m31557 Fractions - 06 1.1 2009/08/24 01:37:05.313 GMT-5 2009/08/24 02:20:04.495 GMT-5 Helen Saayman Helen Saayman mark.horner@shuttleworthfoundation.org Helen Saayman Helen Saayman mark.horner@shuttleworthfoundation.org Helen Saayman Helen Saayman mark.horner@shuttleworthfoundation.org Mathematics and Statistics en

14. a) denominator b) common denominator c) multiple d) tellers e) number f) fractions g) improper fractions h) simplify 15.2 a) = 1221 size 12{ { { size 8{"12"} } over { size 8{"21"} } } } {} + 1421 size 12{ { { size 8{"14"} } over { size 8{"21"} } } } {} = 2621 size 12{ { { size 8{"26"} } over { size 8{"21"} } } } {} = 1 521 size 12{ { { size 8{5} } over { size 8{"21"} } } } {} b) = 510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} + 610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {} = 1110 size 12{ { { size 8{"11"} } over { size 8{"10"} } } } {} = 1 110 size 12{ { { size 8{1} } over { size 8{"10"} } } } {} c) = 3645 size 12{ { { size 8{"36"} } over { size 8{"45"} } } } {} - 2545 size 12{ { { size 8{"25"} } over { size 8{"45"} } } } {} = 1145 size 12{ { { size 8{"11"} } over { size 8{"45"} } } } {} d) = 46 size 12{ { { size 8{4} } over { size 8{6} } } } {} - 36 size 12{ { { size 8{3} } over { size 8{6} } } } {} = 16 size 12{ { { size 8{1} } over { size 8{6} } } } {} 16. a) = 1123 size 12{"11" { { size 8{2} } over { size 8{3} } } } {} + 17 size 12{ { { size 8{1} } over { size 8{7} } } } {} = 111421 size 12{"11" { { size 8{"14"} } over { size 8{"21"} } } } {} + 321 size 12{ { { size 8{3} } over { size 8{"21"} } } } {} p = 111721 size 12{"11" { { size 8{"17"} } over { size 8{"21"} } } } {} b) = 314−19 size 12{3 { { size 8{1} } over { size 8{4} } } - { { size 8{1} } over { size 8{9} } } } {} = 3 936−436 size 12{ { { size 8{9} } over { size 8{"36"} } } - { { size 8{4} } over { size 8{"36"} } } } {} t = 3 536 size 12{ { { size 8{5} } over { size 8{"36"} } } } {} = 6 34 size 12{ { { size 8{3} } over { size 8{4} } } } {} – (3 12 size 12{ { { size 8{1} } over { size 8{2} } } } {} + 1 23 size 12{ { { size 8{2} } over { size 8{3} } } } {}) = 6 34 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 3 36 size 12{ { { size 8{3} } over { size 8{6} } } } {} + 46 size 12{ { { size 8{4} } over { size 8{6} } } } {} = 6 34 size 12{ { { size 8{3} } over { size 8{4} } } } {} – 4 16 size 12{ { { size 8{1} } over { size 8{6} } } } {} = 2 912 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} - 212 size 12{ { { size 8{2} } over { size 8{"12"} } } } {} g = 2 712 size 12{ { { size 8{7} } over { size 8{"12"} } } } {} d) = 9 78 size 12{ { { size 8{7} } over { size 8{8} } } } {} - (4 912 size 12{ { { size 8{9} } over { size 8{"12"} } } } {} + 812 size 12{ { { size 8{8} } over { size 8{"12"} } } } {}) = 9 78 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 5 512 size 12{ { { size 8{5} } over { size 8{"12"} } } } {} = 4 78 size 12{ { { size 8{7} } over { size 8{8} } } } {} - 512 size 12{ { { size 8{5} } over { size 8{"12"} } } } {} = 4 2124 size 12{ { { size 8{"21"} } over { size 8{"24"} } } } {} - 1024 size 12{ { { size 8{"10"} } over { size 8{"24"} } } } {} v = 4 1124 size 12{ { { size 8{"11"} } over { size 8{"24"} } } } {}

