Integers: Class 6 Maths NCERT Chapter 6

Key Features of NCERT Material for Class 6 Maths Chapter 6 – Integers  

In the last chapter 5: Understanding Elementary Shapes, We studied different elementary shapes like triangle, polygon, circles, etc.

In this chapter, we will learn about integers, representation of integers on a number line and mathematical operations on integers

Quick revision notes

Assume you take a container and include 5 chocolates into the container. It is shown by a positive value +6. Take out 6 chocolates from a container so this is represented by a negative value – 6. In any case, would you be able to take out half off or a third of chocolate? NO! So here the integer consistently represents the number of chocolates included or taken.

There are many times when we need to utilize the numbers with a negative sign. This happens when we need to go under zero on the number line. These numbers are under zero and are called negative numbers. If the development of just 1 is made to the right side, we get the successor of the number. In any case, if the development of 1 is made to the left side, we get the predecessor of the number. 

Whole Numbers

Whole numbers consist of zero and all-natural numbers i.e. 0, 1, 2, 3, 4, and so forth.

Integers: Whole numbers

Tag me with a sign 

A portion of the circumstances where we utilize the negative numbers are as per the following: 

  • Height beneath the surface of the sea level 
  • Spending 
  • The temperature underneath 0°C 
  • Amount of debt 
  • Remaining dues.

Integers

The assortment of numbers – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, … is called whole numbers. – 1, – 2, – 3, – 4, … known as negative numbers are negative Integers. 1, 2, 3, 4, … known as positive numbers are positive Integers. 0 is just a number, neither positive nor negative. 

Positive Numbers 

The numbers which have a + (plus) sign on them are called positive numbers. These numbers are available on the right of zero (0). For the most part, a number with no sign is likewise viewed as a positive number. Each positive number is bigger than its negative partner and zero. For instance, 8 is greater than – 8. 

Negative Numbers 

A negative number contradicts a positive number. These are the numbers which have a – (negative) sign. Negative numbers are available on the left of a zero on a number line. Each negative number is lesser than its positive parts.

Zero 

It is not a negative or positive number. It involves the centre point of the number line and is an impartial number.

Representation of Integers on a number line 

Draw one line. Imprint a point as zero on it. Mark a few points at a similar equivalent distance to the right side of 0  and left of 0. Points on the right side of zero are positive numbers and are set apart as +1, +2, +3, and so forth or essentially 1, 2, 3 and so on. Points to the other side of zero are negative whole numbers and are set apart as – 1, – 2, – 3, and so forth. 

Integers: Negative and positive numbers

Ordering of numbers 

The values of the numbers on the right side of ‘0’ on a number line increment as their distance from the point ‘0’ increments. Then again, the values of the numbers on the left side of ‘0’ on a number line decline as their good ways from the point ‘0’ increments. 

Addition of Integers 

To add two numbers, the guidelines below should be followed: 

  • To add two positive numbers, add them and place the positive sign. 
  • To add two negative whole numbers, add them and place the negative sign. 
  • To add two whole numbers, one positive and the other negative, deduct them and put the indication of the greater whole number. [The greater number is chosen by overlooking the indications of the integers.] 

Addition of Integers on a number line 

At the point when we add two positive whole numbers, their total is a positive whole number. At the point when we add two negative whole numbers, their aggregate is a negative whole number. 

when we add a positive whole number to a number, it increases the value of the number, yet when we add a negative whole number to a number, the value of the number lessens. 

Numbers, for example, 2 and – 2, 3 and – 3 when added to one another give the aggregate zero. They are called additive inverses of one another. 

Subtraction of whole numbers on a number line 

To take away a whole number from another number, it is sufficient to add the additive inverse of the Integer that is being deducted to the other integer.

Multiplication of Integers

  • When you multiply a negative and positive integer answer is always a negative integer. 11×−2=−22
  • When you multiply two negative integers answer is always a positive integer. −11×−2=22

Division of Integers

  • negative integer/positive integer or positive integer/negative integer the quotient is always a negative integer 
  • negative integer/negative integer or positive integer/positive integer, the quotient is always a positive integer.

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