CHAPTER 13 SYMMETRY
If a figure can be divided into two identical looking parts, it is said to have symmetry and the figure is said to be symmetrical.
The line that divides the figure into two symmetrical parts is called the ‘line of symmetry’.
A figure may have more than one line of symmetry or none at all.
CHAPTER 12 PROPORTION
When two quantities are compared in terms of ‘how many times’, it is known as ratio.
It is denoted by the symbol ‘:’.
E.g. In a class, say, the number of girls : the number of boys= 1:3 means that for every 1 girl, there are 3 boys.
Note that two quantities can be compared only if they have the same unit.
When you multiply or divide the numerator and denominator of a ratio by the same number, you get equivalent ratios.
When two ratios are equal, they are said to be in proportion. The symbol :: or = is used to denote proportion.
In this method, we first find the value of one unit and then the required value.
E.g. If 10 pencils cost Rs. 100, then how much will 40 pencils cost? 10 pencils cost Rs 100. Therefore, 1 pencil costs Rs (100/10)= Rs. 10. Then 40 pencils will cost 10x40= Rs 400.
CHAPTER 11 ALGEBRA
The value of a variable is not fixed. It can take any value. Any letter can be used aa a variable.
E.g. Let’s say that there are 50 mangoes in one box and there are ‘n’ number of boxes. The total number of mangoes will be 50xn= 50n.
RULES FROM GEOMETRY
RULES FROM ARITHMETIC
An equation is a condition expressed using variables
There are two sides in an equation- LHS and RHS, having an equal (=) sign between them.
CHAPTER 10 MENSURATION
The distance covered along the boundary of a closed figureis called a perimeter.
The surface enclosed by a closed figure is called its area.
CHAPTER 9 DATA HANDLING
Data is a collection of numbers which is gathered in order to give some information.
Representing data in the form of bars of uniform widths is called a bar graph or bar diagram.
A scale can be used for the graph. E.g. 1 unit= 50 students
Data can be represented in a tabular form using tally marks.
It is used to represent data in one the form of pictures or objects.
CHAPTER 8 DECIMALS
When one block is divided into 10 equal parts, each part is one-tenth of the whole.
E.g. 5.6 means 5 wholw parts and 6 parts of the 10 parts of the whole.
When one block is divided into hundred into 100 equal parts, each part is one hundredth of the whole. E.g. 25.25 means 25 whole parts and 25 parts of the 100 parts of the whole.
COMPARISON OF DECIMALS
The comparison is started from the whole part. If the whole part is equal, we compare the tenths part and so on.
ADDITION OF DECIMALS
Addition is done the same way whole numbers are added. E.g. 5.67+3.1= 8.77
SUBTRACTION OF DECIMALS
Subtraction is also donate same way whole numbers are subtracted. E.g. 5.67-3.1= 2.57
CHAPTER 7 FRACTIONS
Fraction means a part of something. For e.g. 7/15 means 7 parts out of 15 equal parts. Here, 7 is the numerator and 15 is the denominator.
When the numerator is less than the denominator, the fraction is called a proper fraction. E.g. 1/3, 9/12.
When the numerator is less than the denominator, the fraction is called improper fraction. E.g. 7/4, 12/9
A combination of a whole and a part is called mixed fraction. E.g. 3½
Converting mixed fraction to improper fractions: 3½ = ((3x2) +1)/2= 7/2
If the fractions, when simplified, represent same number of parts of the whole, the fractions are called equivalent fractions.
E.g. 1/2, 3/6, 4/8
SIMPLEST FORM OF A FRACTION
If the numerator and denominator have no common factor except 1, the fraction is said to be in its simplest form.
When two fractions have the same denominator, they are called like fractions. For e.g. 7/8, 6/8
When two fractions have different denominators, they are called unlike fractions. For e.g. 7/9, 8/10
COMPARING LIKE FRACTIONS
The fraction with greater numerator is the greater fraction.
COMPARING UNLIKE FACTIONS
ADDITION AND SUBTRACTION OF FRACTIONS
CHAPTER 6 INTEGERS
Numbers greater than zero are called positive numbers.
Numbers less than zero are called negative numbers.
In the case of negative integers, greater the number, lesser its value. i.e. -6 < -2
If two numbers are added to each other and the sum is zero, the numbers are said to be the additive inverse of each other.
E.g. (+5)+(-5) = 0 therefore (+5) and (-5) are additive inverse of each other.
Chapter 4 Basic Geometrical Ideas