A relatively common example of someone working without a sense of number is the person at the check-out who tries to charge you a large sum for an inexpensive item simply because the cash register tells them to, without pausing to think that perhaps Once we have developed an understanding of numbers, we can use calculators and computers with some confidence that we can identify any gross data-entry errors. While there are many ways to solve problems with arithmetic, the commonly taught algorithms have remained in constant use because they provide an accurate and efficient means for calculating with whole numbers. The standard algorithms are useful when larger numbers make mental calculations difficult. Division is also central to the calculations of ratios, proportions, percentages and slopes. How many full buses are there and how many children are left over?ģ If you go out to dinner in a group of 12 and split the bill of $600 evenly, how much does each pay?Ĥ If twenty pens are shared equally amongst seven children how many does each child receive, and how many are left over?ĭivision problems arise when we try to break up a quantity into groups of equal size and when we try to “undo” multiplications. Division answers questions such as: 1 How many apples will each friend get if four friends share 24 apples equally between them?Ģ If 421 children are going on an excursion and each bus can carry 35 children, Multiplication therefore provides an early link between arithmetic and geometry.ĭivision is the last of the basic arithmetic operations to be introduced and, technically, The natural geometric model of multiplication as rectangular area connects arithmetic to applications in measurement. What is the total length of wire that Henry has? How many chocolates did Judy have?Ģ Henry has 16 rolls of wire. Multiplication answers questions such as: 1 Judy brought 15 boxes of chocolates. It is much quicker to calculate 6 × 25 by multiplication than by repeated addition. These three questions are examples of three different types of question that require subtraction for their solution.Įxamples of the use of multiplication include calculating the cost of six items costing 25 cents each. How many more chocolates does Terry have? How much do I have left?ģ Terry has 11 chocolates and Marie has 7. How many boys are there in the class?Ģ I have $100 and I spend $20. Subtraction answers questions such as: 1 A class has 30 students and 16 of them are girls. The ability to add numbers in your head is used in everyday life, when you play or watch sport and when you go shopping. Of the four arithmetic operations on numbers, addition is the most natural. Order of operations is an important section of this module and does not appear in any of the above modules. There is some repetition of material from the modules mentioned above but here it is brought together not only for the convenience of the reader but also for the purpose of presenting a more holistic view. Students need to have a sound understanding of whole numbers, including the arithmetic of whole numbers, before they move onto other topics, and in particular algebra. Opposites have the same absolute value since they are both at the same distance from 0.The purpose of this module is to bring together the ideas presented in the above modules for the teachers of the first year of secondary school mathematics. If two numbers are at the same distance from 0 as in the case of 10 and -10 they are called opposites. This distance between a number x and 0 is called a number's absolute value. You notice that all integers, as well as all rational numbers, are at a specific distance from 0. It is a rational number because it can be written as:Ī rational number written in a decimal form can either be terminating as in:Īll rational numbers belong to the real numbers. As it can be written without a decimal component it belongs to the integers. The number 4 is an integer as well as a rational number. Integers include all whole numbers and their negative counterpart e.g. Whole numbers are all natural numbers including 0 e.g. Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.
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