<h1><strong>BASIC OPERATIONS ON WHOLE NUMBERS</strong></h1> CONTENT <ol> <li>Multiplication of Positive and Negative Numbers</li> <li>Division of Integer</li> <li>Word Problems</li> </ol>   <h2><strong>Multiplication of Whole Numbers</strong></h2> The numbers used in multiplication have special names as illustrated below: 141 (factor) × 17 (factor) = 2397 (product) The product is a multiple of each of the factors, i.e. 2397 is a multiple of 141 2397 is a multiple of 17 Multiplication is a short way of writing repeated additions. For example, 3 × 4 = 3 lots of 4 = 4 + 4 + 4 = 12 With directed numbers, (+4) + (+4) + (+4) = 3 lots of (+4) = 3 × (+4) The multiplier is 3. It is positive. Thus, (+3) × (+4) = (+4) + (+4) + (+4) = +12 (+3) × (+4) 1 × (+4)     <span style="color: #ff0000">ILLUSTRATION TO BE ADDED SOON</span>   The illustration above shows 1 × (+4) and (+3) × (+4) as movement on the number line. The movements are in the same direction from 0. Similarly, (-2)+ (-2) + (-2) + (-2) + (-2) = 5 lots of (-2) = 5 × (-2) The multiplier is 5. It is positive. Thus, (+5) × (-2) = (-2) + (-2) + (-2) + (-2) + (-2) = -10 This is illustrated below:

Unfortunately we could not locate the table you're looking for.<h1><strong>LCM AND HCF OF WHOLE NUMBERS</strong></h1> CONTENT <ol> <li>Rules of Divisibility</li> <li>Definitions: Even, Odd, Prime and Composite Numbers</li> <li>Factors, Multiples and Index Form</li> <li>Expressing Numbers as Product of Prime Factors</li> <li>Common Factors and the Highest Common Factor (H.C.F) of Whole Numbers</li> <li>Least Common Multiple (L.C.M) of Whole Numbers</li> <li>Quantitative Reasoning on LCM and HCF</li> </ol>   <h2><strong>Rules of Divisibility</strong></h2> There are some simple rules of divisibility which enable us to find out whether a certain number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 or 11. <strong>CLASS ACTIVITY </strong> 1. Using the rules of divisibility, find out which of the following numbers are divisible by (a) 2 (b) 5 (c) 4 (i) 136 (ii) 4 881 (iii) 372 (iv) 62, 784 (v) 1010 2. Which of the following numbers are divisible by (a) 3 and 9 (b) 4 and 5? (i) 637 245 (ii) 134 721 (iii) 10140.   <h2><strong>Definitions</strong></h2> <strong>Even Numbers:</strong> Even numbers are numbers that when divided by two has no remainder. All numbers that end in 0, 2, 4, 6, and 8 are even. Examples include: 34, 86, 26890, etc. <strong>Odd Numbers:</strong> These set of numbers has a remainder of one when it is divided by 2. All numbers that end in 1, 3, 5, 7 and 9 are odd numbers. Examples are 81, 1247, 30096, etc. <strong>Composite Numbers:</strong> These are numbers that are not prime numbers. They have factors other than 1 and the number itself. All even numbers except 2 are composite numbers. <br> <h2><strong>Factors, Multiples and their Relationship</strong></h2> <strong>Factors: </strong>When two or more smaller numbers multiply to give a bigger number, these smaller numbers are called <strong>factors </strong>of the bigger number<strong>. </strong>In another sense we can say a factor is a number which can divide another number exactly without any remainder. Examples: <ol> <li>The factors of 24 are 1, 2, 3, 4 , 6 , 8 , 12 , and 24.</li> <li>The factors of <strong> </strong>60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.</li> <li>The factors of 50 are 1, 2, 5, 10, 25 and 50.</li> </ol>

