Multiplication and Division of Signed Mumbers: Complete the following equation using the appropriate signs

$-95:-7\text{?}0$

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

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$-412:(+\frac{1}{3})\text{?}0$

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

$-:+=-$

Now the exercise is:

$-?0$

Since we got a negative number, it is necessarily less than zero.

The answer is:

- < 0

>

$-12\frac{1}{8}:0\text{?}0$

Let's solve the exercise on the left page:

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

Let's remember the formula:

$\frac{x}{0}$

Since no number can be divided by 0, the expression has no meaning.

There is no meaning to the expression

$0:-412.5\text{?}0$

Let's solve the exercise on the left page:

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

Let's 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:

$0\text{?}0$

The answer is:

$0=0$

=

$0:+15:-16\text{?}0$

Let's solve the exercise from left to right:

$\frac{0}{15}=$

Let's remember the formula:

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

In other words, if we divide zero by any number, the result will always be zero.

Now we have received the exercise:

$0:-16?0$

Let's solve the exercise:

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

We'll remember the formula we wrote earlier, and we can see that the result is zero.

So the final exercise will look like this:

$0\text{?}0$

Therefore, the appropriate sign is:

$0=0$

=

$+314:-209:-5\frac{1}{3}\text{?}0$

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

$+:-=-$

Now the exercise is:

$-:-?0$

Now we are dividing a negative number by a negative number, so:

$-:-=+$

Therefore, the final exercise will look like this:

$+?0$

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

The answer is:

+ > 0

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Fill in the corresponding sign for the following question

$(-5)\cdot(?3)=15$

Let's think about what we need to multiply by negative to get a positive number.

Let's remember the rule:

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

Therefore, the answer will be:

$-3$

$(-)$

Fill in the corresponding sign for the following question

$(4)\cdot(?3)=-12$

Let's consider what we would need to multiply by a positive in order to obtain a negative number.

Let's remember the rule:

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

Therefore, the answer will be:

$-3$

$(-)$

Fill in the corresponding sign for the following question

$(-2)\cdot(?3)=-12$

Let's think about what we need to multiply by negative to get a negative number.

Let's remember the rule:

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

Therefore, the answer will be:

$+3$

$(+)$

$+800:-4:a\text{?}0$

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.

It is not possible to calculate

$-0.9:-9:-4\text{?}0$

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

$-:-=+$

Now the exercise is:

$+:-?0$

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

$+:-=-$

So the final exercise will look like this:

$-?0$

Since we got a negative number, it is necessarily less than zero.

The answer is:

- < 0

>

Fill in the corresponding sign for the following question

$(-5)\cdot(?4)=20$

Let's think about what we need to multiply by negative to get a positive number.

Let's remember the rule:

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

Therefore, the answer will be:

$-4$

$(-)$

Fill in the corresponding sign for the following question

$(-6)\cdot(?5)=30$

Let's think about what we need to multiply by negative to get a positive number.

Let's remember the rule:

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

Therefore, the answer will be:

$-5$

$(-)$