Question

Evaluate the given expression,
$10-2\dfrac{1}{3}\times 3+3\dfrac{3}{4}\div 2\dfrac{1}{2}=?$

Answer 1

Hint: Evaluate the given expression by using BODMAS rule, first undergo division, then multiplication, followed by addition and subtraction. Convert the value $2\dfrac{1}{3},3\dfrac{3}{4},2\dfrac{1}{2}$ into fraction for easy calculation.

Complete step-by-step answer:

We have been given an expression, which we need to evaluate, we can do it with the help of BODMAS rule. Now, BODMAS starts for brackets of division, multiplication addition and subtraction. According to Bodmas rule, if an expression contains brackets, we have to solve or simplify the bracket followed by division, multiplication, addition and subtraction from left to right. Now let us check our expression

$10-2\dfrac{1}{3}\times 3+3\dfrac{3}{4}\div 2\dfrac{1}{2}....................\left( i \right)$

Here no brackets has been given, we have to do the operations of division, multiplication, addition and subtraction. Before we move on let us convert the mixed fraction $2\dfrac{1}{3},3\dfrac{3}{4},2\dfrac{1}{2}$ into fraction. Thus to convert the mixed fraction $2\dfrac{1}{3}$ into fraction

$\begin{align}
  & =\dfrac{\left( \text{quotient }\!\!\times\!\!\text{ divisor} \right)+\text{remainder}}{\text{divisor}} \\

 & 2\dfrac{1}{3}=\dfrac{\left( 2\times 3 \right)+1}{3}=\dfrac{7}{3} \\

\end{align}$

Hence we got

$2\dfrac{1}{3}=\dfrac{7}{3}$

Similarly

$\begin{align}

  & 3\dfrac{3}{4}=\dfrac{\left( 3\times 4 \right)+3}{4}=\dfrac{15}{4} \\

 & 2\dfrac{1}{2}=\dfrac{\left( 2\times 2 \right)+1}{2}=\dfrac{5}{4} \\

\end{align}$

Then put

$2\dfrac{1}{3}=\dfrac{7}{3},3\dfrac{3}{4}=\dfrac{15}{4},2\dfrac{1}{2}=\dfrac{5}{2}$ in

equation (i)

$\therefore 10-\dfrac{7}{3}\times 3\dfrac{15}{4}\div \dfrac{5}{2}$

According to BODMAS, no brackets so divide first in,

$\begin{align}

  & \left( \dfrac{15}{4}\div \dfrac{5}{2} \right) \\

 & 10-\dfrac{7}{3}\times 3+\dfrac{15}{4}\div \dfrac{5}{2}=10-\dfrac{7}{3}\times 3+\dfrac{15}{4}\times \dfrac{2}{5} \\

 & =10-\dfrac{7}{3}\times 3+\dfrac{3}{2} \\

\end{align}$

Here $\left( \dfrac{15}{4}\div \dfrac{2}{5} \right)$ can also be written as $\dfrac{\dfrac{15}{4}}{\dfrac{2}{5}}$ which is of the form $\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}$ , thus we can write

$\dfrac{a}{b}\times \dfrac{d}{c}\Rightarrow \dfrac{15}{4}\times \dfrac{5}{2}=\dfrac{3}{2}$
Thus we have completed division. Now, let us move on to multiplication

$\begin{align}

  & 10-\dfrac{7}{3}\times 3+\dfrac{3}{2}=10-\left( \dfrac{7}{3}\times 3 \right)+\dfrac{3}{2} \\

 & =10-7+\dfrac{3}{2} \\

\end{align}$

Now, the next step is addition,

$\begin{align}

  & =10-\left( 7+\dfrac{3}{2} \right) \\

 & =10-\dfrac{14+3}{2} \\

 & =10-\dfrac{14}{2} \\

\end{align}$

Thus the final step is subtraction

$10-\dfrac{17}{2}=\dfrac{20-17}{2}=\dfrac{3}{2}$

Note: BODMAS gives us an order to solve a given expression. If you perform the order wrongly then the answer will be wrong, you have to follow the order of division, multiplication, addition and subtraction. Don’t change this order of solving.