Properties of Addition and Subtraction of Integers

For any integer $a$, what is $(-1)\times a$ equal to?

Find the integer whose product with $\left(-1\right)$ is $\left(-22\right)$.

Determine the integer whose product with $(-1)$ is $37$.

Verify the following:
$\left(-21\right)\times \left[\left(-\mathrm{}4\right)+\left(-\mathrm{}6\right)\right]=\left[\left(-21\right)\times \left(-\mathrm{}4\right)\right]+\left[\left(-21\right)\times \mathrm{}\left(-\mathrm{}6\right)\right]$

$(-4)+\left[15+\left(-3\right)\right]=\left[-4+15\right]+$_____

$[13+(-12\left)\right]+($_____$)=13+\left[\left(-12\right)+\left(-7\right)\right]$

$17+$_____$=0$

$-53+$_____$=-53$

Fill in the blank to make the following statement true:

 $\left(-5\right)+\left(-8\right)=(-8)+($_____$)$

Write a negative integer and a positive integer whose sum is $-5.$

Write a negative integer and a positive integer whose difference is $-3.$

Write down a pair of integers whose sum is $0$.

Write down a pair of integers whose difference is $-10$.

A water tank has steps inside it. A monkey is sitting on the topmost step (i.e. the first step). The water level is at the ninth step. After drinking water, he wants to go back. For this, he jumps $4$ steps up and then jumps back $2$ steps down in every move. In how many jumps will he reach back the top step?

A water tank has steps inside it. A monkey is sitting on the topmost step (i.e. the first step). The water level is at the ninth step. 

He jumps $3$ steps down and then jumps back $2$ steps up. 

After drinking water, he wants to go back. For this, he jumps $4$ steps up and then jumps back $2$ steps down in every move. 

If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves by completing the following:

$\left(a\right) -3+2-\_\_\_\_\_=-8$

$\left(b\right) 4-2+\_\_\_\_\_=8$

In $\left(a\right)$ the sum $\left(-\mathrm{}8\right)$ represents going down by eight steps. So, what will the sum $8$ in$\left(b\right)$represent?

Use the sign of $>,\mathrm{}<$ or $=$ to give the following statement meaning:

$-231+79+51 \_\_\_\_\_ -399+159+81$

Use the sign of $>,\mathrm{}<$ or $=$ to make the statement true.

 $39+(-24)-\left(15\right) \_\_\_\_ 36+(-52)-(-36)$
 

Use the sign of $>,\mathrm{}<$ or $=$ to make the statement true.

$23-41+11 \_\_\_\_ 23-41-11$
 

Use the sign of $>,\mathrm{}<$ or $=$ to make the statement true.

$\left(-3\right)+7-\left(19\right)\_\_\_\_\_15-8+\left(-9\right)$
 

Use the sign of $>,<$ or $=$.

$\left(-8\right)+\left(-4\right)$ _____ $\left(-8\right)-\left(-4\right)$