We learned in the previous article about the number line AND we also talked about positive and negative numbers. In this article we move on and call them integers.

What are integers?

The term "integer" refers to any number to the left of which there is a plus sign (+) or minus sign (-).

  • The plus sign (+ + ) indicates that the number is positive (greater than zero). The minus sign (-) means that the number is negative (less than zero).
  • When a number appears without one of these two signs, it means that the number is positive.
  • Exception: The number 0 0 . Zero is the only number that is neither positive nor negative. It is possible to write "+0 +0 " or "0 -0 ", but in this case the signs will have no meaning.
Negative and Positive integers

Practice Signed Numbers (Positive and Negative)

Examples with solutions for Signed Numbers (Positive and Negative)

Exercise #1

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

(2)(12)= (-2)\cdot(-\frac{1}{2})=

Video Solution

Step-by-Step Solution

Let's recall the law:

(x)×(x)=+x (-x)\times(-x)=+x

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

2×12=+1 -2\times-\frac{1}{2}=+1

Answer

Positive

Exercise #2

Determine the resulting sign of the following exercise:

1412= \frac{1}{4}\cdot\frac{1}{2}=

Video Solution

Step-by-Step Solution

When there is no minus or plus sign before the numbers, we usually assume that these are positive numbers as shown below:

(+1/4)*(+1/2)=

The dot in the middle represents multiplication:

So the question in other words is - what happens when we multiply two positive numbers together?

We know that two positive integers when multiplied result in a positive integer:

Therefore the answer is "positive".

Answer

Positive

Exercise #3

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

5(12)= 5\cdot(-\frac{1}{2})=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(x)=x (+x)\times(-x)=-x

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

+5×12=212 +5\times-\frac{1}{2}=-2\frac{1}{2}

Answer

Negative

Exercise #4

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

(4)12= (-4)\cdot12=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(x)=x (+x)\times(-x)=-x

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

4×+12=48 -4\times+12=-48

Answer

Negative

Exercise #5

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

(6)5= (-6)\cdot5=

Video Solution

Step-by-Step Solution

Remember the law:

(+x)×(x)=x (+x)\times(-x)=-x

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

6×+5=30 -6\times+5=-30

Answer

Negative

Exercise #6

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

63= 6\cdot3=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(+x)=+x (+x)\times(+x)=+x

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

+6×+3=+18 +6\times+3=+18

Answer

Positive

Exercise #7

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

2(2)= 2\cdot(-2)=

Video Solution

Step-by-Step Solution

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.

+2×2=4 +2\times-2=-4

Answer

Negative

Exercise #8

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

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

Video Solution

Step-by-Step Solution

Let's remember the rule:

(x)×(x)=+x (-x)\times(-x)=+x

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

3×4=+12 -3\times-4=+12

Answer

Positive

Exercise #9

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

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

Video Solution

Step-by-Step Solution

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

You can use this guide:

Answer

Positive

Exercise #10

Determine the resulting sign from the following exercise:

(+314):(+25) (+3\frac{1}{4}):(+\frac{2}{5})

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

+:+= +:+=

Since we are dividing a positive number by a positive number, our result must be positive.

Answer

+

Exercise #11

Determine the resulting sign from the following exercise?

(+7.5):(+3) (+7.5):(+3)

Video Solution

Step-by-Step Solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

+:+= +:+=

Since we are dividing a positive number by a positive number, the result must be a positive number.

Answer

+

Exercise #12

Fill in the missing number:

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

Video Solution

Step-by-Step Solution

Remember the following law:

(x)×(+x)=x (-x)\times(+x)=-x

Let's think about which number we need to multiply by 2 to get 4:

2×2=4 2\times2=4

Now let's put the numbers together with the appropriate sign as written in the law above as follows:

2×(+2)=4 -2\times(+2)=-4

Answer

2 2

Exercise #13

Fill in the missing number:

(6)?=12 (-6)\cdot?=-12

Video Solution

Step-by-Step Solution

Let's remember the law:

(x)×(+x)=x (-x)\times(+x)=-x

Let's think about which number we need to multiply by 6 to get 12:

6×2=12 6\times2=12

Now let's put the numbers together with the appropriate sign as written in the law above, as follows:

6×(+2)=12 -6\times(+2)=-12

Answer

2 2

Exercise #14

Fill in the missing number:

(3)?=9 (-3)\cdot?=-9

Video Solution

Step-by-Step Solution

Remember the following law:

(x)×(+x)=x (-x)\times(+x)=-x

Let's think about which number we need to multiply by 3 to get 9:

3×3=9 3\times3=9

Now let's put the numbers together with the appropriate sign as written in the law above as follows:

3×(+3)=9 -3\times(+3)=-9

Answer

3 3

Exercise #15

Fill in the missing number:

2?=8 2\cdot?=-8

Video Solution

Step-by-Step Solution

Remember the following law:

(x)×(+x)=x (-x)\times(+x)=-x

Let's think about which number we need to multiply by 2 to get 8:

2×4=8 2\times4=8

Now let's put the numbers together with the appropriate sign as written in the law above as follows:

+2×(4)=8 +2\times(-4)=-8

Answer

4 -4