Question

Solve: \[45+3\left\{ 34-18-14 \right\}\div 3\left\{ 17+3\times 4-\left( 2\times 7 \right) \right\}\] .

Answer 1

Hint: Write the expression and solve it according to BODMAS rule at first operations under brackets then power or exponents, further division multiplication and addition and finally subtraction.

Complete step-by-step answer:
In the question we are given on expression \[45+3\left\{ 34-18-14 \right\}\div 3\left\{ 17+3\times 4-\left( 2\times 7 \right) \right\}\] and we have to find the value of this given expression.
Generally in these type of large simplification we generally use the BODMAS rule to solve them easily,
BODMAS is an acronym and it stands for Bracket, of, Division, Multiplication, Addition and subtraction.
It explains the order of operation to solve the expression. According to BODMAS rule if an expression contain brackets $\left( {} \right),\left\{ {} \right\},\left[ {} \right]$ we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division , multiplication , addition and subtraction from left to right. Also if solving is not done according to proper rules then the answer will be wrong.
Now we are given that,
\[45+3\left\{ 34-18-14 \right\}\div 3\left\{ 17+3\times 4-\left( 2\times 7 \right) \right\}\]
Now in this we will first solve those expression in ( ) solve can rewrite expression as,
$45+3\left\{ 34-18-14 \right\}\div 3\left\{ 17+3\times 4-14 \right\}$ or, it can be written as< $45+3\left\{ 34-18-14 \right\}\div 3\left\{ 17+12-14 \right\}$ .
Now we will do operations in { } so, we get,
$45+3\left\{ 2 \right\}\div 3\left\{ 15 \right\}$ .
So we can rewrite the expression as,
$45+6\div 45$ .
Now we will do division first and write $6\div 45$ as $\dfrac{\text{6}}{\text{45}}$ or, $\dfrac{\text{2}}{\text{15}}$ .
So, the expression is $45+\dfrac{2}{15}$ .
Hence the value is $\dfrac{\text{675+2}}{\text{15}}$ or $\dfrac{\text{677}}{\text{15}}$ .
So, the answer is $\dfrac{\text{677}}{15}$ .

Note: Somewhere instead of BODMAS , PEDMAS is also written where P stands for parentheses and E for exponents while others are called order which involve powers and square – roots.