Q9. - Algebra 1

Question

The simplified value of the expression $-32.4÷\left(21.3\right)$.

Step-by-Step Solution

Answer

The simplified value of the expression $-32.4÷\left(21.3\right)$ is $-1.52$.

Step 1.

The expression $-32.4÷\left(21.3\right)$.

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 $-32.4÷\left(21.3\right)$.

 

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,

$\begin{array}{c}-32.4÷\left(21.3\right)=-32.4\left(\frac{1}{21.3}\right)\\ =\frac{-32.4}{21.3}\end{array}$

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,

$\begin{array}{c}-32.4÷\left(21.3\right)=-32.4\left(\frac{1}{21.3}\right)\\ =\frac{-32.4}{21.3}\\ =-\frac{32.4}{21.3}\\ =-1.5211\end{array}$

 

Rounding off to the nearest hundredth, we get,

$-32.4÷\left(21.3\right)=-1.52$

 

Thus, the simplified value of the expression $-32.4÷\left(21.3\right)$ is $-1.52$.