MATHS DEPARTMENT SYNA INTERNATIONAL SCHOOL CLASS V 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 3 X 6 = 18 3 X 7 = 21 3 X 8 = 24 3 X 9 = 27

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1 LEARNING PAPERS FOR CLASS V TABLE 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 2 X 6 = 12 2 X 7 = 14 2 X 8 = 16 2 X 9 = 18 2 X 10 = 20 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 3 X 6 = 18 3 X 7 = 21 3 X 8 = 24 3 X 9 = 27 3 X 10 = 30 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 4 X 6 = 24 4 X 7 = 28 4 X 8 = 32 4 X 9 = 36 4 X 10 = 40 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25 5 X 6 = 30 5 X 7 = 35 5 X 8 = 40 5 X 9 = 45 5 X 10 = 50 6 X 1 = 6 6 X 2 = 12 6 X 3 = 18 6 X 4 = 24 6 X 5 = 30 6 X 6 = 36 6 X 7 = 42 6 X 8 = 48 6 X 9 = 54 6 X 10 = 60 7 X 1 = 7 7 X 2 = 14 7 X 3 = 21 7 X 4 = 28 7 X 5 = 35 7 X 6 = 42 7 X 7 = 49 7 X 8 = 56 7 X 9 = 63 7 X 10 = 70 1

2 8 X 1 = 8 8 X 2 = 16 8 X 3 = 24 8 X 4 = 32 8 X 5 = 40 8 X 6 = 48 8 X 7 = 56 8 X 8 = 64 8 X 9 = 72 8 X 10 = 80 9 X 1 = 9 9 X 2 = 18 9 X 3 = 27 9 X 4 = 36 9 X 5 = 45 9 X 6 = 54 9 X 7 = 63 9 X 8 = 72 9 X 9 = 81 9 X 10 = X 1 = X 2 = X 3 = X 4 = X 5 = X 6 = X 7 = X 8 = X 9 = X 10 = X 1 = X 2 = X 3 = X 4 = X 5 = X 6 = X 7 = X 8 = X 9 = X 10 = X 1 = X 2 = X 3 = X 4 = X 5 = X 6 = X 7 = X 8 = X 9 = X 10 = X 1 = 13 X 2 = 13 X 3 = 13 X 4 = 13 X 5 = 13 X 6 = 13 X 7 = 13 X 8 = 13 X 9 = 13 X 10 =

3 14 X 1 = 14 X 2 = 14 X 3 = 14 X 4 = 14 X 5 = 14 X 6 = 14 X 7 = 14 X 8 = 14 X 9 = 14 X 10 = X 1 = 15 X 2 = 15 X 3 = 15 X 4 = 15 X 5 = 15 X 6 = 15 X 7 = 15 X 8 = 15 X 9 = 15 X 10 = X 1 = 16 X 2 = 16 X 3 = 16 X 4 = 16 X 5 = 16 X 6 = 16 X 7 = 16 X 8 = 16 X 9 = 16 X 10 = X 1 = 17 X 2 = 17 X 3 = 17 X 4 = 17 X 5 = 17 X 6 = 17 X 7 = 17 X 8 = 17 X 9 = 17 X 10 = X 1 = 18 X 2 = 18 X 3 = 18 X 4 = 18 X 5 = 18 X 6 = 18 X 7 = 18 X 8 = 18 X 9 = 18 X 10 = X 1 = 19 X 2 = 19 X 3 = 19 X 4 = 19 X 5 = 19 X 6 = 19 X 7 = 19 X 8 = 19 X 9 = 19 X 10 = X 1 = X 2 = X 3 = X 4 = X 5 = X 6 = X 7 = X 8 = X 9 = X 10 = 200 3

4 1) NUMBERS AND NUMERATIONS 4 Places in 4 digit numbers are Thousand, Hundred, Tens, Ones 5 Places in 5 digit numbers are Ten Thousand, Thousand, Hundred, Tens, Ones 6 Places in 6 digit numbers are Lakh, Ten Thousand, Thousand, Hundred, Tens, Ones Crores Periods Lakhs Periods Thousands Period Ones period T. Crore Crore T. Lakh Lakh Ten Thousand Thousand Hundred Tens ones ,38,694 = Four crore One lakh Thirty eight thousand Six hundred ninety four International place value chart 4

5 Place value and face value Place value of a digit in any number is the position of that digit in that number Face value of a digit is always the same digit itself. Ex: Write place value and face value of 3 in the given number 23,456 solution : Place value is thousand i.e. 3 X 1000 = 3000 is the place value. Face value of 3 is number itself i.e. 3 Comparison of numbers The number with more number of digits is always greater. If number of digits are same, start from the left and compare the digits until you find two different digits at the same place. Forming the smallest and the greatest number For greatest : Arrange the numbers in descending order. For smallest : Arrange the numbers in ascending order. If one of the digit is 0 so, put 0 at second place from left. ROUNDING OFF NUMBERS Nearest tens: 1) Digit at ones place less than 5, replace it by 0. 2) If it is greater than 5, replace it 0 and add 1 to the digit at ones place. Ex. 73 rounds to 70 Nearest hundreds:1) Digit at ones place is replace by 0,look at digit at tens place. 2) If less than 5 replace it by 0. 3) If it is 5 or greater, replace it by 0 and add 1 to the digit at hundreds place. 4) The other digits will remain the same. 5

6 Ex. 743 rounds to 700 Nearest thousand:1) Digit at ones and tens place is replace by 0,look at digit at hundred place. 2) If less than 5 replace it by 0..3) If it is 5 or greater, replace it by 0 and add 1 to the digit at thousand place. 4) The other digits will remain the same. Ex rounds to 2000 ROMAN NUMERAL Roman numerals are a numeral system of ancient Rome based on letters of the alphabet, which are combined to signify the sum (or in some cases, the difference) of their values. The first ten Roman numerals are I 1, V 5, X 10, L 50, C 100, D 500, M or K ) When a symbol of lower value is placed on the left of a symbol of higher value then its value is subtracted. Ex. IV 4 2) When a symbol of lower value is placed on the right of a symbol of higher value then its value is added. Ex.. V I 6 3) For larger number a bar ( ) is used when its placed over a numeral its value is multiplied by ) No symbol can be repeated more than three times. Repetition of Roman numerals means addition. Ex : CCC, XXX. 5) The symbols V, L and D can never be repeated and never be subtracted. 1 Lakh = 100 thousands 10 Lakhs = 1 millions 1 crore = 10 millions 6

7 10 crores = 100 millions Test yourself : Write place value and face value of 9 in9,99, 89,232. Write 96,96,679 in expanded form. Write in Roman numeral : 1225, 56560, ) MULTIPLES AND FACTORS Even numbers: Numbers divisible by 2. Eg : 2,4,6 Odd numbers: Numbers not divisible by 2. Eg: 3,5,7 Prime number:those numbers having only two factors, i.e., 1 and itself. Ex. 2,5 Composite number: The numbers which have more than two factors. Ex. 4,12,15 Co prime : If two numbers do not have any other common factor except 1. Ex. 7,10 Two prime numbers whose difference is 2 are called twin prime numbers. Ex. 3 and 5, 5 and 7. Test for Divisibility: By 2 : Last digit or digit at unit place of the number should be even number. Ex: 482, 588 By 3 : The sum of the digits of the number should be divisible by 3. Ex. 69 i.e. 6+9 = 15 (divisible by 3 ) means 69 is divisible by 3 By 4: A number is divisible by 4,if the number formed by the tens and ones digits can be divided by 4 or is zero. Ex. 108 By 5: Last digit of the number should be 0 or 5. Ex. 150, 10 By 6: If a number is divisible by 2 as well as 3 so it is divisible by 6. Ex. 12, 30 7

8 By 8: A number is divisible by 8,if the number formed by the hundreds, tens and ones digits can be divided by 8 or is zero. Ex. 168, 80 By 9: The sum of the digits of the number should be divisible by 9. Ex. 54 i.e. 5+4=9(divisible by 9) means 54 is divisible by 9 By 10: Last digit of the number should be 0. Ex. 20,60 Factors: A number is a factor of another large number if it divides the larger number exactly. 1 is factor of every number. A number is a factor of itself Multiple : Multiple of any number is a number which can be exactly divided by that number. Ex. 18 is a multiple of 9 because 18 is completely divisible by 9. A number can have unlimited multiples. Every number is multiple of itself. Multiple of a number is always greater than or equal to the number itself. Prime Factorization : Expressing a composite number as the product of prime numbers HCF:The HCF of two or more numbers is the greatest of their common factors. Ex. 12, 15 HCF =3 LCM: The LCM of two or more numbers is the smallest number which can be exactly divided by each of the given numbers of their common factors. 6, 12 LCM is 24. Methods: i). Multiple method ii ). Prime Factorisation method iii). Division method. Relation between HCF and LCM 8

9 First number X Second number = LCM X HCF. Every odd number is not a prime number. 2 is the smallest prime number. 3 is mallest odd prime number. 4 is the smallest composite number. 3) FRACTIONAL NUMBERS : i) A fraction is the part of whole. ii) A number in the form of p/q, in which number above the line segment ( ) is numerator and the number below the line segment is denominator. Like Fraction: Fractions with same denominator. Unlike Fraction: Fractions with different denominators. Mixed fraction: Quotient X Reminder/ Divisor Improper fraction:(whole number part X Denominator ) + Numerator/same denominator Lowest term: When the numerator and the denominator do not have any common factor other than 1. Comparison of fractions : Like Fraction: We compare the numerators only and the fraction with the greater numerator is greater. Ex. 5 3 > 8 8 Unlike Fraction: (with same numerator) We compare the denominator only and the fraction with the greater denominator is greater. Ex. 5 5 > 6 3 Unlike Fraction: (with different numerator) First we change the unlike fractions to like fractions. 9

10 Multiplication of fractions: Multiply the numerators. Multiply the denominators. Reduce to its simplest form. Multiplicative inverse or reciprocal : Numbers are multiplicative inverse of each other when their product is 1. Ex. 2, ½ 1 is only the number whose reciprocal is also 1. 0 has no reciprocal. 4) DECIMALS A Decimal number consists two parts a whole part and decimal part. Eg in which 25 whole part and 336 is a decimal part Like and unlike decimals : The numbers those have same number of decimal places are like decimals. Ex The numbers those have different number of decimal places are like decimals. Ex Multiplication A) Decimal by whole Do the multiplication by usual method and count the number of digits from the right equal to the number of decimal places and put decimal point. 10

11 B) Decimal by decimal Do the multiplication by usual method and count the number of digits from the right in both the numbers and equal to the sum of the number of decimal places put the decimal point. C) By 10,100,1000 When multiplication is by 10,100,1000, then the decimal point is shifted towards the right According to the number of zeros. Division A) Decimal by whole Ex by 4 Do the division by usual method and when you reach at tengths place, put the decimal in the Quotient just above the decimal in the dividend and proceed further in the same manner. B) By 10,100,1000 When division is by 10, 100, 1000, then the decimal point is shifted towards the left according to the number of zeros. 5) BASIC GEOMETRICAL CONCEPTS Point : A point determines a definite position. Line: A line is a straight move with two arrow heads. Line Segment : It is a part of a line. Ray : A ray is a part of a line starting at a point and going endlessly in one direction. Angle: An angle formed by two rays with the same initial point. 11

12 Name of an angle always consists three letters and the letter a the vertex always comes in between the two letters. < AOB O Vertex, OB Arm, OA Arm. Type of angles a)acute angle : Angle measure lies between 0 0 and 90 0 b)right angle : An angle measure 90 0 c)obtuse angle : Angle measure lies between 90 0 and d) Straight angle : Angle measures exactly e) Reflex angle: Angle measures more than and f) Complementary angles: If sum of the two angles is 90 0 andthey are said to be complementary angles and each of the angle is called complement of other. Ex and 40 0 g) Supplementary angles : If sum of the two angles is and they are said to be supplementary angles and each of the angle is called supplement of other. Ex and 30 0 PARALLEL AND PERPENDICULAR LINES Parallel lines:the lines in the same plane which do not intersect each other at any point called parallel lines. Symbol used to represent II. Ex. Opposite edges of a ruler, Steps of a ladder. Perpendicular lines : Two lines which intersect each other at right angle 12

13 Triangles : A triangle is a closed figure bounded by three line segment s. It has 3 angles, 3 vertices, 3 sides.. Types (on the basis of sides) Equilateral triangle :Triangle with all sides equal. Isoscales triangle: Triangle with two sides equal. Scalene triangle: Triangle with all three sides are of different length Types (on the basis of angles) Acute angled triangle :Triangle with all three angles less than Obtuse angled triangle: Triangle with one angle lies between 90 0 and Right triangle : Triangle one of whose angle is of Properties : i) The sum of the angles of a triangle is (angle sum property) Circle : Locus of all those points which are equidistance from a fixed point. Parts of the circle: i) Radius: A radius of the circle is that line which joins centre of the circle with any point of the circle. ii) Diameter : A diameter of the circle contains two radii of the circle. Therefore, Diameter = 2 X radius. iii) Semi circle: a diameter divides the circle into two halves,each is called semi circle. iv) Circumference: The length of the boundary of a circle or its perimeter. Circumference= 2 = 22 } 7 13

14 v) Chord: A line segment joining two points on the circle. vi) Arc: An arc is a part of the circle. vii) Concentric circles : Two or more circles having same centre. 6) MEASUREMENT OF LENGTH,MASS AND CAPACITY System of measurement is known as metric system. A unit which majority of the people use as a basic unit of measurement is called a standard unit Conversions: To convert a bigger into smaller unit, we multiply by 10,100 or 1000 Ex. 14m into cm = 14 X 100 =1400 cm To convert a smaller into bigger unit, we divide by 10,100 or 1000 Ex. 14m into km = 14 /1000 =0.014 km 7) AREA AND PERIMETER Perimeter- The length of the boundry of the closed figureis called its perimeter. Area: Amount of surface covered by a figure. Perimeter = 2(L + B) Area = Length X Breadth Perimeter = 4 X side Area = Side X side Area Breadth= Length Area Length= Breadth 14

15 8) SOLID FIGURES Figures which can be touch are known as solid figures Edges 12, vertices 8, Faces 6 VOLUME :The space which an object is occupies or a box can be hold. Volume of cuboid = length x breadth x height(cubic unit) Area Length = Breadth Area Breadth = Length Volume of a cube = Edge X Edge X Edge (cubic unit) 15

16 9) TIME a) Half an hour= 2 1 X 60 = 30 minutes b) Quarter of an hour = 1 X 60 = 15 minutes 4 c) Three Quarters of an hour = 4 3 x 60 = 45 minutes d) 1 day = 24 hr. e) 1 hr = 60 min f) 1 min = 60 seconds g) Time from 12 o clock noon to 12 o clock mid night is shown by letters pm (post meridian) h) Time from 12 o clock midnight to 12 o clock noon is shown by letters am (ante meridian) Conversion: Hours to mins multiply by 60 CALENDER Minutes to seconds multiply by 60 Minutes to Hours divide by 60 Seconds to minutes divide by 60 1 year = 12 months 1 week = 7 days 1 year = 52 weeks. The earth completes one round around the sun in 365and ¼ days. But ¼ th day is not counted in every year. Thus in four years this ¼ th day adds upto 1 day. This one day is added in every fourth year. This year is called a leap year. So a leap year has 366 days.this additional day is counted in the monh of February. Therefore,a leap year is a year which has 29 days. 16

17 10) TEMPERATURE The degree of measurement of temperature is degree ( 0 ). The normal human body temperature is 37 0 C. Freezing Point of water is 0 0 C or 32 0 F. Boiling Point of water is C or F Conversion 1) 0 C into 0 F Multiply by 9 Divide by 5 Add 32 2) 0 F into 0 C Subtract 32 Multiply by 5 Divide by 9 17

18 11) SYMMETRY Symmetry is when one shape becomes exactly like another if you flip, slide or turn it. Rotational Symmetry With Rotational Symmetry, the shape or image can be rotated some amount and it still looks the same. This image can be rotated to three different positions and it would look the same. Order of rotational symmetry: The number of times a figure matches itself or can be rotated to get the original shape. Reflection symmetry : A type of symmetry where one half is the reflection of the other half. In the figure the black line is known as the line of reflection Line of reflection : A reflection is the transformation that results from flipping a figure across a line, called line of reflection. 18

19 12) DATA HANDLING Data : A data is a collection of facts and figures Pictograph: A pictograph shows the information in the form of pictures and symbols. Tally Marks: Representation of numbers in the form of vertical lines. 19

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