Question

How do you simplify $4+\dfrac{4\left( 5+8 \right)}{15\cdot 4}$?

Answer 1

Hint: The expression given in the above question involves multiple operators, which are addition, multiplication, and division. For simplifying the given expression, we need to use the BODMAS rule, according to which the bracket needs to be simplified first, and then division and multiplication are to be carried out and then finally the required addition and subtraction are to be performed. Following this rule, we need to simplify the term inside the bracket, which is $5+8$ to get $13$. Then we have to multiply it with $4$, in the numerator along with the multiplication $15\cdot 4$. Then we have to divide the numerator and the denominator to get the quotient which finally is to be added to $4$.

Complete step by step solution:
Let us consider the expression given in the above question as
$\Rightarrow E=4+\dfrac{4\left( 5+8 \right)}{15\cdot 4}$
Since the above expression contains multiple operators, we need to use the BODMAS rule in order to simplify it. The BODMAS rule tells us the order of the operators in which they must be considered. According to this rule, we have to solve for the bracket first, in the above expression which is written as \[\left( 5+8 \right)\] which will be simplified as \[13\]. So the above expression will be written as
$\Rightarrow E=4+\dfrac{4\cdot 13}{15\cdot 4}$
After solving the bracket, we have to solve for the multiplication. The numerator \[4\cdot 13\] will be simplified as \[52\] and the denominator $15\cdot 4$ will be simplified as $60$ so that we can write the above expression as
$\Rightarrow E=4+\dfrac{52}{60}$
Now, after the multiplication, we have to perform the division of $52$ by $60$ to get
$\Rightarrow E=4+\dfrac{13}{15}$
Now, finally we have to perform the addition. But the above expression involves the addition of a number with a fraction. So we multiply and divide the denominator of the fraction with the number to get
$\begin{align}
  & \Rightarrow E=4\times \dfrac{15}{15}+\dfrac{13}{15} \\
 & \Rightarrow E=\dfrac{60}{15}+\dfrac{13}{15} \\
 & \Rightarrow E=\dfrac{60+13}{15} \\
 & \Rightarrow E=\dfrac{73}{15} \\
\end{align}$
Hence, the given expression is simplified as $\dfrac{73}{15}$.

Note:
It is not required to perform the final division for the simplification to write the final expression in the form of decimal. Also, we must note that in the BODMAS rule, the order for the multiplication and the division can be exchanged. Likewise, the order for the addition and the subtraction can also be exchanged. So we could directly cancel $4$ from the numerator and the denominator in the given expression $4+\dfrac{4\left( 5+8 \right)}{15\cdot 4}$ for the simplification.