# Integers

🏆Practice signed numbers (positive and negative)

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 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 $0$ . 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.

## Test yourself on signed numbers (positive and negative)!

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:

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

## Exercises with integers

### Exercise 1

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

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

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### Exercise 2

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 $-8.89$.

### Exercise 3

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

$7²=49$

$2$

Do you know what the answer is?

### Exercise 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: $\frac{8}{27}$

$\frac{8}{27}$

### Exercise 5

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

Solution

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

$12+2=14$

$14$

### Exercise 6

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

Solution

First we put the signs in order.

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

Now we solve as a common exercise:

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

### Exercise 7

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.

Negative

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

Positive numbers, negative numbers and zero

The real line

Opposite numbers

Absolute Value

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?

## Review questions

### What are integers?

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.

### How to order integers?

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.

#### Example 1

$3+5=8$

Both numbers are positive and the result is still positive.

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

#### Example 2

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

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.

### Example 3

$6-8=-2$

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.

### What is an integer, simply?

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?

### Which numbers are not integers?

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

$1.5$

$\frac{5}{6}$

$\pi=3.141592\ldots$

## Examples with solutions for Signed Numbers (Positive and Negative)

### Exercise #1

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

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

### 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:

Positive

### Exercise #2

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

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

### Step-by-Step Solution

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

### Exercise #3

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

$(-4)\cdot12=$

### Step-by-Step Solution

Let's remember the rule:

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

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

$-4\times+12=-48$

Negative

### Exercise #4

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

$(-6)\cdot5=$

### Step-by-Step Solution

Remember the law:

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

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

$-6\times+5=-30$

Negative

### Exercise #5

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

$2\cdot(-2)=$

### 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.

$+2\times-2=-4$