CLASS 6 MATH

CONTENTS OF THIS PAGE:

What is a prime number /  list of prime numbers between 1 and 100

What are decimal numbers?

How to add decimal numbers / addition of decimals 

How to subtract decimal numbers / subtraction of decimals

Introduction to integers / what is an integer / integers

How to add integers using number line / adding integers using number line

How to subtract integers using number line / subtracting integers using number line

How to simplify integers / rules of integers / positive sign and negative sign

What is algebra ?  Introduction to algebra /  Like and unlike terms in algebra / algebraic expressions / coefficients / variables / constants

How to evaluate algebraic expressions / How to find the value of algebraic expressions

How to find patterns in algebra / Finding patterns using algebraic rules

Properties of a square

Properties of a rectangle

Properties of a rhombus

Properties of a parallelogram

Triangle

Types of triangles  based on sides

Types of triangles based on angles (degrees)

Prime numbers are numbers that have exactly 2 factors namely 1 and the number itself.  

Composite numbers are numbers that have more than 2 factors.

1 is neither prime nor composite as it does not satisfy any of the above two conditions.

Following is the list of prime numbers between 1 and 20

2, 3, 5, 7, 11, 13, 17, 19

All other numbers 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20 are all composite numbers and we can see that they all have more than two factors as shown below:

Factors of 4: 1, 2, and 4

Factors of 6: 1, 2, 3 and 6 

ADDITION OF DECIMAL NUMBERS:

In the fractional part of a decimal number, the ending zeros have no values. Let us take an example where we represent the whole number 15 in different ways as a decimal number.

15.0 (no fractional part)

15.00 

15.000  

Let us  now see how to write a  decimal number by including zeros

22.6

22.60

22.600

In the above example, the value is 22.6 only. Ending zeros have no value in a decimal number.  So we try to include zeros wherever required for the purpose of clarity. 

In the case of addition of decimal numbers, we write the numbers in such a way that the fractional parts of the all the decimal numbers to be added have the same number of decimal places.  For this purpose, we include zero wherever required. This is mainly done to do calculations with ease.

SUBTRACTION OF DECIMAL NUMBERS:

While subtracting decimal numbers, the usual method of subtraction is followed. In the fractional part, zeros are included based on requirement. This is just to make equal number of decimal places for all the numbers.

MULTIPLICATION OF DECIMAL NUMBERS:

Let us first multiply the decimal numbers with 10, 100 and 1000.  

Multiplying by 10:

Write the given number without the decimal point and after the units place, write one zero.  Towards the left, place the decimal point according to the decimal places present in the number given.

Example: 6.4 x 10 = 64.0 (= 64 as ending zero has no value in a decimal number)

Multiplying by 100:

 Write two zeros after the units place of the number given and continue as explained earlier.

Example:  34.526 x 100 = 3452.600 = 3452.6

Multiplying by 1000:

Write three zeros after the units place of the number given and proceed in the same manner as before.

Example: 789.43 x 1000 = 789430.00 = 789430

ADDITIVE INVERSE:

Additive inverse of a number is that number which when added or subtracted gives the result zero.

Let us see some examples:

The number 5 on the number line says it is 5 more than zero.  So to make it zero, we have to subtract 5.

Mathematically, we write 5 - 5 =0 

So the additive inverse of 5 is -5

For the number -12 which is  not on the number line of the whole number system, we say it is 12 less than zero.  So, to make it zero, we have to add 12.

Mathematically, we write -12 + 12 =0

So the additive inverse of -12 is 12

INTRODUCTION TO INTEGERS:

Integers are numbers that include the whole numbers and the additive inverses of whole numbers.  On the number line, we call the right side of zero that is the whole numbers 1, 2, 3, ...as the set of positive integers.  

In integers, we include left side of zero which form the additive inverses of the whole numbers 1, 2, 3, ... and name them as negative integers.

Zero is neither positive nor negative.

Zero is lesser than all positive integers.

Zero is greater than all negative integers.

We mean to say that the numbers go on increasing as we move towards the right side of the number line and go on decreasing as we move towards the left side of the number line.

Why do we need integers?

We use opposites or antonyms to distinguish between two words where the meaning of one word opposes the meaning of the other. The same way, in Mathematics, we use integers to distinguish two opposite words using positive sign '+' and negative sign '-' as shown below.

INTRODUCTION TO ALGEBRA:

Algebra is the branch of Mathematics that deals with numbers and letters. An algebraic expression has variables and constant associated with the basic operations of Mathematics.  

An algebraic expression can be formed with one or more terms.  A term can be a variable (letters) or a number. In a term the  number that comes along with a variable is called a coefficient. If a term has only a number, then it is called a constant.

An algebraic expression with a single term is called a monomial.
Examples: 4x, 2t, 6y, -9m

An algebraic expression with two terms is called a binomial.

Examples: 2x + 6z, 3t + 5s, 3a - 4b, 4s-5t

An algebraic expression with three terms is called a trinomial.

Examples: x+y+z, 2x-7y+36, 5a-9b+4c, -100x-70y-90

In general, an algebraic expression with many terms is called a polynomial.

Examples: 9x-8y+5z+2, x+7y+9z-12

Algebraic terms are classified into two types: LIKE TERMS and UNLIKE TERMS.

Like Terms are those terms having the same variable. The coefficients may be different. 

Examples: 3x, -7x, 5x/2, -200x

Unlike Terms are those terms having different variables.

Examples: 4x, 3y, 7z, 100t