7th Class

INTEGERS   FUNDAMENTALS

• In lower classes, you would have read about counting number. 1, 2, 3,.........
• They are called natural numbers (N).

N= (1, 2, 3, 4,............)   Elementary Question - 1: Which is the smallest natural number? Ans.: 1  

• Representation of natural numbers on a number line. To represent natural numbers on a number line, we should draw a line and write the number at equal distances on it as shown below:

     

• Whole Number (W): The set of natural numbers together with zero is known as the set of whole numbers.

  Elementary Question - 2: Which is the smallest whole number? Ans.: 0 W= (0, 1, 2, 3,............)

• In set notation, set of whole more...

RATIONAL NUMBERS   FUNDAMENTALS   

• Natural numbers (N): 1, 2, 3, 4, 5..... ..etc., are called natural numbers.
• Whole numbers (W): 0, 1, 2, 3, 4, etc.., are called whole numbers.
• Integers (Z): 1.......\[-4,-3,-2,-1,\,\,0,\,\,1,\,\,2,\,\,3,\,\,4\]........ etc.., are called integers. (denoted by I or Z) 1, 2, 3, 4, .. ...etc., are called positive integers denoted by \[{{Z}^{+}}\]or \[{{I}^{+}}\].

\[-1,\,\,-2,\,\,-3,\,\,-4,\].......etc.., are called negative integers denoted by \[{{Z}^{-}}\] or \[{{I}^{-}}\].   Note: 0 is neither positive nor negative numbers.

• Fractions: The numbers of the form \[\frac{x}{y}\], where \[x\] and \[y\]c are natural numbers, are known as fractions. e.g., \[\frac{2}{5},\,\,\frac{3}{1},\,\,\frac{1}{122},.....\]etc.

Elementary questions: Identify which of the following number is a whole number as well as a fraction? (a) \[\frac{3}{36}\]                                 (b) \[\frac{36}{3}\]                                 (c) \[\frac{20}{8}\]                                      (d) \[\frac{8}{20}\]   Ans. (b) \[\frac{36}{3}=12\] which can be expressed as a fraction \[\left( \frac{12}{1} \right)\] more...

FRACTIONS AND DECIMALS   FUNDAMENTALS

• A fraction is a part of a whole.
• A number of the form\[\frac{p}{q}\], where p and q are whole numbers and \[q\ne 0\]is known as a fraction.
• In the fraction\[\frac{p}{q}\], p is called the numerator and q is called the denominator.

  Various Types of Fractions

Improper fraction: A fraction whose numerator is greater than or equal to its denominator is called an improper fraction. If number is written as\[\frac{N}{D}\], then \[N~\underline{>}\,D\]where N = numerator D = Denominator e.g.,\[\frac{100}{100},\] \[\frac{51}{50},\] \[\frac{45}{2},.....\]etc.

Proper fraction: A fraction whose numerator is less than its denominator is called a proper fraction. e.g.,\[\frac{3}{8},\,\,\frac{6}{7},\,\,\frac{9}{16},\,\,\frac{8}{18},......\]etc.

Decimal fraction: A fraction whose denominator is 10, 100, 1000 etc., is called a decimal fraction. e.g., \[\frac{2}{10},\,\,\frac{8}{100},\,\,\frac{26}{1000},\,\,\frac{1312}{1000},......\]etc.

Vulgar fraction: A fraction whose denominator is a whole number other than 10, 100, 1000, etc., is called a vulgar fraction. more...

LINEAR EQUATION IN ONE VARIABLE   FUNDAMENTALS  

• Variable: A symbol which takes various values is known as a variable. Normally it is denoted by letters x, y etc.
• Constant: A symbol having a fixed numerical value is called a constant.

Symbols used to denote a constant are generally, 'c', 'k' etc...

• Coefficient: In the product of a variable and a constant, each is called the coefficient of the other. Sometimes, symbols like a, b, 1, m etc..., are used to denote the coefficients.
• Expression: An expression can be defined as a combination of constant, variables and coefficients by some or all of the four fundamental mathematical operations \[(+,\,\,-,\,\,\times \,\,\text{and}\,\,\div ).\]

e.g., 2x - 6; here, 2 is the coefficient of \['x';\,\,'x'\] is the variable and \[-6\]is the constant. Similarly in \[ay+b;\,\,a\] is the coefficient of \[y;\,\,'y'\] is more...

ALGEBRAIC EXPRESSIONS   FUNDAMENTALS

• Algebra: It is a branch of mathematics in which we use literal numbers and statements symbolically. Literal numbers can be positive or negative. They are Variables.
• Variable: A symbol which takes various values is known as a variable. Normally it is denoted by x, y, z etc.
• Coefficient: Symbols like a, b, 1, m etc.., are used to denote the coefficients. Coefficients that are numbers are called numerical coefficients.
• Algebraic expression: A combination of constants and variables connected by some or all of the four fundamental operations \[+,\text{ }-,\text{ }\times \]and \[\div \] is called an algebraic expression.

e.g., \[-5x+6\]is an algebraic expression. Here \[-\text{ }5\]is the coefficient of the variable 'x' and 6 is the constant.

• Like and unlike terms: In a given algebraic more...

EXPONENTS AND POWER   FUNDAMENTALS

•                       Exponential form is nothing but repeated multiplication.

There are two part of an exponent. Exponent \[\to \] base, Power/ Index Example:

•                         Base denotes the number to be multiplied and the power denotes the number of times the base is to be multiplied.

\[a\text{ }\times \text{ }a\text{ }\times \text{ }a={{a}^{3}}\] (read as 'a' cubed or 'a' raised to the power 3) \[a\text{ }\times \text{ }a\text{ }\times \text{ }a\text{ }\times \text{ }a\text{ }\times \text{ }a\text{ }\times \text{ more...

COMPARING QUANTITIES   FUNDAMENTALS A. Ratio and Proportion

•                         Ratio is a method of comparing two quantities of the same kind by division.
•                        The symbol used to write a ratio is ':' and is read as 'is to'.
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LINES AND ANGLES               FUNDAMENTALS

•               Point: A point is a geometrical representation of a location, it is represented by a dot.
•               Line: more...

PROPERTIES OF TRIANGLE   FUNDAMENTALS

•            A triangle (denoted as A delta) is a closed figure bounded by three line segments, it has three vertices, three sides and three angles. The three sides and three angles of a triangle are called its six elements.

  Elementary Question -1 Identify triangle among following figures and more...

CONGRUENCE OF TRIANGLES   FUNDAMENTALS      

•          Two figures, having exactly the same shape and size are said to be congruent.
•          Two triangles are said to be congruent, if pairs of corresponding sides and corresponding angles are equal.

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