Question

number b In BODMAS RULE​

Answer 1

Given :

$\boxed{\bf1\dfrac{1}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}-\dfrac{1}{4}\times\dfrac{1}{2}+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\right\}\right]}$

To Find :

The evaluation.

Solution :

Using BODMAS rule,

$\\ =\sf1\dfrac{1}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}-\dfrac{1}{4}\times\dfrac{1}{2}+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\right\}\right]$

Converting whole number to mixed fraction,

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}-\dfrac{1}{4}\times\dfrac{1}{2}+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}-\dfrac{1}{4}\times\dfrac{1}{2}+\left(\dfrac{2+1}{3}\right)\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}-\dfrac{1}{4}\times\dfrac{1}{2}+\left(\dfrac{3}{3}\right)\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}-\dfrac{1}{4}\times\dfrac{1}{2}+\left(\dfrac{\not{3}}{\not{3}}\right)\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}-\dfrac{1}{4}\times\dfrac{1}{2}+1\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}-\dfrac{1}{8}+1\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1}{2}+1-\dfrac{1}{8}\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{1+2}{2}-\dfrac{1}{8}\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{3}{2}-\dfrac{1}{8}\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{12-1}{8}\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\left\{\dfrac{11}{8}\right\}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\div\dfrac{11}{8}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{2}\times\dfrac{8}{11}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{\not{2}}\times\dfrac{\not{8}\ \ ^4}{11}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{1}{1}\times\dfrac{4}{11}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\left[\dfrac{4}{11}\right]$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\ of\ \dfrac{1}{2}+\dfrac{4}{11}$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{6}\times\dfrac{1}{2}+\dfrac{4}{11}$

$\\ =\sf\dfrac{4}{3}\div\dfrac{1}{12}+\dfrac{4}{11}$

$\\ =\sf\dfrac{4}{3}\times\dfrac{12}{1}+\dfrac{4}{11}$

$\\ =\sf\dfrac{4}{\not{3}}\times\dfrac{\cancel{12}\ \ ^4}{1}+\dfrac{4}{11}$

$\\ =\sf\dfrac{4}{1}\times\dfrac{4}{1}+\dfrac{4}{11}$

$\\ =\sf4\times4+\dfrac{4}{11}$

$\\ \Rightarrow\sf16+\dfrac{4}{11}$

$\\ =\sf\dfrac{176+4}{11}$

$\\ =\sf\dfrac{180}{11}$

$\\ =\sf16\dfrac{4}{11}$

$\\ \therefore\boxed{\bf16\dfrac{4}{11}.}$

Explanation :

• We had to solve it by BODMAS rule.
• So, first we have to convert the mixed fraction into whole number.
• Then we have to solve the problem that is given in () this bracket.
• Whatever we will get from () bracket we will evaluate it with the {} bracket.
• Same for this step.
• Solving all the three (), {}, [] brackets we will go for of as it is said BODMAS.
• Then solving it according to BODMAS we will get the answer.

Explore More :

BODMAS stands for :

• B – Brackets

• O – of

• D – Division

• M – Multiplication

• A – Addition

• S – Subtraction