Q64. - Algebra 1

Question

Are the expressions $\mathbf{(}\mathbf{30}\mathbf{+}\mathbf{17}\mathbf{)}\mathbf{\times }\mathbf{10}$ and $\mathbf{10}\mathbf{\times }\mathbf{30}\mathbf{+}\mathbf{10}\mathbf{\times }\mathbf{17}$ equivalent? Explain why or why not.

Step-by-Step Solution

Answer

Yes, the given expressions are equivalent.

Step 1 –Applying BODMAS rule for simplification

According to 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

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

Step 3 - DESCRIPTION OF STEP

Two expressions are said to be equivalent if their values equal respectively.

Now, the simplification of $\left(30+17\right)\times 10$ can be obtained as:

$\begin{array}{c}\left(30+17\right)\times 10\\ =47\times 10\\ =470\end{array}$

Similarly, the simplification of $\left(10\times 30\right)+\left(10\times 17\right)$ can be obtained as:

$\begin{array}{c}\left(10\times 30\right)+\left(10\times 17\right)\\ =300+170\\ =470\end{array}$

Hence, it can be seen that the values of both the expressions are equivalent.