Chapter 1.4, Problem 33PPE

To determine

To evaluate expressions $a[(b-c)÷d]-f$ and $a\cdot b-c÷d-f.$

Answer to Problem 33PPE

  $h-f$

  $p-q-f$

Explanation of Solution

Given:

  $a[(b-c)÷d]-f$

  $a\cdot b-c÷d-f$

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:

  $=a[(b-c)÷d]-f$

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

  $=a[e÷d]-f$ (Assume $b-c=e$ )

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

  $=a\cdot g-f$ (Assume $e÷d=g$ )

Solving the terms being multiplied (Q BODMAS Rule)

  $=h-f$ (Assume $a\cdot g=h$ )

Calculation:

  $=a\cdot b-c÷d-f$

Solving the terms being divided (Q BODMAS Rule)

  $=a\cdot b-q-f$ (Assume $c÷d=q$ )

Solving the terms being multiplied [ ] (Q BODMAS Rule)

  $=p-q-f$ (Assume $a\cdot b=p$ )

Conclusion:

The evaluation of the expression $a[(b-c)÷d]-f$ comes out to be $h-f.$

The evaluation of the expression $a\cdot b-c÷d-f$ comes out to be $p-q-f.$