Multiplication and Division of Signed Numbers Practice

Let's recall the law:

$(-x)\times(-x)=+x$

Therefore, the sign of the exercise result will be positive:

$-2\times-\frac{1}{2}=+1$

Let's recall the rule:

$(-x)\times(-x)=+x$

Therefore, the sign of the exercise result will be positive:

$-3\times-1=+3$

Let's begin by converting 5.8 into a simple fraction:

$-5.8=-\frac{58}{10}$

Let's proceed to convert 3.4 into a simple fraction:

$-3.4=-\frac{34}{10}$

Below is the resulting exercise

$-\frac{58}{10}:-\frac{34}{10}=$

Let's now convert the division exercise into a multiplication exercise, not forgetting to swap the numerator and denominator in the second fraction:

$-\frac{58}{10}\times-\frac{10}{34}=$

Let's reduce the 10 in both fractions in order to obtain the following:

$+\frac{58}{34}=$

Let's now break down the numerator and denominator into multiplication exercises:

$\frac{2\times29}{2\times17}=$

Finally let's reduce the 2 in both the numerator and denominator of the fraction and we should obtain:

$\frac{29}{17}$

To solve this problem, we need to find the inverse of the number 3. In mathematics, the term "inverse" in this context refers to the multiplicative inverse. The multiplicative inverse or reciprocal of a number is defined as a number which, when multiplied by the original number, gives a product of 1.

Given the number 3, its reciprocal is calculated by dividing 1 by the number:

$\text{Reciprocal of 3} = \frac{1}{3}$

This means that the multiplicative inverse of 3 is $\frac{1}{3}$.

Therefore, the solution to the problem is $\frac{1}{3}$.

Let's remember the rule:

$(+x)\times(-x)=-x$

Therefore, the sign of the exercise result will be negative:

$-16\times+1=-16$