Q6. - Algebra 1

Question

The simplified value of the expression $108÷\left(-0.9\right)$.

Step-by-Step Solution

Answer

The simplified value of the expression $108÷\left(-0.9\right)$ is $-120$.

Step 1.

The expression $108÷\left(-0.9\right)$.

Step 2. Concept.

The product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \mathrm{or}·$.

 

Division in real numbers is multiplication by reciprocal. If $b\ne 0$, then,

$\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$           

 

Here, $\frac{1}{b}$ is the multiplicative inverse.

Step 3. Calculation.

Consider the expression $108÷\left(-0.9\right)$.

 

Recall that division in real numbers is multiplication by reciprocal. If $b\ne 0$, then,

$\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

           

Here, $\frac{1}{b}$ is the multiplicative inverse.

 

Apply it,

$\begin{array}{c}108÷\left(-0.9\right)=108\left(\frac{1}{-0.9}\right)\\ =\frac{108}{-0.9}\end{array}$         

Step 4. Simplification.

Recall that product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \mathrm{or}·$.

 

Simplify it,

$\begin{array}{c}108÷\left(-0.9\right)=108\left(\frac{1}{-0.9}\right)\\ =\frac{108}{-0.9}\\ =-\frac{108}{0.9}\\ =-120\end{array}$

Thus, the simplified value of the expression $108÷\left(-0.9\right)$ is $-120$.