Signed Numbers (Positive and Negative) - Examples, Exercises and Solutions

a is negative number.

b is negative number.

What is the sum of a+b?

Let's check an example:

Let's say a = -1

b = -2

-1 + (-2) =

-1-2= 

-3

As the example shows us, what we can also do with additional examples,

is that adding two negative numbers will always result in a negative number.

Negative

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

It's important to remember: when we multiply a negative by a negative, the result is positive!

You can use this guide:

Positive

What will be the sign of the result of the next exercise?

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

Let's remember the rule:

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

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

$-3\times-4=+12$

Positive

What will be the sign of the result of the next exercise?

$(-2)\cdot(-\frac{1}{2})=$

Let's recall the law:

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

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

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

Positive

Will the result of the exercise below be positive or negative?

$5\cdot(-\frac{1}{2})=$

Let's remember the rule:

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

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

$+5\times-\frac{1}{2}=-2\frac{1}{2}$

Negative

What will be the sign of the result of the next exercise?

$(-4)\cdot12=$

Let's remember the rule:

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

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

$-4\times+12=-48$

Negative

What will be the sign of the result of the next exercise?

$(-6)\cdot5=$

Remember the law:

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

For the sum of the angles of a triangle is always:

$-6\times+5=-30$

Negative

What will be the sign of the result of the next exercise?

$6\cdot3=$

Let's remember the rule:

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

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

$+6\times+3=+18$

Positive

What will be the sign of the result of the next exercise?

$2\cdot(-2)=$

To solve the exercise you need to remember an important rule: Multiplying a positive number by a negative number results in a negative number.

$(−)×(+)=(−)$
Therefore, if we multiply negative 2 by 2 the result will be negative 4.

That is, the result is negative.

$+2\times-2=-4$

Negative

What will be the sign of the result of the exercise?

$\frac{-0.9}{1.1}:(-4)$

Let's see if the number is negative or positive.

As you can see, in the expression the numerator is negative and the denominator is positive.

That is, the division exercise will look like this:

$\frac{-}{+}:-=$

The result of the expression will be a negative number, since we are dividing a negative number by a positive number.

Therefore, the exercise that will be obtained will look like this:

$-:-=+$

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

+

a and b are negative numbers.

Therefore, what kind of number is is a-b?

We test using an example:

We define that

a = -1

b = -2

Now we replace in the exercise:

-1-(-2) = -1+2 = 1

In this case, the result is positive!

We test the opposite case, where b is greater than a

We define that

a = -2

b = -1

-2-(-1) = -2+1 = -1

In this case, the result is negative!

Therefore, the correct solution to the whole question is: "It's impossible to know".

Impossible to know.

A and B are positive numbers.

Therefore, A - B results in...?

Let's define the two numbers as 1 and 2.

Now let's place them in an exercise:

2-1=1

The result is positive!

Now let's define the numbers in reverse as 2 and 1.

Let's place an equal exercise and see:

1-2=-1

The result is negative!

We can see that the solution of the exercise depends on the absolute value of the numbers, and which one is greater than the other,

Even if both numbers are positive, the subtraction operation between them can lead to a negative result.

Impossible to know

a is a negative number.

b is a positive number.

Therefore, a - b is....?

We test using an example:

We define that

a = -1

b = 2

Now we replace in the exercise:

-1-(2) = -1-2 = -3

In this case, the result is negative!

We test a case where the value of b is less than a

We define that

a = -2

b = 1

-2-(1) = -2-1 = -3

In this case, the result is again negative.

Since it is not possible to produce a case where a is greater than b (because a negative number is always less than a positive number),

The result will always be the same: "negative", and that's the solution!

Negative

a is negative number.

b is negative number.

What is the sum of a+b?

Let's check an example:

Let's say a = -1

b = -2

-1 + (-2) =

-1-2= 

-3

As the example shows us, what we can also do with additional examples,

is that adding two negative numbers will always result in a negative number.

Negative

The sum of two numbers is positive.

Therefore, the two numbers are...?

Testing through attempts:

Let's assume both numbers are positive: 1 and 2.

1+2 = 3

Positive result.

Let's assume both numbers are negative -1 and -2

-1+(-2) = -3

Negative result.

Let's assume one number is positive and the other negative: 1 and -2.

1+(-2) = -1

Negative result.

Let's test a situation where the value of the first number is greater than the second: -1 and 2.

2+(-1) = 1

Positive result.

That is, we can see that when both numbers are positive, or in certain types of cases when one number is positive and the other negative, the sum is positive.

Answers a+c are correct.