Q66. - Algebra 1

Question

SHORT RESPONSE

Simplify: $\left[10+15\left(2^3\right)\right]÷\left[7\left(2^2\right)-2\right]$

Step 1: $[10+15(8\left)\right]÷\left[7\right(4)-2]$

Step 2: $[10+120]÷[28-2]$

Step 3: $130÷26$

Step 4: $\frac{1}{5}$

Which is the first incorrect step? Explain the error.

Step-by-Step Solution

Answer

In the given steps the error is in step 4.

Step 1. Finding division.

It is known that $a÷b$ means a divided by. That is $a÷b=\frac{a}{b}$.

Step 2. Example of applying BODMAS rule.

The expression $\frac{{(2+3)}^2}{5(4-3)}$ can be written as

$\begin{array}{l}\frac{{(2+3)}^2}{5(4-3)}=\frac{5^2}{5\left(1\right)}\\ =\frac{5\times 5}{5\times 1}\\ =\frac{25}{5}\\ =5\end{array}$

Step 3. DESCRIPTION OF STEP.

In step 4, it is given that, $130÷26$ that is 130 divided by 2.6

Therefore, $130÷26=\frac{130}{26}=5$

Which gives the final answer to be 5.

 

Hence, the error is in the calculation of step 4.