## Topic outline

### Whole Number

Mark as done Place - ValueThe numbers we use in counting like 1, 2, 3 … are called natural numbers. When we include zero in thenatural numbers, i.e. 0, 1, 2, 3, 4, 5 … we now have what is called the set of positive whole numbers.In other words, the difference between the set of natural numbers and the set of positive wholenumbers is the 0 which the latter has.When any whole number is written, the value of each digit depends on its position in the number. Inthe common decimal system that we use, the value of a digit increases each time it moves from left toright by ten times.The first six on the right-hand side is six units; the next six is six tens, the next to that is six hundredswhile the last six on the left is six thousands.Therefore, the place value of any digits in any number in units, tens, hundreds, thousands, millions andbeyond is determined by the position of the digits in the number.Place Value of Whole NumbersExample 1Find the place value of each digit in 7654932.Solution2 (unit)30(Tens)900 (Hundred)4000 (Thousand)50000 (Ten thousand)600000 (Hundred thousand)7000000 (Million)Example 2Find the place value of 2 in 325669.SolutionThe place value of 2 is 20,000 → Ten thousand.Roman System of CountingThis is one of the ancient methods of writing numbers that is still in use till today. A study of thefollowing will aid our understanding of the reading and writing in Roman number system. The Romanform of the numbers is indicated against each of the following numbers:Rule 1:Whenever a less number is written to the left of a greater one in Roman figures, it means that youshould subtract the less number from the greater one, i.e IV means 1 is less than 5 or (5 – 1 = 4) i.e. IV stands for 4. IX means 1 is less than10 or (10 – 1 = 9) i.e. Ix stands for 9.Example 1Write the following in Arabic numeralsa) XXV (b) MDC (c) LViiiSolutiona. XXV -XX = 20V = 5Therefore, XXV = 25b. MDC –M = 1000D = 500C= 100Therefore, MDC = 1600c. LVIIILV =55III = 3Therefore, LVIII = 58Rule 2Whenever a less number is written to the right of a greater one in Roman figures, it means that youshould add the less number to the greater one.Example1. VI means 1 more to 5 or (5 + 1 = 6) i.e. VI stands for 6.2. XI means 1 more to 10 or (10 + 1 = 11) i.e. XI stands for 11.Writing of Large NumbersExampleWrite each of the following in words and in figures.a) 1 billion (b) ₦4.8 billion (c) 13. 4 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛Solutiona) 1 billion is a short way of writing 1 000 000 000b) ₦4.8 billion = ₦4.8 X 1 000 000 000= ₦4 800 000 000In words: four billion, eight hundred million naira.c) 134 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛 = 1. 75 trillion= 1.75 X 1 000 000 000 000= 1750 000 000 000In words: one trillion, seven hundred and fifty billion.Evaluation1. What is the total of 350, 786000 and 468050? Write your answer in figures and words2. A million million is called -------------------(c) 13. 4 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛

