Chapter 1.2, Problem 59HP

To determine

To find: whether the expression simplifications $[4(10)-3^2]+6(4)$ are correct or not.

Answer to Problem 59HP

Incorrect

Explanation of Solution

Given:

Simplification 1:

  $\begin{array}{l}=[4(10)-3^2]+6(4)\\ =[4(10)-9]+6(4)\\ =4(1)+6(4)\\ =4+6(4)\\ =4+24\\ =28\end{array}$

Simplification 2:

  $\begin{array}{l}=[4(10)-3^2]+6(4)\\ =[4(10)-9]+6(4)\\ =(40-9)+6(4)\\ =31+6(4)\\ =31+24\\ =55\end{array}$

Concept Used:

BODMAS Rule:

B→Bracket − ( ) or [] or {}

O→Order or Power - $\sqrt{}$ or ( )²

D→Division $(÷)$

M→Multiplication $(\times )$

A→Addition $(+)$

S→Subtraction $(-)$

Calculation:

  $=[4(10)-3^2]+6(4)$

Solving the term having round brackets ( ) within the square brackets [ ] (Q BODMAS Rule)

  $=[40-3^2]+6(4)$

In simplification 1, the term having power term is solved before than the term having brackets, which is violating the BODMAS Rule.

Further, in simplification 2, the term 10 in brackets with the term 9 are subtracted before multiplying with the term 4, which is violating the BODMAS Rule.

Solving the term having order $2$ within square brackets [ ] (Q BODMAS Rule)

  $=[40-9]+6(4)$

Solving the expression within square brackets [ ] (Q BODMAS Rule)

  $=31+6(4)$

Solving the term having round brackets ( ) (Q BODMAS Rule)

  $=31+24$

  $=55$

Conclusion:

Therefore, according to BODMAS rule: Both simplifications are incorrect