Unfortunately we could not locate the table you're looking for.<h1><strong>COUNTING IN BASE 2</strong></h1> CONTENT <ol> <li>Number Bases</li> <li>Counting in Group of Twos</li> <li>Conversion from Base 10 Numerals to Binary Numbers</li> <li>Conversion from Binary to Decimal</li> </ol>   <h2><strong>Number Bases</strong></h2> In Mathematics, a <strong>base</strong> or <strong>radix</strong> is the number of different digits or combination of digits and letters that a system of counting uses to represent numbers. For example, the most common base used today is the decimal system. Because "dec" means 10, it uses the 10 digits from 0 to 9. Most people think that we most often use base 10 because we have 10 fingers. A base can be any whole number bigger than 0 (if it was 0, then there would be no digits). The base of a number may be written next to the number: for instance, 23₈ means 23 in base 8 (which is equal to 19 in base 10). The popularity of the base 2, 8 and 16 is because of its use in modern technology.   <h2><strong>Counting in Groups of Twos (Binary)</strong></h2> A Binary Number is made up of only <strong>0</strong>s and <strong>1</strong>s. An example is 110100

<h1><strong>FRACTIONS </strong></h1> CONTENT <ol> <li>Definition and Types of Fractions</li> <li>Conversion of Fraction to Decimal and Vice Versa</li> <li>Conversion of Fractions to Percentages and Vice Versa</li> <li>Quantitative Aptitude on Fractions</li> </ol> <br> <h2><strong>What are fractions?</strong></h2> Fractions are portion or part of whole number that describes quantities. Examples Consider the shapes below: <img class="size-full wp-image-23522 aligncenter" src="https://classhall.com/wp-content/uploads/2018/06/fractions.jpg" alt="Fractions" width="490" height="150" /> <h2><strong>Types of Fractions</strong></h2> Fractions are divided into four basic types: (i) <strong>A Proper Fraction</strong> It is a fraction having both numerator and denominator. And such is said to be rational. In a proper fraction, its numerator is smaller in quantity than its denominator. We can use a funny example to explain. Suppose a 15 years old boy is made to carry on his head two small tubers of yam. We can see that he can comfortably and conveniently carry them without feeling the heaviness of the weight of the tubers, on his neck. If we let the boy be the denominator and the two tubers of yam to be numerator, we can reason or compare that the <strong><em>numerator</em></strong> (the yam tubers) and the 15 year-old boy (the <strong><em>denominator</em></strong>) are not equal in weight. Obviously in this example the numerator is lighter than the denominator. It is a proper thing for anyone to do when placing loads on a child’s head. The load on a child’s head should not be heavier than the body mass of that child. So, it is proper. That is exactly what a <strong>proper fraction</strong> looks like. Examples of <strong>proper fractions</strong> are : \(\frac{4}{19}, \frac{1}{13}, \frac{12}{13}, \frac{43}{81}, \frac{34}{43}, \frac{122}{123}, \frac{72}{144},\) etc. (ii)<strong> An Improper Fraction</strong>

<h1><strong>FRACTIONS</strong></h1> CONTENT <ol> <li>Equivalent Fractions</li> <li>Ordering of Fractions</li> <li>Quantitative Reasoning</li> </ol>   <h2><strong>Equivalent Fractions </strong></h2> <h3><strong>When are fractions said to be equivalent?</strong></h3> Two or more fractions are said to be equivalent or exactly the same if they have the same quantity or have same value. In other words two or more fractions are equivalent if they can be reduced to the same lowest terms. <em>Examples</em>: \(\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{7}{14} = \frac{14}{28} =\)... These entire fractions are same, as they all have same amount, value or quantity. The same thing applies to these ones: \(\frac{3}{7} = \frac{9}{21} = \frac{12}{28} = \frac{15}{35} = \frac{21}{49} =\)... They are all equal and are therefore equivalent value.   <h2><strong>Test of Equivalent Fractions </strong></h2> If two fractions \(\frac{m}{n}\) and \(\frac{t}{k}\) are equivalent then, \(m × k = n × t\). So to test whether or not two fractions are the same we equate them and then cross multiply. If the two results of cross multiplying are exactly the same then it shows that the two fractions are equivalent. <strong>Examples</strong><strong>: </strong> (a) If \(\frac{3}{7} = \frac{9}{21}\), then 3 × 21 = 7 × 9 = 63. (b) If \(\frac{5}{10} = \frac{7}{14}\), then 10 × 7 = 5 × 14 = 70. (c) If \(\frac{9}{7} = \frac{18}{14}\), then 7 × 18 = 9 × 14 = 126.   <strong>ALTERNATIVELY:</strong> Each of the fractions can be reduced to its lowest term. If the lowest terms are equal to each other or to one another after the reduction, then it shows the equivalence. However, if after reduction the results are not the same, it then means the fractions are not equivalent. <strong>NOTE: </strong>Teacher to demonstrate this approach to students with few examples.

