Question

The simplified value of the expression $-78÷\left(-1.3\right)$.

Short answer

The simplified value of the expression $-78÷\left(-1.3\right)$is $60$.

Step-by-step solution

Step 1. Given

The expression $-78÷\left(-1.3\right)$.

Step 2. Concept.

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 $-78÷\left(-1.3\right)$.

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,

$\begin{array}{c}-78÷\left(-1.3\right)=-78\left(\frac{1}{-1.3}\right)\\ =\frac{-78}{-1.3}\end{array}$

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,

$\begin{array}{c}-78÷\left(-1.3\right)=-78\left(\frac{1}{-1.3}\right)\\ =\frac{-78}{-1.3}\\ =\frac{78}{1.3}\\ =60\end{array}$

Thus, the simplified value of the expression $-78÷\left(-1.3\right)$is 60.