ASSIGNMENT 1 Option 1: Numbers and fractions Divisibility of whole numbers


In order to determine whether a given whole number is divisible by some prime numbers the following rules for divisibility are useful: • Divisibility by 2: any even number, for example a number of which the units digit is 0 or 2 or 4 or 6 or 8


• Divisibility by 5: any whole number of which the units digit is 0 or 5 • Divisibility by 3: any whole number of which the sum of the digits is divisible by 3, for example 168: 1 + 6 + 8 = 15 which is divisible by 3 There are no easy rules for divisibility by prime numbers like 7, 11, 13 and so on. To find the prime factors of whole numbers bigger than 100 can be quite challenging (using long division) unless you can use a calculator. 1.1 Complete the following list of prime numbers up to 53: 2; 3; 5; 7; 11; 13; 17; … 53


1.2 Use the rules of divisibility above as well as a calculator, if necessary, to determine the prime factors of: 1.2.1 78


1.2.5 2 299 1.2.9 7 955


1.2.2 385 1.2.6 2 261 1.2.10 2 491


1.2.3 230 1.2.7 10 469


1.2.4 1 131 1.2.8 1 147


(15)


2 Any finite or recurring decimal number is a rational number. 2.1 Complete the following sequence of rational numbers: 1,253; 1,254; 1,255; …; …; 1,258; …; …; 1,261


2.2 Write down a finite decimal number between 1,253 and 1,254 2.3 Write down a recurring decimal number between 1,253 and 1,254 3 Any common fraction like 5 3.1 a common fraction between 5 3.2 a common fraction between − 7


__ 8 or − 7


3.3 the decimal form of: 3.3.1 1 5


4 Express each of the following recurring decimal fractions as a common fraction:


__ 6


4.1 0, ˙ 6 4.2 1, ˙ 3 ˙ 5 4.3 1, ˙ 1 ˙ 2 ˙ 3


5.2 In four years’ time, what percentage of the same kind of bread will cost R12?


Assignment 1: Option 1: Numbers and fractions (3)


5.1 If the current retail price of a loaf of bread is R12, what will the same kind of bread cost 4 years from now if the price is raised at a rate of 5% per year? (3)


(3)


Total: 40 marks 427


__ 8 and 3


3.3.2 1


__ 7


__ 5 and − 6


__ 4


__ 5


__ 5 is a rational number. Write down


(2) (2) (2)


(2) (2)


(2)


(4)


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43