Current Affairs 4th Class

Factor and Multiples

Factor and Multiples   Synopsis
• When two or more numbers are multiplied, a product is obtained. Each number is called a factor of the product. The product is called • Multiples of a multiple of each of the numbers.
e.g., $\text{5 }\times \text{ 7 }\times \text{ 9}=\text{315}$ 5, 7 and 9 are factors of 315 and 315 is a multiple of each of 5, 7 and 9.
• The multiples which appear in both the lists of multiples of the given numbers are called their common multiples.
e.g.., Multiples of $\therefore$ Common multiples of 2 and 4 are 4, 8, 12, ......
• A number is said to be the factor of another if it can divide the other completely. So, a factor is also called the divisor. The factors of a number are less than or equal to the number.
• 1 is a factor of every number. Every number is a factor of itself.
• A number is the greatest factor of itself and 1 is the least factor of a number.
• Every multiple of a number is greater than or equal to the number itself.
• Every number is a multiple of 1.
• Every number is a multiple of itself.
• There is no greatest multiple of a number.
Even Number: A number which when divided by 2, leaves zero as remainder, is an even number. e.g., 2, 4, 6, 8, 10,...   Odd Number: A number which when divided by 2, leaves one as remainder, is an odd number. e.g., 1, 3, 5, 7, 9,...   Prime Number:
• A number that has only 2 factors, that is, 1 and the number itself is known as a prime number, g., 2, 3, 5, 7, 11, ...
Composite Number:
• A number which has more than two factors is called a composite number.
• g., 4, 6, 8, 9, . ..
• Number 1 has only one factor. It is neither prime nor composite. It is called a unique number.
• 2 is the only even prime number and also the smallest prime number.
• All prime numbers except 2 are odd numbers.
• All even numbers except 2 are composite numbers.
Co-prime Numbers:
• 4 Two numbers which have no other common factor except 1 are called co-prime numbers. g., 3, 4; 4,7; etc.,
Twin-prime Numbers:
• Consecutive prime numbers with a difference of 2 between them are called twin primes.
e.g.,   3, 5; 5, 7; 11, 13; etc., The factors which divide both the given numbers are called their common factors. more...

Fractions

Fractions     Synopsis   Fraction:
• A fraction represents a part of a whole.
• In a fraction, two numerals are written one below the other separated by a line. The written above the line is called the numerator and the numeral below the line is denominator.
e.g., • In a fraction, the denominator tells us how many equal parts the whole has been divided into and the numerator tells us how many parts of the whole are being considered.
Like fractions: Fractions which have a common denominator are called like fraction e.g., $\frac{2}{9},\frac{4}{9},\frac{5}{9}$etc.,   Unlike fractions: Fractions with different denominators are called unlike fraction; e.g., $\frac{2}{3},\frac{4}{5}$   Proper fraction: In a fraction, if the numerator is less than the denominator, it I called a proper fraction. e.g., $\frac{2}{5},\frac{7}{11}$etc.,   Improper fraction: In a fraction, if the numerator is greater than or equal to the denominator it is called an improper fraction.
 Note: if the numerator is equal to the denominator, the fraction represents a whole number, i.e., 1
Unit fractions: Fractions with 1 or unity as the numerator are called unit fractions e.g., $\frac{1}{3},\frac{1}{5}$etc.,   Mixed fraction:  A fraction which is a combination of a whole number and a fraction is called a mixed fraction or mixed number           e.g., $1\frac{3}{4},7\frac{1}{11}$   Equivalent fractions: The fractions that represent the same part are called equivalent fractions. Both $\frac{2}{8}$ and $\frac{1}{4}$ represent the same part of a whole. So $\frac{2}{8}=\frac{1}{4}$.   Comparing fractions:   (a) Fractions with the same numerators: Of two fractions with a common numerator, the fraction that has a smaller denominator is greater. e.g.,  $\frac{3}{5}$and $\frac{3}{7}$ Since, the numerators are the same, comparing their denominators, we get $\text{5}<\text{7}$. $\therefore$    $\frac{3}{5}>\frac{3}{7}$    (b) Fractions with the same denominators: Of two fractions with a common denominator, the fraction that has a larger numerator is greater                  e.g., $\frac{2}{9}$and $\frac{7}{9}$ Since the denominators are the same, comparing their numerators, we get $7>2$.  $\therefore$    $\frac{7}{9}>\frac{2}{9}$   (c) Fractions with different numerators and denominators: To compare fractions with different numerators and denominators, first convert them to get the same denominator by writing their equivalent fractions and then compare. e.g., $\frac{3}{4}$ and $\frac{5}{6}$   Step 1: Check if numerators or denominators are the same. The given fractions do not have the same numerators or denominators. Step 2: Find equivalent fractions with common denominators. $\frac{3\times 3}{4\times 3}=\frac{9}{12}$ and $\frac{5\times 2}{6\times 2}=\frac{10}{12}$ Step 3: Compare more...