### Exercises in Four Basic Operations

Mark as done Can you answer this?7 - 1 x 0 + 3 ÷ 3 =?In arithmetic, there are two types of components: the numbers themselves and the operators (alsocalled operations) that tell you what to do with those numbers. The basic operators in arithmetic areaddition (sum), subtraction (difference), multiplication (product) and division (quotient).So, in the sum 7 x 3 + 5 there are three numbers; 7, 3 and 5 and two operators, a multiplication (x)and an addition (+). The order of operations used throughout mathematics, science, technology andmany computer programming languages is expressed here. Exponents (index)and roots Multiplication and division Addition and subtractionThe definitive order of operations is summed up in the acronym BODMAS, which stands for: Brackets, Order, Divide, Multiply, Add, Subtract.It would be easier if BODMAS was recognized worldwide, but unfortunately it isn’t.n the USA it’s normally called PEMDAS, which stands as: Parenthesis, Exponent, Multiply, Divide, Add, Subtract.Canadians sit in the middle with BEMDAS: Brackets, Exponent, Multiply, Divide, Add, Subtract).Regardless of the exact terminology, the sequence remains the same:Step 1: BracketsThe highest level order is defined by anything contained in brackets. These sums are always calculatedfirst. But what if there is more than one set of brackets? The rule then is to start at the innermost setand work outwards. Performing each bracketed calculation should leave you with a single number,allowing that set of brackets to be removed.Step 2: Order or ExponentThe terms Order or Exponent all relate to operations containing powers or indices such as squaringor square rooting. These calculations are all performed second.Steps 3 and 4: Divide and MultiplyThe third and fourth steps, division and multiplication, have equal weight and so form a third levelorder of operations that are carried out at the same time. Importantly, when two or more operationsof the same order appear one-after-another, the operations should be carried out from left to right.So, if faced with a sum like:18 ÷ 6 × 4 ÷ 8You just work from left to right. Eighteen over six is three, times four is twelve, and divided by eightis 1.5.Steps 5 and 6: Add and SubtractAgain, these carry equal weight. Therefore the addition and subtractions form the fourth and finallevel order of operations The third and fourth steps, division and multiplication, have equal weightand so form a third level order of operations that are carried out at the same time, again workingfrom left to right.Can you answer this NOW?7 - 1 x 0 + 32÷ 3 = ?Here’s the solution:7 – 0 + 3 = 10Addition and Subtraction by Place ValueA digit is any symbol used to write a whole number. A digit is one of the symbols 0, 1, 2, 3, 4, 5, 6, 7,8, or 9. All numbers are made up of one or more digits. A group of three digits is called a period. Asmall space separate the periods. At each space, say the name of the period. A place-value chartshows the value of the digits in a number.Example 1Evaluate 4 9 1 + 654Solution4 9 1+6 5 411 4 5Subtraction of Place ValueExample 1Evaluate 2037 - 849Solution2 0 3 7- 8 4 91 1 8 8Multiplication of Place ValueExample 1Evaluate 6 8 X 7SolutionDivisionExample 1Evaluate the following:(a) 9 ÷ 3(b) ¼ of 8Solution(a) 9 ÷ 3 = 3(b) ¼ of 8 = ¼ X 8 = 2Multiplication of Whole NumbersThe numbers used in multiplication have special names as illustrated below:141(factor) x 17 (factor) = 2397 (product)The product is a multiple of each of the factors, i.e.2397 is a multiple of 1412397 is a multiple of 17Multiplication is a short way of writing repeated additions. For example,3 x 4 = 3 lots of 4= 4 + 4 + 4= 12Division of Whole NumbersDivision by a number, e.g., 4 is best considered as multiplication by 1/4, and then we can use the resultsfor the multiplication that we have established. Thus,+8 ÷ (+2) = + 1/2 X (+8) = + 4-8 ÷ (+2) = + 1/2 X (-8) = -4+8 ÷ (-2) = - 1/2 x (+8) = -48 ÷ (-2) = - 1/2 x (-8) = +4In general:(+a) ÷(-b) = - (a ÷ 𝑏)10(-a) ÷(-b) = + (a ÷ 𝑏)Example 1Simplify the following:1. 5 + 8 ÷ (+4)2. (-3 + (-5)) ÷ (-2)3. (+6 – (- 8)) ÷ (-4)Solution1. 5 + 2 x (+4)Since 2 x (+4) = 8,Then 5 + 8 =132. (-3 + (-5)) ÷ (-2)First, (-3 + (-5)) = -3-5 = -8Therefore, (-3 + (-5)) ÷ (-2) = -8 ÷ -2= + (8 ÷ 2) = 4(+6 – (-8)) ÷ (-4)= (6 + 8) ÷ (-4)= 14 ÷ (-4)= - (14 ÷ 4)= -31/2Evaluation1) Simplify the followingi)(+20) ÷ (-10)ii)(+60) ÷ ((-3) x (-5))iii) ((-2) x (-12)) ÷ (+6)2