![]() Much money she has made in total on that day. You can then do what you did in question 1(a), without writing the separate terms of the expanded form.Ĭalculate each of the following without using a calculator.Ī farmer buys a truck for R645 840, a tractor for R783 356, a plough for R83 999 and a bakkie for R435 690.Ħ82 in one day on the stock market and then loses R264 359 on It is only possible to use the shorter method if you add the units first, then add the tens, then the hundreds and finally, the thousands. This is a bit harder on theĮxplain how the numbers in each of steps 1 to 4 are obtained. You can calculate \(3 758 + 5 486\) as shown on the left below.Īs shown on the right. Write \(5 486\) in expanded notation, as shown in 1(b). What you did in question 4 is called compensating for errors.Įstimate each of the following by rounding off the numbers to the nearest 100.įind the exact answer for each of the calculations in question 5, by working out the errors caused by rounding, and compensating for them. Now also correct the error that was made by subtracting R300 instead of R273. How can this error be corrected: by adding R23 to the R500, or by subtracting it from R500?Ĭorrect the error to get a better estimate. Will each person get \(2\), \(4\) or 2\(\frac500\).īy working with R800 instead of R823, an error was introduced into your answer. Two remaining slabs are divided as shown here? After completing this tutorial, you should be able to: Graph a point on a real number line. WTAMU> Virtual Math Lab > Intermediate Algebra. Much more than two full slabs can each person get, if the Intermediate Algebra Tutorial 3: Sets of Numbers. Will each person get more or less than two full slabs of chocolate?Ĭan each person get another half of a slab? You may use a calculator to calculate the following: Within the set of integers, the sum of twoĬalculate the following without using a calculator. They do not include fractions or decimals. To the whole number 5 and the negative number What is a whole number Whole numbers are a set of positive integers which can be described as the primary number sequence, 1,2,3 and their negative counterparts -1, -2, -3, A simple whole numbers definition is that they are numbers that can also be called non-negative integers or counting numbers. ForĮach whole number, there is a negative number that corresponds Set of whole numbers forms part of the set of integers. \quad \leftarrow \quad \leftarrow \quad \leftarrow \quad -5 \quad -4 \quad -3 \quad -2 \quad -1 \quad 0 \quad 1 \quadĢ \quad 3 \quad 4 \quad 5 \quad 6 \quad \rightarrow \quad \rightarrow \quad \rightarrow \quad. ![]() The whole numbers start with 0 and extend in \(-3\) is read as "negative 3" or "minus 3". But there is anĪnswer to this subtraction in the system of integers. For example there is no whole number that The cardinality of the set of whole numbers (and also the set of even numbers) is called aleph-null or aleph-zero, denoted by. Is there an identity element for multiplication in the wholeĪnswer is available when you subtract a number from a number ![]() Natural numbers there is no identity element for addition. The answer is just the number you start with: \(24 + 0 = 24\).Ĭalled the identity element for addition. If you are working with whole numbers, in other words If you are working with natural numbers and youĪdd two numbers, the cd will always be different from any ForĮxample, all the numbers that belong in the yellow cells below Symbol for 10, all multiples of 10 and some other numbers. Note: closure property does not hold for division and subtraction operations. We can generalize this property for whole set of whole numbers is as follows. In each of the following cases, say whether the answer is a natural number or not. Hence whole numbers also closed with respect to multiplication. Other natural numbers? If so, what is it? Is there a largest natural number, in other words, a natural number that is larger than all Is there a smallest natural number, that means a natural number that is smaller than all other natural We call it the real line.Is not closed under subtraction or division. We choose a point called origin, to represent $$0$$, and another point, usually on the right side, to represent $$1$$.Ī correspondence between the points on the line and the real numbers emerges naturally in other words, each point on the line represents a single real number and each real number has a single point on the line. One of the most important properties of real numbers is that they can be represented as points on a straight line. In this unit, we shall give a brief, yet more meaningful introduction to the concepts of sets of numbers, the set of real numbers being the most important, and being denoted by $$\mathbb$$$īoth rational numbers and irrational numbers are real numbers.
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