$
Substituting the same, we get,
$\Rightarrow {\displaystyle \frac{12}{\left({\displaystyle \frac{2}{3}}\right)}}$
$\Rightarrow {\displaystyle \frac{3\times 12}{2}}$
$\Rightarrow 3\times 6$
$\Rightarrow 18$
The result obtained is correct.