All Operations in Signed Numbers: Identify the greater value

Note that we are dividing a negative number by a positive number:

$-:+=-$

Therefore, the exercise is:

$-?0$

Since we have a negative number, it must be less than zero.

Therefore, the answer is:

$- < 0$

Note that we are dividing a negative number by a negative number, therefore:

$-:-=+$

This means the final exercise looks like this:

$+?0$

Since we got a positive number, it must be greater than zero.

The answer is:

$+ > 0$

Let's first turn our attention to the exercise on the left hand side :

$\frac{-12\frac{1}{8}}{0}=$

Remembering the below formula:

$\frac{x}{0}$

Since no number can be divided by 0 we are able to ascertain that the expression has no meaning.

Note that in the first step we are dividing a positive number by a negative number:

$+:-=-$

Therefore, we the exercise is:

$-:-?0$

Now we are dividing a negative number by a negative number, that is:

$-:-=+$

Therefore, the final exercise will look like this:

$+?0$

Since we have a positive number, it is greater than zero.

Therefore, the answer is:

$+ > 0$

First let's solve the exercise on the left-hand side:

$\frac{0}{-412.5}=$

Here we must remember the formula:

$\frac{0}{x}=0$

In other words, when we divide 0 by any number, the result will always be 0.

Now we have:

$0\text{?}0$

Therefore, the answer is:

$0=0$

Let's solve the exercise from left to right:

$\frac{0}{15}=$

Remember the formula:

$\frac{0}{x}=0$

If we divide zero by any number, the result will always be zero.

Now we are left with the following exercise:

$0:-16?0$

Let's solve the exercise:

$\frac{0}{-16}=$

If we remember the formula above, we should see that the result is zero.

The final exercise will look like this:

$0\text{?}0$

Therefore, the missing sign is:

$0=0$

Making use of the following rule:

$-(-x)=+$

Let's rewrite the given exercise in its proper form:

$15+(5)+1=$

And solve accordingly:

$20+1=21$

Since 21 is greater than 1, the appropriate sign is:

$21 > 1$

Note that in the first stage we are dividing a positive number by a negative number:

$+:-=-$

Now the exercise is:

$-:a?0$

Since we don't know whether a is a positive or negative number, we cannot determine the sign.

Note that in the first step we are dividing a negative number by a negative number:

$-:-=+$

This means that the exercise can be written as follows:

$+:-?0$

Now we are dividing a positive number by a negative number:

$+:-=-$

Therefore, the final exercise will look like this:

$-?0$

We are left with a negative number, meaning a number less than zero.

Therefore, the answer is:

$- < 0$

Let's begin by solving the following equation:

$2+(-4)+(-4)=$

We'll locate the number 2 on the number line, and move 4 steps left from zero (since minus 4 is less than zero):

We reach minus 2.

Now let's move 4 steps left again from minus 2 (since minus 4 is less than zero):

We reach minus 6.

Therefore:

$2+(-4)+(-4)=-6$

So the correct sign will be:

$-6 < 6$

Let's first solve the following equation:

$5+(-4)+(-2)=$

Now we will locate the number 5 on the number line and move 4 steps to the left (since minus 4 is less than zero):

This brings us to the number 1.

Now let's move two steps to the left (since minus 2 is less than zero):

This leaves us on the number -1.

Therefore, the solution to the equation is:

$5+(-4)+(-2)=-1$

The missing sign is:

$-1<0$

Let's first solve the equation:

$(-6)+(-7)+13=$

We'll need to locate -6 on the number line and then move 7 steps to the left (since -7 is less than zero):

After doing this, we will have reached the number -13.

Now we'll move 13 steps to the right (since 13 is greater than zero):

After doing this, we will have reached the number 0.

The solution to the equation is:

$(-6)+(-7)+13=0$

Therefore, the appropriate sign will be:

$0=0$

First let's solve the equation:

$(-4)+2+(-3)=$

We'll locate -4 on the number line and move two steps to the right (since 2 is greater than zero):

This takes us to the number -2.

Now let's move three steps to the left (since minus 3 is less than zero):

This takes us to -5.

The solution to the equation is:

$(-4)+2+(-3)=-5$

Therefore, since $5$ is greater than $-5$, the missing sign must be: $<$.

Let's solve the equation:

$(-3)+(-4)+(-7)=$

We'll first need to locate -3 on the number line and move four steps to the left (since minus 4 is less than zero):

This will bring us to the number -7.

Now let's move seven steps to the left (since minus 7 is less than zero):

This leaves us at the number -13..

The solution to the equation is:

$(-3)+(-4)+(-7)=-14$

Therefore, the missing sign must be:

$-14>-15$

Let's first solve the following equation:

$(-12)+(-2)+4=$

We'll then locate -12 on the number line and move two steps to the left (since -2 is less than zero):

This puts us at the number -14.

Now let's move 4 steps to the right (since 4 is greater than zero):

We've reached the number minus 10.

Therefore, the solution to the equation is:

$(-12)+(-2)+4=-10$

The appropriate sign will be:

$-10>-15$

Let's recall the laws:

$-(-x)=+x$

$+(-x)=-x$

We'll solve the left side first:

$-5-5=-10$

$-10-5=-15$

$-15-5=-20$

Now let's solve the right side:

$5-15=-10$

Since the right side is larger, the appropriate sign will be:

$-20 < -10$

Let's remember the laws:

$-(-x)=+x$

$+(-x)=-x$

We'll solve the left side first.

Let's write the exercise in the appropriate form:

$-3-3-3=$

We'll solve the exercise from left to right:

$-3-3=-6$

$-6-3=-9$

Now let's solve the right side:

$3+3+3=$

$3+3=6$

$6+3=9$

Since the right side is larger, the appropriate sign will be:

$-9 < 9$

Let's solve the left side first, remembering the following rules:

$-(-x)=+x$

$+(-x)=-x$

Now, let's rewrite the expression in the appropriate form:

$13+3-4=$

Let's now solve the expression from left to right:

$13+3=16$

$16-4=12$

Next, we will solve the right-hand side, using the laws we covered earlier.

Let's now rewrite the expression in the appropriate form:

$12+2-2=$

Now, we can solve the expression from left to right:

$12+2=14$

$14-2=12$

Since both sides are equal, the appropriate sign is:

$12=12$

First we need to remember the following laws:

$-(-x)=+x$

$+(-x)=-x$

We'll solve the left side first.

Let's rewrite the expression in the appropriate form:

$10+2-3=$

Next, we'll solve the exercise from left to right:

$10+2=12$

$12-3=9$

Now let's solve the right-hand side, using the laws we reminded ourselves of earlier.

We'll then rewrite the expression in the appropriate form and solve:

$4+4=8$

Since the left-hand side is larger, the appropriate sign will be:

$9 > 8$

Let's solve the left side first.

Let's remember the rule:

$-(-x)=+x$

Let's write the exercise in the appropriate form:

$-2+2+3=$

On the number line, we'll locate negative 2 and move two steps to the right (since 2 is greater than zero):

We can see that we reached the number 0, and now we'll move three more steps to the right (since 3 is greater than zero):

We can see that we reached the number 3.

Now let's solve the right side:

Again, let's remember the rule:

$-(-x)=+x$

Let's write the exercise in the appropriate form and solve it:

$4+2=6$

Now we can see that the right side is greater than the left side, therefore:

$3 < 6$