Q60. - Algebra 1

Question

Explain how to evaluate $a\left[\right(b-c)÷d]-f$ if you were given values for a, b, c, d, and f. How would you evaluate the expression differently if the expression was $a\cdot b-c÷d-f?$

Step-by-Step Solution

Answer

The value of the expression of $a\left[\right(b-c)÷d]-f$ is $h-f$.

The value of the expression of $a\cdot b-c÷d-f.$ is $p-q-f$.

Step 1. Apply the BODMAS rule.

According to the BODMAS rule of simplification, at first, the bracket operation must be completed followed division, by multiplication, addition, and finally subtraction.

Step 2. Example of applying BODMAS rule.

The expression $b(c-d)-e$ can be written as

$\begin{array}{l}b(c-d)÷e=\left[\right(b\times c)-(b\times d\left)\right]÷e\\ \hspace{0.17em}=(bc-bd)÷e\\ \hspace{0.17em}=\frac{(bc-bd)}{e}\end{array}$

Step 3. DESCRIPTION OF STEP.

$a\left[\right(b-c)÷d]-f$

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 $a\cdot g=h$)

$a\cdot b-c÷d-f$

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 $a\cdot b=p$)