Number Sense and Numeration

Number Sense and Numeration   Numbers Numbers are mathematical objects by which we express date, time, position, quantity etc.   Writing and Reading Numbers Numbers are written using symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) called numerals. For example, 3564 is a numeral in which four digits (3, 5, 6 and 4) are used. In this section, we will study two types of numeration.              (i)     Indian system of numeration.             (ii)    International system of numeration.   Indian System of Numeration This method of numeration is based on the place value chart. This system is also known as Hindu - Arabic system. Given below is the Indian place value chart
 Period Kharab Arab Crores Lakhs Thousands Ones Places ten Kharab (T-kh) 1000000000000 Kharab (kh) 00000000000 Ten Arab (T-A) 1000000000 Arab (A) 100000000 Ten Crores (T-C) 10000000 Crores (C) 1000000 Ten lakhs (T-L) 100000 Lakhs (L) 10000 Ten thousands (T-TH) 10000 Thousands (TH) 1000 Hundred (H) 100 Ones (0) 0
•           Example
Name the numeral given in the place value chart.
Period Arab Crores Lakhs Thousands Ones
Places Ten Arab (T-A) (10000000000) more...

Roman Numerals

Roman Numerals   Introduction The numerals we use is commonly known as Indo-Arabic Numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ______ etc., are example of indo -Arabic numerals in ancient time Romans developed a system of numerations (numbering) which is known as Roman Numerals. I, II, III, IV, V, VI, VII, VIII, IX, _______ etc. are example of Roman Numerals.   Roman numerals are formed by using the following symbols:
 Roman Numerals Hindu-Arabic Numeral I 1 V 5 X 10 L 50 C 100 O 500 M 1000
Rules to write Roman Numerals Rule 1: more...

Operation on Numbers: Addition and Subtraction

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.
•           Example
Add 545641323 and 565655656. Solution: Arrange the numbers according to place value chart and add the digits of same column. 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. \begin{align} & \,\,\,\,766061\to First\,addend \\ & \underline{+\,586505}\to Second\,addend \\ & \underline{1352566\to }\,Sum \\ \end{align}
•            Example
Add 56 lakhs and 40 lakhs. Solution: $56\text{ }lakhs+40\text{ }lakhs=96\text{ }lakhs$
•            Example
Jack makes a set of three numbers$\left\{ \mathbf{2315648},\mathbf{54995331},\mathbf{5499895},\mathbf{6562236} \right\}$. He added two numbers given in the set and gets the result 61557567. Which numbers did he added (a) 2315648, 54995331                                       (b) 54995331, 5499895 (c) 5499895, 6562236                                         (d) 54995331, 6562236 (e) None of these Ans.     (d) Explanation: \begin{array}{*{35}{l}} \,\,\,54995331 \\ \begin{align} & \underline{+\,6562236} \\ & 61557567 \\ \end{align} \\ \end{array}   Subtraction Subtraction is the method by which we know the remaining, after taken away some quantity from a certain quantity.
•            Example
Subtract 2655854 from 6544553, Solution: Arrange the digits according to more...

