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.

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.

**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****$0$**. Zero is the only number that is neither positive nor negative. It is possible to write "$+0$" or "$-0$", but in this case the signs will have no meaning.

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

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

**Examples:**

- $-6$
- $+5$
- $+49.342$
- $-174$
- $-1.9$

**Depending on the location of numbers on the number line, the following rules can be determined:**

- A positive number is always larger than a negative number. $(2>-9), (4>-11)$
- If we have two positive numbers, the number whose absolute value is larger will be the larger number. $(3>1), (53>32), (3.6>0.689)$
- If we have two negative numbers, the number whose absolute value is smaller will be the smaller number. $(-9>-45), (-0.432>-11.3)$

**Write in the blank one of the following signs**: **$<, >, =$**

- $-4$__ $-3.5$
- $25$ __$'5$
- $0$ __ $'3.9$
- $17$ __ $¿17$
- $+3$ __ $0$

Test your knowledge

Question 1

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

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

Question 2

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

\( (-4)\cdot12= \)

Question 3

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

\( (-6)\cdot5= \)

**Read the following sentences, and determine which one is true or false:**

- Every positive number is greater than zero.
- The negative sign can be omitted.
- The sign is always written to the left of the number.
- "$3.98$" and "$¿3.98$" are two ways of writing the same number.
- The number $-6$ appears on the number line to the right of the number $2$.
- All negative numbers appear on the number line to the left of the number $0$.
- The number $-9$ is smaller than the number $-8.89$.

**Question**

What is the value we will have to input to solve the following equation?

$7^{\square}=49$

**Solution**

To answer this question it is possible to answer in two ways:

One way is replacement:

We place power of $2$ and it seems that we have arrived at the correct result, ie:

$7²=49$

**Another way is by using the root**

$\sqrt{49}=7$

**That is**

$7²=49$

**Answer:**

$2$

Do you know what the answer is?

Question 1

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

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

Question 2

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

\( (-16)\cdot(-5)= \)

Question 3

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

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

**Question**

What is the result of the following power?

$(\frac{2}{3})^3$

To solve this question we must first understand the meaning of the exercise.

$(\frac{2}{3})\cdot(\frac{2}{3})\cdot(\frac{2}{3})$

$\frac{2}{3}\cdot\frac{2}{3}\cdot\frac{2}{3}$

Now everything is simpler... Correct?

$2\cdot2\cdot2=8$

$3\cdot3\cdot3=27$

**We obtain**: $\frac{8}{27}$

**Answer**

$\frac{8}{27}$

**Task**

$12-\left(-2\right)=$

**Solution**

Pay attention that minus multiplied by minus becomes plus, and therefore

$12+2=14$

**Answer**

$14$

Check your understanding

Question 1

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

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

Question 2

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

\( \frac{1}{4}\cdot\frac{1}{2}= \)

Question 3

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

\( 6\cdot3= \)

**Task**

$-27-\left(-7\right)+\left(-6\right)+2-11=$

**Solution**

First we put the signs in order.

$-27+7-6+2-11=$

**Now we solve as a common exercise:**

$-27+7-6+2-11=-35$

**Answer**

**Task**

**Given that:**

$a$ Negative number

$b$ Negative number

What is the sum of $a+b$?

**Solution**

When we add two negative numbers, the result we will get will be a negative number.

**Answer**

Negative

**If you are interested in this article you may also be interested in the following articles:**

Positive numbers, negative numbers and zero

Elimination of parentheses in real numbers

Addition and subtraction of real numbers

Multiplication and division of real numbers

**On the** **Tutorela**** blog** **you will find a variety of articles on mathematics**.

Do you think you will be able to solve it?

Question 1

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

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

Question 2

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

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

Question 3

Fill in the missing number:

\( 10\cdot?=-100 \)

Whole numbers can be written without a decimal point and never with a fraction, for example $5.83,\frac{6}{5}$ are not whole numbers. Therefore, integers are positive numbers, negative numbers (without decimal) and zero.

**For example:**

$\left\lbrace\ldots-5,-4,-3,-2,-1,0,1,2,3,4,5\ldots\right\rbrace$ i.e. the natural numbers with their respective negatives.

The integers can be placed on the number line in the following way:

There are rules to be able to count integers, let's look at the case of addition:

- If we add two positive integers, we only add the absolute values and keep the positive sign.

$3+5=8$

Both numbers are positive and the result is still positive.

- When adding negative numbers they are added together and the result is still negative.

$-7+\left(-5\right)=-12$

The absolute values are added, but the result is still negative.

- When we have numbers with different signs they are subtracted, that is to say, we subtract the smaller number from the larger number and the result will have the sign of the number with the larger absolute value.

Test your knowledge

Question 1

Fill in the missing number:

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

Question 2

Fill in the missing number:

\( 2\cdot?=-8 \)

Question 3

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

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

$6-8=-2$

In this operation we can see that we have numbers with different signs, so we subtract them and we will put the sign of the bigger number, in this case the result is negative.

$-9+15=6$

Here we subtract the smaller number from the bigger number and in this case the result will be positive because the bigger number has a positive sign.

An integer is a neative OR positive whole number that does not have any decimal point or a number that cannot be written as a fraction.

Do you know what the answer is?

Question 1

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

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

Question 2

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

\( (-4)\cdot12= \)

Question 3

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

\( (-6)\cdot5= \)

Decimal numbers, rational numbers and irrational numbers are not integers, such as:

$1.5$

$\frac{5}{6}$

$\pi=3.141592\ldots$

Check your understanding

Question 1

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

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

Question 2

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

\( (-16)\cdot(-5)= \)

Question 3

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

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

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

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?

$2\cdot(-2)=$

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

Related Subjects

- The Order of Basic Operations: Addition, Subtraction, and Multiplication
- Order of Operations: Exponents
- Order of Operations: Roots
- Division and Fraction Bars (Vinculum)
- The Numbers 0 and 1 in Operations
- Neutral Element (Identiy Element)
- Order of Operations with Parentheses
- Order or Hierarchy of Operations with Fractions
- Multiplicative Inverse
- Advanced Arithmetic Operations
- The commutative property
- The Commutative Property of Addition
- The Commutative Property of Multiplication
- The Associative Property
- The Associative Property of Addition
- The Associative Property of Multiplication
- The Distributive Property
- The Distributive Property for Seventh Graders
- The Distributive Property of Division
- The Distributive Property in the Case of Multiplication
- Subtracting Whole Numbers with Addition in Parentheses
- Division of Whole Numbers Within Parentheses Involving Division
- Subtracting Whole Numbers with Subtraction in Parentheses
- Division of Whole Numbers with Multiplication in Parentheses
- The commutative properties of addition and multiplication, and the distributive property
- Exponents and Roots - Basic
- What is a square root?
- Square Root of a Negative Number
- Exponents and Exponent rules
- Basis of a power
- The exponent of a power
- Powers