Multiplication is essentially a scaling (bigger/smaller). When you multiply real numbers by $2$, you are essentially scaling the real number line by two times, with centre of expansion at $0$. So $1$ goes to $2$, and $-3$ goes to $-6$. Note that the numbers have remained in order, in that if $a < b$, then $2a < 2b$. This is not the case for multiplication in general. When you imagine multiplying real numbers by $r$ where $r$ is decreasing from $1$ to $0$, it is like shrinking the real line from its original down to nothing. We can carry on intuitively with $r$ going negative, where clearly we expect the real line to expand again but now with every point on the opposite side. This is really what multiplying by a negative number is like in the real world. One can easily see that multiplying real numbers by any negative real number causes the numbers to now be in reverse order. Also, multiplying real numbers by $0$ causes the order to collapse. Division by a real number $r$ is simply undoing multiplication by $r$, which is possible only when $r \ne 0$ since multiplication by $0$ can never be undone! Again, it is clear that division by a positive real number keeps the numbers in order, whereas division by a negative real number causes them to reverse order.
Addition/subtraction is essentially a translation (shift). When you add $2$ to real numbers, you are essentially moving the real number line by two units in the positive direction. Adding $-2$ to real numbers is essentially moving the real number line by two units in the negative direction. Subtraction of $r$ is simply undoing addition of $r$, so subtracting $2$ is the same as adding $-2$, and subtracting $-2$ is the same as adding $2$. Note that whatever we add or subtract, the real numbers remain in the same order as before.
And by the way, you must really understand what you are doing in mathematics so that you actually can not only correctly interpret mathematical statements but also can justify them to other people. Otherwise mathematics will forever be a place governed by rules that you cannot grasp. If my above explanation is not sufficient to tell you the meaning of multiplication and ordering, ask away.