MATHEMATICS

  CLASS 6 th  MATHEMATICS CHAPTER - Number INTRODUCTION Successor: (after) When we add 1 to a number we get its successor . Example : 2+1=3 5000+1=5001 Predecessor: (Before) When we subtract 1 from a number we get its predecessor. Example: 5-1=4 5000-1=4999 GREATER 1 DIGIT NUMBER    +    1 = SMALLEST 2 DIGIT NUMBER 10 TEN GREATER 2 DIGIT NUMBER    +    1 = SMALLEST 3 DIGIT NUMBER 100 HUNDRED GREATER 3 DIGIT NUMBER    +    1 = SMALLEST 3 DIGIT NUMBER 1000 THOUSAND GREATER 4 DIGIT NUMBER    +    1 = SMALLEST 3 DIGIT NUMBER 10,000 TEN THOUSAND GREATER 5 DIGIT NUMBER    +    1 = SMALLEST 3 DIGIT NUMBER 1,00,000 LAKH GREATER 6 DIGIT NUMBER    +    1 = SMALLEST 3 DIGIT NUMBER 10,00,000 TEN LAKH    INDIAN SYSTEM :   INTERNATIONAL SYSTEM : WE WILL SEE THE DIFFERENCE BETWEEN INDIAN SYSTEM AND INTERNATIONAL SYSTEM:

Profit(P) The amount gained by selling a product with more than its cost price. Loss(L) The amount the seller incurs after selling the product less than its cost price is mentioned as a loss. Cost Price (CP) The amount paid for a product or commodity to purchase is called a cost price. Also, denoted as CP. This cost price is further classified into two different categories: Fixed Cost:  The fixed cost is constant, it doesn’t vary under any circumstances Variable Cost:  It could vary depending as per the number of units and other factors Selling Price (SP) The amount for which the product is sold is called the Selling Price. It is usually denoted as SP. Also, sometimes called a sale price. Marked Price Formula (MP) This is basically labelled by shopkeepers to offer a discount to the customers in such a way that, Discount = Marked Price – Selling Price And Discount Percentage = (Discount/Marked price) x 100 Profit and Loss Formulas Now let us find profit formula and loss formula. The pro

  1)  There are five squares (one 3x3 and four 1x1) formed with 20 matchsticks, as shown in the illustration. Move two matchstick to get seven squares. Overlapping or breaking of matchsticks or "loose ends" are not allowed. ANSWER: Seven squares are formed: five 1x1 squares, one 2x2 square, and one 3x3 square. 2) What is unique about 8549176320 ? It is the digits 0 to 9 in  alphabetical  order. Note: it can also be exactly divided by all of the digits 1-9 except 7 (thanks to "The Hermit") 3) 4) 5) ANSWER:14 6) ANSWER: 27 7)

  Ratio  A ratio is a comparison of two quantities. ● A ratio can be written as a fraction; ratios are mostly written in the simplest form. ● In the above example, the ratio of rice to water in terms of the number of cups can be written in three different ways as 1 : 2 or 1/2 or 1 to 2 . Properties of Ratio ● A ratio has no unit. It is a number. For example, the ratio of 8 km to 4 km is written  as 8 : 4 = 2 : 1 and not 2 km : 1 km. ● The two quantities of a ratio should be of the same unit. The ratio of 4 km to 400 m  is expressed as (4 × 1000) : 400 = 4000 : 400 = 10 : 1 ● Each number of the ratio is called a term. ● Order of the terms in a ratio cannot be reversed.  We can get equivalent ratios by multiplying or dividing the numerator and denominator by a common number. Proportion When two ratios are equal , we say that the ratios are in Proportion. This is denoted as a : b : : c : d and it is read as ‘a is to b as c is to d’.  Proportionality law If two ratios are in proportion ie.

VEDIC MATHEMATICS VEDIC MATHEMATICS IS THE TRICKS FOR FAST CALCULATIONS   ·         Vedic Mathematics  is a collection of Techniques/Sutras to solve mathematical arithmetics in easy and faster way. It consists of 16 Sutras (Formulae) and 13 sub-sutras (Sub Formulae) which can be used for problems involved in arithmetic, algebra, geometry, calculus, conics. ·         Vedic Mathematics is a system of mathematics which was discovered by Indian mathematician  Jagadguru Shri Bharathi Krishna Tirthaji  in the period between A.D. 1911 and 1918 and published his findings in a  Vedic Mathematics Book by  Tirthaji Maharaj ·         Veda is a Sanskrit word which means ‘Knowledge’. ·         Using regular mathematical steps, solving problems sometimes are complex and time consuming. But using Vedic Mathematic’s General Techniques (applicable to all sets of given data) and Specific Techniques (applicable to specific sets of given data), numerical calculations can be done very fast.

BODMAS:   As per the  BODMAS rule , we have to calculate the expressions given in the brackets first.  The full form of BODMAS is Brackets, Orders, Division, Multiplication, Addition and Subtraction.  Hence, the second preference in BODMAS is given here to the orders or exponents (x n ).   Later we perform the  arithmetic operations  ( ÷, ×, +, -) .  We will solve examples based on this rule in the below sections. It explains the order of operations to be performed while solving an expression.  According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by ‘order’ (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right.  Solving the problem in the wrong order will result in a wrong answer. Tips to Remember BODMAS Rule: The rules to simplify the expression using BODMAS rule are as follows: First, simplify the brackets Solve the exponent or root terms Perform