<h1><strong>BASIC OPERATIONS ON FRACTIONS</strong></h1> CONTENT <ol> <li>Addition and Subtraction of Fractions</li> <li>Multiplication and Division of Fractions</li> </ol>   <h2><strong>Addition of Fractions</strong></h2> <strong>Examples:</strong> 1. Add the fractions \(\frac{2}{3}\) and \(\frac{4}{5}\). <strong>Solution:</strong> \(\frac{2}{3} + \frac{4}{5} = \frac{5 × 2 + 3 × 4}{15} \\ = \frac{10 + 12}{15} = \frac{22}{15} = 1\frac{7}{15}\). 2. Add the fractions \(4\frac{3}{11}\), \(7\frac{1}{3}\). <strong>Solution:</strong> \(4\frac{3}{11} + 7\frac{1}{3} = \frac{47}{11} + \frac{22}{3} \\ = \frac{47(3) + 11(22)}{33} \\ = \frac{141 + 242}{33} = \frac{383}{33}\) = \(11\frac{20}{33}\) (in mixed fraction). (<strong>Note</strong>: In this method, we first change the mixed fractions to Improper fractions before adding).

Unfortunately we could not locate the table you're looking for.<h1><strong>WHOLE NUMBERS</strong></h1> CONTENT <ol> <li>Development of number system</li> <li>Place values</li> <li>Counting: tens; hundreds; thousands; millions;…trillions</li> <li>Translating numbers written in figures to words</li> <li>Quantitative reasoning</li> </ol> <br> <h2><strong>Development of Number System</strong></h2> There were many ancient ways of writing numbers part of which are the Hindu Arabic system, tally system, Roman system, etc. While so many have gone into extinction, the Roman system is still in use up to date.   <h2><strong>The Roman Number System</strong></h2> The Roman number system was developed about 300BC. The Romans used capital letters of the alphabet for numerals. The tables below show how to use the letters. <strong>Example 1: </strong>Write these numbers in Roman numerals. (a) 25 (b) 105 (c) 49 (d) 2011 <strong>Solution:</strong> (a) 25 = XXV (b) 105 = CV (c) 49 = XLIX (d) 2011 = MMXI   <strong>Example 2: </strong>What numbers do these Roman numerals represent? (a) XLVI (b) XCIX (c) MMCMLIV (d) MMMDCI Solution: (a) XLIV = 46 (b) XCIX = 99 (c) MMCMLIV = 2954 (d) MMMDCI = 3601 <strong>CLASS ACTIVITY</strong> 1. Write these numbers in Roman Numerals (a) 352 (b) 1 257 (c) 2456 2. Add the following Roman numerals and give your answers in figures (a) XXV and CV (b) XXIV and MDCIX.   <h2><strong>What are whole numbers? </strong></h2>

<h1><strong>WHOLE NUMBERS</strong></h1> CONTENT <ol> <li>Order of Operations (PEMDAS/BODMAS)</li> <li>Addition and Subtraction of Numbers with Place Values</li> <li>Use of Number Line</li> <li>Addition and Subtraction of Positive and Negative Numbers</li> </ol> <br> <h2><strong>Order of Operations (PENDAS/BODMAS)</strong></h2> <strong>Can you answer this?</strong> 7 - 1 × 0 + 3 ÷ 3 = ? In arithmetic, there are two types of components: the numbers themselves and the operators (also called operations) that tell you what to do with those numbers. The <strong><em>basic operators</em></strong> in arithmetic are addition (sum), subtraction (difference), multiplication (product) and division (quotient). So, in the sum 7 × 3 + 5 there are three numbers; 7, 3 and 5 and two operators, a multiplication (×) and an addition (+). The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here. <ol> <li>Exponents (index) and roots</li> <li>Multiplication and division</li> <li>Addition and subtraction</li> </ol> The definitive order of operations is summed up in the acronym <strong>BODMAS</strong>, which stands for Brackets, Order, Divide, Multiply, Add, Subtract. It would be easier if BODMAS was recognised worldwide, but unfortunately it isn’t. <img class="size-full wp-image-23462 aligncenter" src="https://classhall.com/wp-content/uploads/2018/06/whole-numbers-BODMAS.jpg" alt="Whole numbers - BODMAS" width="458" height="149" />