Introduction to integers — lesson. Mathematics State Board, Class 7.

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Integers are the set of positive and negative numbers and zero.

Integers is nothing but a whole number with negative numbers.

Usually for better understanding integers are represented in a number line.

Negative numbers will be on the left side of the number line, and positive numbers will be on the right side of the number line.

Example:

The examples of negative integers are

$-1$ ,

$-2$ ,

$-2199$ .

The examples of positive integers are

$1$ ,

$38$ ,

$48$ ,

$122$ .

The number

$0$ is neither negative nor positive.

Negative numbers are always lesser than zero and positive numbers.

$\begin{array}{l} 1) - 3 < 0 \\ 2) - 311 < 0 \\ 3) 210 > - 51000 \\ 4) - 200 < 500 \end{array}$

Reflection of a number:

Reflection of a number will have the same absolute value as that number but with a different sign.

Reflection of a number will be

$=-($ absolute value of the number

$)$

Example:

Reflection of

$-1$ is

$-(-1) = +1$

Reflection of

$20$ is

$-20$

The distance between the positive number and zero in a number line will be equal to the distance between the reflection of the same negative number and zero.

Distance between

$(-x)$ and

$0$ in number line

$=$ Distance between

$x$ and

$0$ in a number line.

Example:

Let us take a number

$+1$ its distance in the number line from

$0$ is

$1$ .

Reflection of

$+1$ will be

$-(1)$ and its distance in the number line from

$0$ is also

$1$ .

Distance between

$-20$ and

$0$ is

$20 =$ Distance between

$20$ and

$0$ .

Important!

Numbers with decimals (

$0.21$ ,

$2.35$ ), irrational numbers

$π≈3.14$ , square roots -

$\sqrt{2}$ ,

$\sqrt{3}$ are not integers.

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1. Introduction to integers

Theory: