Current Affairs 4th Class

                                    Operation on Numbers Addition and Subtraction   Introduction In our daily life, we come across many activities when we need to apply the method of addition and subtraction. We are aware of numbers and number system. Now we will discuss two simple algebraic operations, that is, addition and subtraction.   Addition Addition is one of the very common arithmetic operation used in mathematics. Addition is the operation to know the total quantity, when two or more than two quantities are taken together.  

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Add 545641323 and 565655656. Solution: Arrange the numbers according to place value chart and add the digits of same column. \[+\begin{matrix}    545641323  \\    565655656  \\    1111296979  \\ \end{matrix}\]   Terms related to addition (i) Addends: The numbers which are added to each other are called addends. (ii) Sum: The result of the addition is called sum. Look at the example given below.    

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Add 56 lakhs and 40 lakhs. Solution: \[56\text{ }lakhs+40\text{ }lakhs=96\text{ }lakhs\]   Subtraction Subtraction is the method by which we know the remaining, after taken away some quantity from a certain quantity.  

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Subtract 2655854 from 6544553. Solution: Arrange the digits according to the place value chart and subtract ones from ones, tens from tens and so on as follows: \[-\begin{matrix}    6544553  \\    2655854  \\    3888699  \\ \end{matrix}\]   Terms related to subtraction (i) Minuend: The number from which other number is subtracted. (ii) Subtrahend: The number which is subtracted from other number. (iii) Difference: When a number is subtracted from a greater number, the result is called difference. Look at the example given below.    

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Subtract 10 lakhs from 2 crores. Solution: 2 crores - 10 laks = 1 crores + 90 laks 100 laks - 10 laks = 1 crores + 90 laks So, \[2\text{ }crores-10\text{ }lakhs=1\text{ }crores+90\text{ }lakhs\].  

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Choose the number from the following that should be subtracted from the sum of 784568 and 784562 such that the difference becomes 784564. (a) 784566                     (b) 784570       (c) 784574                     (d) 784578 (e) None of these   Answer (a) Explanation: 785468 + 784562 = 1569130 1569130 - 784564 = 784566

                                      Operation on Numbers Multiplication and Division   Introduction In this chapter we will study two important arithmetic operations "multiplication and division". Multiplication is repeated addition of a specific quantity, whereas division is a distribution of a quantity into some equal parts. Let us study them.   Multiplication When a quantity is added to itself for a number of times, we use operation of multiplication to find the resulting quantity.  

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Find correct option for \[7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg\]\[+7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg.\] (a) \[7\times 7.5\,kg\]                   (b) \[9\times 7.5\,kg\] (c) \[11\times 7.5\,kg\]                 (d) \[13\times 7.5\,kg\] (e) None of these   Answer (a) Explanation: \[7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg+\] \[7.5\text{ }kg+7.5\text{ }kg=~\]\[7\times 7.5\text{ }kg\]  

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There are 7546 books and each of the books contains 245 pages. Find the total of pages. Solution: Total number of pages = \[7546\times 245\] = 1848770   Terms Related to Multiplication (i) Multiplicand: In the multiplication, the number which is multiplied is known as multiplicand. (ii) Multiplier: The number by which the multiplicand is multiplied is known as (iii) Product: The answer or the result of multiplication is known as product. Look at the example given below:   Multiplication of Two Natural Number Place the multiplicands and multipliers of multiplicands with the first number multiplication by second number of the line in column, leaving the first place the products, the result is your answer Look at the example below: Example Find the product of 24 and 15 \[24\times 15=360\]  Solution:   Word Problems Based on Multiplication

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An aeroplane is flying with the speed 1072 km/h. How much distance will it cover in 720 minutes? Solution:        Distance covered by the aeroplane       Note: The product of two natural numbers is always a natural number.   Division Division is the distribution of a quantity into some equal parts in such a way that each part contains equal amount.  

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Distribute 433035 kg wheat into 45 equal parts. Find the amount of wheat each part contains. Solution: Amount of wheat contained in each part \[=\frac{433035}{45}kg=9623\,kg\]  

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If 264 apples are distributed among 24 peoples, find the number of apples that everyone will get. Solution: Number of apples each people will get \[=\frac{264}{24}=11\]   Terms Related to Division Dividend: The quantity that is to be divided is called dividend. Divisor: Number of parts in which the quantity to be divided is called Divisor. Quotient: The amount that each group gets is termed as Quotient. Remainder: The extra amount which is left after equally distribution is called remainder. Relation between the terms of division. \[Dividend=Divisor\times Quotient+\operatorname{Re}mainder\]  

• Example

Divide and verify more...

                                                             Factors and Multiples   Factors of a Number All the numbers, which divide a certain number exactly, without leaving a remainder are called factors of that number. For example:   \[\Rightarrow \]1, 2, 3, 4, 6 and 12 are factors of 12. Note: Factors of a number always include 1 and the number itself.    

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Find the factors of 15.              Solution: The factor of 15 are \[\Rightarrow \]1, 3, 5 and 15 are factors of 15.  

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Which among the following is not a factor of 10? (a) 2                              (b) 5 (c) 10                            (d) 3 (e) None of these   Answer (d) Explanation: Clearly \[10\div 1=10,\,10\div 2=5,\,10\div 5=2\,and\,10\div 10=1\]\[\Rightarrow \]1, 2, 5 and 10 are factors of 10.   Properties of factors: (i) 1 is a factor of every number. (ii) Every non-zero number is a factor of intself. (iii) Every non-zero number is a factor of zero. (iv) Division by 0 is meaningless. (v) The factor of a non-zero number is either less than or equal to the number.  

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Which among the following statements is not ture?  (a) 2 is a factor of 2. (b) 26 is a factor of 0 (c) 28 is not a factor of 4. (d) 4 is not a factor of (e) None of these   Answer (d) Explanation: Every number is a factor of itself so 2 is a factor of 2. Every non-zero number is a factor of 0. So 26 is a factor of 0.          The factor of a non-zero number cannot be greater than the number. So, 28 can't be a factor of 4. \[28=1\times 2\times 2\times 7\] \[\Rightarrow \]1, 2, 4, 7, 14 and 28 are factors of 28.           Even and odd Numbers Even numbers: A number is called an even number if 2 is a factor of the number. In other words, A number, which is a multiple of 2 is called an even number.  For example: 0, 2, 4, 6, 8, 10, 12, 14, 16 are even numbers.             Odd numbers: A number, which is not a multiple of 2 is called an odd number.        For example 1, 3, 5, 7, 9, 11, —— are odd numbers.  

• Example

Which one among the following is not an even number? (a) 0                              (b) 89990 (c) 1049                         (d) 2032 (e) None of these   Answer (c) Explanation: 1049 is not a multiple of 2 and so is not an even number.         Prime Factors Factors of a number written in primes are called prime factors of that number. For example: \[24=2\times 2\times 2\times 3\] \[\Rightarrow \]Prime factors of 24 are \[2\times 2\times 2\times 3\]   Multiples          You already know that multiples of 2 more...

                                                               Fractions and Decimals   Fraction Fraction is used to indicate a part of a whole. Fraction is written as\[\frac{a}{b}\]. The top number in a fraction is called numerator and the bottom number is called denominator of the fraction. Hence in the given example 'a' is numerator and 'b' is denominator. Look at the shaded part in the following figures which has been represented by fractions:    

• Example

Tom cuts an apple into 5 equal parts. He eats one part. Give the part of the apple eaten by Tom in fraction. Solution: Tom eats 1 out of 5 parts. So parts of apple eaten by Tom \[=\frac{1}{5}\]   Like Fraction The fractions having same denominator are called like fractions. For example, \[\frac{1}{5,}\,\frac{4}{5},\,\frac{7}{5}\] are like fractions.  

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Choose the like fractions from the following? \[\frac{45}{41},\,\,\frac{25}{13},\,\,\frac{13}{25},\,\,\frac{57}{61},\,\,\frac{6565}{13}\]   Solution: \[\frac{25}{13}\]and \[\frac{6565}{13}\]are like fractions because they have same denominator.   Unlike Fraction The fractions having different denominators are called unlike fractions. For example, \[\frac{1}{2},\,\,\frac{6}{8},\,\,\frac{14}{17},\,\,\frac{13}{9}\]are unlike fractions.  

• Examples

Which of the following are unlike fractions? \[\frac{4}{7},\,\,\frac{3}{5},\,\,\frac{8}{9},\,\,\frac{7}{5},\,\,\frac{11}{12},\,\,\frac{13}{17}\] Solution: \[\frac{4}{7},\,\,\frac{8}{9},\,\,\frac{11}{12},\,\,\frac{13}{17}\] Are unlike fraction because they have different denominators. Conversion of Unlike Fraction into Like Fraction Multiply the numerator and denominator of each fraction by a suitable number (one number for one fraction) such that denominator becomes same in all fraction.  

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Convert \[\frac{5}{7}and\frac{7}{8}\] into like fractions. Solution: \[\frac{5\times 8}{7\times 8}=\frac{40}{56}\] And, \[\frac{7\times 7}{8\times 7}=\frac{49}{56}\]are tike fractions. \[\frac{40}{56}and\frac{49}{56}\]are like fractions.   Equivalent Fraction The fractions which have same value are called equivalent fractions. For example, \[\frac{7}{9}and\frac{28}{36}\]are equivalent fractions. Finding an Equivalent Fraction of Given Fraction To find an equivalent fraction of a given fraction, numerator and denominator of the fraction is multiplied or divided by same number.  

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Find an equivalent fraction of\[\frac{15}{17}\]. Solution: Equivalent fraction of \[\frac{15}{17}=\frac{45}{51}\] Note: You may find other equivalent fraction of \[\frac{15}{17}\]   Unit Fraction The fractions in the form \[\frac{p}{q}\](p = 1, q is a natural number) are Called unit fractions. For example, \[\frac{1}{4},\,\,\frac{1}{5},\,\,\frac{1}{6}\] are unit fractions.   Proper Fraction The fractions having greater denominator are called proper fractions. For example, \[\frac{21}{25}\] is a proper fraction because in this fraction numerator is smaller than denominator.   Improper Fraction The fractions having smaller denominator are called improper fractions. For example, \[\frac{21}{17}\] is an improper fraction because in this fraction numerator is greater than denominator.   Mixed Fraction Mixed fraction is a sum of a whole number and a proper fraction. For example, \[1\frac{4}{17}\]is a mixed fraction, because 1 is a whole number and \[\frac{4}{17}\] is a proper fraction. Conversion of Mixed Fraction into Improper Fraction If \[a\frac{b}{c}\] is a mixed fraction, then \[\frac{(a\times c)+b}{c}\] is an improper fraction equivalent to given mixed fraction.  

• Example

Convert \[12\frac{3}{11}\]into the improper fraction. Solution: \[12\frac{3}{11}=\frac{11\times more...

                                                             Unitary Method   Unitary Method Unitary method is a method under which a calculation is carried out to find the value of the number of items, by first finding the value of one item. From daily life experience, we know that when we increase the quantity of articles, their cost increases and when we decrease the quantity of articles, their cost decreases. In other words, more articles have more value and less articles have less value.   Note: In unitary method: (i) To get more value we multiply. (ii) To get less value we divide. To solve the problems by unitary method we follow two steps: Step 1: Get the value of a single unit. Step 2: Then find the value of required units.  

• Example

If price of 12 cycles is Rs. 18720, find the price of 18 such cycles. Solution: Price of 1 cycle = Rs.\[\frac{18720}{12}\]= Rs. 1560 Price of 18 cycles = Rs.\[1560\times 18\] = Rs. 28080   Some Other Problems Related to Unitary Method Problems related to unitary method may also be as follows:  

• Example

If price of 14 kg oranges is Rs. 537.60. Find the price of 15 kg oranges. Solution: Price of 1 kg orange = Rs. \[\frac{537.60}{14}\] = Rs. 38.40 Price of 15 kg oranges = Rs. \[38.40\times 15\]= Rs. 576.    

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A car covers the distance 410 km in 5 hours. Find the distance covered by the car in 7 hours. Solution: Distance covered by the car in 1 hour =\[\frac{410}{5}km=82km\] Distance covered by the car in 7 hours =\[82km\times 7=574km\]  

                                                                Geometrical Figures   Introduction In our day to day life we come across a number of objects. All the objects has a specific shape and size. We recognize a number of objects by their shape. Therefore, to know about the objects and of their shapes is very important. In this chapter we will study about the shapes of different geometrical figures.   Point To show a particular location, a dot (.) is placed over it, that dot is known as a point. \[\centerdot \,\xrightarrow{{}}A\] A is a point   Line Segment Line segment is defined as the shortest distance between two fixed points. It has fixed length.    

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How many line segments are there in the following figure? Solution: There are 6 line segments in the given figure.   Ray It is defined as the extension of a line segment in one direction up to infinity.  

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How many rays are there in the following figure? Solution: There are 12 rays.   Line Line is defined as the extension of a line segment up to infinite in either direction.      

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How many lines are there in the following figure? Solution: There are two lines.   Angle Inclination between two rays having common end point is called angle. \[\angle ABC\] is a angle A Right Angle An angle whose measure is exactly \[90{}^\circ \]is a right angle.   \[\angle ABC\]is a right angle   An Acute Angle An angle whose measure is less than \[90{}^\circ \]is an acute angle. \[\angle DEF\]is an acute angle.   An Obtuse Angle An angle whose measure is greater than \[90{}^\circ \] but less than \[180{}^\circ \]is an obtuse angle. \[\angle LMN\]is an obtuse angle  

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The following angle is a____. Solution: It is an obtuse angle, because its measure is greater than\[90{}^\circ \].   Polygon A Simple closed figure formed of three or more line segments is called a polygon. Line segments which form a polygon are called its sides. The point at which two adjacent sides of a polygon meet, is called a vertex of polygon. In the given figure, triangle, quadrilateral, pentagon and hexagon, all are examples of polygon. Types of Polygons Regular and Irregular Polygon A regular polygon has all sides equal and all angles equal, more...

                                                                  Area and Perimetre   Introduction In the previous chapter we have studied about the shape and size of some geometrical figures. In this chapter we will study about area and perimetre of some close geometrical figures.   Area Area is referred as the surface occupied by the geometrical shapes   Area of a Triangle Area of a triangle \[=\frac{1}{2}\times Base\times Height\] Where base is one side of a triangle and height is the length of altitude drawn from opposite vertex on the given base.   Area of the triangle ABC\[=\frac{1}{2}\times AD\times BC\] Where BC is the base and AD is the height.  

• Example

Find the area of the triangle whose base is 5 cm and height is 8 cm. Solution: Area of the triangle \[=\frac{1}{2}\times 5cm\times 8cm=20c{{m}^{2}}\]   Area of a Rectangle Area of a rectangle \[=Length\times Breadth\] Area of the rectangle ABCD =\[=AB\times BC\]  

• Example

Find the area of the rectangle whose length is 9 cm and width is 7 cm. Solution: Area of the rectangle \[=9cm\times 7cm=63c{{m}^{2}}\]   Area of a Square Area of a square \[=Side\times Side\] Area of the square ABCD\[=AB\times AB\]

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Find the area of the square whose length of one side is 6 cm. Solution: Area of the square ABCD \[=6cm\times 6cm=36c{{m}^{2}}\]   Perimetre Perimetre is referred as the length of the boundary line which endorsee area.   Perimetre of the Triangles Perimetre of a triangle = Sum of length of all three sides. Perimetre of the triangle \[ABC=AB+BC+CA\]  

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Find the perimetre of the given figure. Solution: Perimetre of the figure \[=6.5\text{ }cm+7\text{ }cm+4\text{ }cm=17.5\text{ }cm\]   Perimetre of a Quadrilateral The perimetre of a quadrilateral = Sum of the length of all four sides. Perimetre of the quadrilateral ABCD \[=AB+BC+CD+DA\]  

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Find the perimetre of the quadrilateral whose length are 4 cm, 7 cm, 3 cm and 5.2 cm. Solution: Perimetre of the quadrilateral \[=4\text{ }cm+7\text{ }cm+3\text{ }cm+5.2\text{ }cm=19.2\text{ }cm\]   Perimetre of a Rectangle Perimetre of a rectangle \[=2\,\,(Length+Breadth)\] Perimetre of the rectangle ABCD \[=2\,\,(AB+BC)\]

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Find the perimetre of the rectangle whose length and breadth are 9 cm and 8 cm. Solution: Perimetre of the rectangle \[=2\text{ (}9\text{ }cm+8\text{ }cm)=34\text{ }cm\]   Perimetre of a Square Perimetre of a square \[=4\times \]length of one side of the square. Perimetre of the square ABCD \[=4\times AB\] more...

                                                              Data and Handling   Introduction In our day to day life, time to time we come across graphs while reading or watching news etc. The graphs are prepared with the help of data. Data is collected through survey or other means. The data can be arranged in a specific order as per our need by using table. In this chapter we will study about some of the graphical representation of data, how to make the graphs and how to extract information’s contained by the graphs.   Data The information which is collected in the form of numerals is called data.   Raw Data The initial data that the observer collects himself is called raw data.   Grouped Data To extract the information’s contained in the data easily, the data is arranged in ascending or descending order using tables.   Graphical Representation of Data Data can be represented graphically by using Pictographs, Bar graphs, Pie charts etc. In this chapter we will learn about Pictographs and Bar graphs.   Pictograph When the data is represented on the graph with the help of pictures the graph is known as Pictograph.  

• Example:

Number of sixes hit by Sehwag against different team in a tournament has been shown in the following pictograph.  

Australia
Pakistan
South Africa
Newzealand
England

  Onerepresents one six.       (a) Against which country Sehwag more...