Operation on Numbers - Multiplication and Division

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,
•           Example
Find correct option for $\mathbf{7}.\mathbf{5}\text{ }\mathbf{kg}+\mathbf{7}.\mathbf{5}\text{ }\mathbf{kg}+\mathbf{7}.\mathbf{5}\text{ }\mathbf{kg}+\mathbf{7}.\mathbf{5}\text{ }\mathbf{kg}+\mathbf{7}.\mathbf{5}\text{ }\mathbf{kg}+\mathbf{7}.\mathbf{5}\text{ }\mathbf{kg}+\mathbf{7}.\mathbf{5}\text{ }\mathbf{kg}.$ (a) $7\times 7.5\text{ }kg$                                                          (b) $9\times 7.5\text{ }kg$ (c) $11\times 7.5\text{ }kg$                                                         (d) $13\times 7.5\text{ }kg$ (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$   Ø  Example There are 7546 books and each of the books contains 245 pages. Find the total number 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 Multiplier.                    (iii)   Product: The answer or the result of multiplication is known as Product. Look at the example given below: Multiplication of a Number by Power of 10 When a number is multiplied by power of 10, the number of 0 is added to the right to the number, as the number of zeroes in the power of 10.
•            Example
Multiply 89456 by 1000 Solution: $89456\times 1\underline{000}=89456\underline{000}$   Multiplication of Two Natural Numbers Place the multiplicands and multipliers in columns. Then multiply both the numbers of multiplicands with the first number of the multiplier from right. Now do the multiplication by second number of the multiplier and write the product in the next line in column, leaving the first place from the left, as shown below. Now add both the products, the result is your answer. Look at the example below:   more...

Fractions and Decimals

Fractions and Decimals   Fraction Fraction is used to indicate a part of a whole. Fraction is written, for example, 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 tractions.
•            Example
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.
•            Example
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 fractions 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.
•             Example
Convert $\frac{5}{7}$ and, $\frac{7}{8}$ into like fractions. Solution: $\frac{5\times 8}{7\times 8}=\frac{40}{56}$ And, $\frac{7\times 7}{8\times 7}=\frac{49}{56}$ $\frac{40}{56}$ 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. more...

Unitary Method

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.
•             Example
If the price of one video game is Rs.15600, find the price of 7 such video games. Solution: Price of 7 video games $=Rs.15600\times 7=Rs.109200$
•            Example
If price of 9 computers is Rs. 7546500. Find the price of one computer. Solution: Price of 1 computer $=Rs.\frac{7546500}{9}$             $=Rs.838500$   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 $=Rs\frac{537.60}{14}=Rs38.40$ Price of 15 kg oranges $=Rs.\,38.40\times 15=Rs.576.$
•             Example
A car covers the distance 410 km in 5 more...

Money

Money   Introduction We require a number of things in our day to day life. We buy these things from the market and in return we pay money as per the rate of the article. So money is of great importance to us.   Different countries use different currencies. Indian currency is known as rupees. Short form of the rupees is Rs, written by the symbol Rs. We write 78 rupees as Rs. 78.   Conversion of Rupees into Paise One rupee is equal to 100 paise, so to convert rupees into paise, we multiply the Rs. by 100.
•           Example
Convert Rs. 14 into paise. Solution: $Rs.\,14=14\times 100p$ $=1400p$
•            Example
Convert $Rs.\,\mathbf{5}.\mathbf{45}$ into paise. Solution: $Rs.\,5.45=5.45\times 100p$ $=545p$   Conversion of Paise into Rupees To convert the paise into rupees we divide the paise by 100.
•            Example
Convert 675 paise into rupees. Solution: $675paise=Rs.\,\frac{675}{100}=Rs.\,6.75$
•            Example
Convert 544566 paise into rupees. Solution: 544566 paise= Rs. 5445.66   Addition of Rupees to Paise and Vice Versa In addition of rupees to paise or paise to rupees, either paise is converted into rupees or rupees is converted to paise then addition is performed.
•            Example
Add Rs. 139 and 5460 paise Solution: Problems Based on Money Problems based on money may be on addition, subtraction, multiplication and division.
•           Example
Add Rs. 2353.25, Rs. 85,670 and Rs. 352,70 Solution: $Rs.\,2353.25+Rs.\,85.670+Rs.\,352.70=Rs.\,2791.62$
• more...

Geometrical Figures

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. A is a point   Line Segment Line segment is defined as the shortest distance between two fixed points. It has fixed length. •            Example
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. •            Example
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. •            Example
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 more...

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