Question

The simplified value of the expression $42.3÷\left(-6\right)$.

Short answer

The simplified value of the expression $42.3÷\left(-6\right)$is $-7.05$.

Step-by-step solution

Step 1.

The expression $42.3÷\left(-6\right)$.

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,

$a÷b=a\left(\frac{1}{b}\right)$

$=\frac{a}{b}$

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

Step 3. Calculation.

Consider the expression $42.3÷\left(-6\right)$.

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

$a÷b=a\left(\frac{1}{b}\right)$

$=\frac{a}{b}$

Here, role="math" localid="1641975666613" $\frac{1}{b}$is the multiplicative inverse.

Apply it,

$42.3÷\left(-6\right)=42.3\left(\frac{1}{-6}\right)$

$=\frac{42.3}{-6}$

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,

$42.3÷\left(-6\right)=42.3\left(\frac{1}{-6}\right)$

$=\frac{42.3}{-6}$

$=-\frac{42.3}{6}$

$=-7.05$

Thus, the simplified value of the expression $42.3÷\left(-6\right)$is $-7.05$.