14. Addition and subtraction of fractions LET US REVISE. The answers to the following questions are hidden below. Circle them when you find them and then complete the sentences. a b t t t s o n k o f m n d e n o m i n a t o r y u e d e l u o a e n r a j m n k l l l e a m d o c p e o h a e t m l e i n t o r m m v r i e d r g e i o a i n i s p r f e s g o g t n s u x l m g p t t n h o a e q k e l v o l e s t r t d e f s h j r k l e e s o q w e r t y p y o l u h r s d a z d o m u b g e s s i m p l i f i e d e l h a) We can only add or subtract fractions if the.................................................. are the same. b) If the denominators differ, we must find .................................................. fractions with the same denominators. c) We can find the common denominator easily by using .................................................. d) We only add the.................................................. together. e) The .................................................. stays unchanged when we add or subtract. f) When we add mixed numbers together, we first add the natural numbers and then the .................................................. g) When we subtract mixed numbers, we can first change them to ................................................. fractions. h) Answers must always be .................................................. as far as possible. 15.1 Do you still remember? When we add or subtract e.g. one third ( 13 size 12{ { { size 8{1} } over { size 8{3} } } } {}) + four fifths ( 45 size 12{ { { size 8{4} } over { size 8{5} } } } {}) or five sixths ( 56 size 12{ { { size 8{5} } over { size 8{6} } } } {}) – two nineths ( 29 size 12{ { { size 8{2} } over { size 8{9} } } } {}) we must first make the DENOMINATORS the same. To do this we must look for the Lowest Common Multiple (LCM). If we want the LCM of 3 and 5 we can work as follows: 3: 3 ; 6 ; 9 ; 12 ; 15 ; 18 ; 21 ; etc. 5: 5 ; 10 ; 15 ; 20 ; 25 ; etc. Thus we change both denominators to 15: 1 × 5 3 × 5 = 5 15 en 4 × 3 5 × 3 = 12 15 Thus: 13+45515+121517151215alignl { stack { size 12{ { { size 8{1} } over { size 8{3} } } + { { size 8{4} } over { size 8{5} } } } {} # = { { size 8{5} } over { size 8{"15"} } } + { { size 8{"12"} } over { size 8{"15"} } } {} # = { { size 8{"17"} } over { size 8{"15"} } } {} # =1 { { size 8{2} } over { size 8{"15"} } } {} } } {} 15.2 Calculate the following: a) x=47+23 size 12{x= { { size 8{4} } over { size 8{7} } } + { { size 8{2} } over { size 8{3} } } } {} ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ b) y=12+35 size 12{y= { { size 8{1} } over { size 8{2} } } + { { size 8{3} } over { size 8{5} } } } {} ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ c) d=45−59 size 12{d= { { size 8{4} } over { size 8{5} } } - { { size 8{5} } over { size 8{9} } } } {} ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ d) k=23−12 size 12{k= { { size 8{2} } over { size 8{3} } } - { { size 8{1} } over { size 8{2} } } } {} ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ 16. Work together with a friend and calculate: a) p=723+417 size 12{p=7 { { size 8{2} } over { size 8{3} } } +4 { { size 8{1} } over { size 8{7} } } } {} ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ b) t=514−219 size 12{t=5 { { size 8{1} } over { size 8{4} } } - 2 { { size 8{1} } over { size 8{9} } } } {} ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ c) g=634−212+123 size 12{g=6 { { size 8{3} } over { size 8{4} } } - left (2 { { size 8{1} } over { size 8{2} } } +1 { { size 8{2} } over { size 8{3} } } right )} {} ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ d) v=978−334+123 size 12{v=9 { { size 8{7} } over { size 8{8} } } - left (3 { { size 8{3} } over { size 8{4} } } +1 { { size 8{2} } over { size 8{3} } } right )} {} ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ 17. CHALLENGE! Divide into groups of three. Complete the following table by filling in the number of hours you spent doing homework last week: NAME Mon Tues Wed Thur Fri e.g Nomsa 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} 2 1 4 size 12{2 { { size 8{1} } over { size 8{4} } } } {} 3 3 4 size 12{3 { { size 8{3} } over { size 8{4} } } } {} 1 1 2 size 12{1 { { size 8{1} } over { size 8{2} } } } {} 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 1. ............................................... ............ ............ ............ ............ ............ 2. ............................................... ............ ............ ............ ............ ............ 3. ............................................... ............ ............ ............ ............ ............ Answer the following questions: a) How many hours did each member of the group spend on homework last week? 1. _________________________________ 2. _________________________________ 3. _________________________________ b) Who spent the most time on homework? _______________________________ c) Who learnt the least? _________________________________ d) Calculate the difference between b en c’s answers. ___________________________________________________ ___________________________________________________ ___________________________________________________ ___________________________________________________ e) Ask another group to check your answers.

Learning Outcome 1:The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. Assessment Standard 1.7: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve: 1.7.3: addition, subtraction and multiplication of common fractions.