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arithmetic part2 - arithmetic calculating fractions part 2...

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Unformatted text preview: arithmetic calculating fractions part 2 — When you have worked through part 2, you should be able to - select from sets of equivalent fractions those with a common denominator ' addf subtract proper fractions I addf subtract mixed numbers This is the second part of a 3-part UNIT. Pre—requisite: You should know how to generate sets of equivalent fractions. Addition and . Example- Caiculaeifi Subtraction which have a common denominator, in this case, 6. Then %+% = 2 +% = 2 (adding the numerators) 6 The fractions from each set which had the smallest common denominator were 4 chosen. This is desirable, though not essential. We might have used E and E1 — . with common denominator 12; i + i = i + E. = 1—9. 12 s 2 12 12 1:: . 10 . . . . 5 and then said 1—,: 15 equivalent to the simpler fraction Choosing the smallest common denominator simplifies the work and saves time. . 2 3 Examples 1. Fmd 3+? (pd sifiaeee_201 “ml was 15‘10‘15’20’25*3o‘ss‘ 40 “50‘ d {3: 2 i _I2 _15 1 a“ 3’ 16’ 24’ 32’ 40 "'1 and choose fractions with common denominator 40. 23161531 Then ~—+—=-++——=— (addingnumerators). 5 3 40 4'1] 40 i . 3 4 2. Find 5 - 7. a . 3 6 9 12 15 18 21 l L. cl t — -_ _ _. _ _... _.. mm m“ 15’ 10’ 15 20’ 25’ 30* as l and __8... E E E i T14“ 1' 23' 35 1 Then 2—i2E-Ezi {subtractingnumerators}. 5 7 ’3‘? 35 The process can he speeded up. It is not essential to generate whole sets of equivalent fractions each time. Step {i} Look for a common denominator In this example, that is a number that 5 and '5” will divide into. Choose 35. E _ 4 i 5 7 35 35 Step {ii} Find equivalent fractions 3 P’ E h 33 Ask yourself “What has 5 been multiplied 13}; to give 35”. The answer is .7. Multiply the numerator bv the same number. Then §=fl:3}tl 5 a7 35 Repeat the argurnent fer i i = £32 = 2—2. 3 7 7’ 7 3x: Step {iii} Add er subtract as required. Further 3. Calculate 3+§_i Examples 5 4 2 . 2 3 l 5'" ? ? 3919(1) 34—1—5 = Tia-tifi-fi eernrnen denerninater 20 Step-(e) 3:2X4=_8_. 5 5x4 EU 3 _ 3x5 _ 4 ‘ 4x5 ‘ 20 l>< If} 10 3 l 8 15 it} 13 _+__._..._.._._._— E E 20 20 zit—E E fill "e e; Lnllfl + I II While we eften en 13.? write the calculatien as in step (iii), the theught preeesses in {i} and {ii} are essential. 4. Mixed. Numbers 2:113: 6 4 3 and a bit! by adding the whele numbers. 5 3 10 9 19 se 6 4 12 12 12 adding the fraeeens. New % is greater than 1 and can be written as %+% Let l+-132- er 1%. Adding the three whele numbers, the tetal stun is 41%. 5 q:_132§_: '4883 Here we need te change ene ef the whele numbers inte eighths. 7 35' __ 8 8 m _8 67 —[+8+8 3 HF' equal te E = 1 adding /subtrarting numeraters ee|~a Sum mary 1. Addfsubtraet whale numbers Find smallest eemen denemfl'lster fer the fractions. Find equivalent fractiens. Add! subtract numereters of fractions, if possible. P1P?!” If Step 4 cannot be done, change 1 whole number into a fraetien. Then do Step 4. 6. Can the final fraefien be simplified? Exercise Calculate the fellewing: 1 %+%+% 2. es s 3%; 4 2%+%—1% s 3%—1%+2% Solutions 1. %=I% 2+ % 3 2130. 4 1% ...
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