HOME-SCHOOLING: GRADE 8 - Curriculum
center-43815000HOME-SCHOOLING: GRADE 8 MATHEMATICS WORKSHEETS: 18 May 2020TOPIC: COMMON FRACTIONS: Equivalent forms INTRODUCTION: Revision (Suggested time: 10 Minutes)Consider the following figures. What fraction is the shaded part? Give answers in simplest form. 312 = 416 = 612= 816= 912= 620= What name is given to these kinds of fractions?_______________________________________________________________________________LESSON DEVELOPMENT (Suggested time: 30 minutes)Activity 1: Express your responses in the introduction above as a percentage and as a decimal fraction.37649153048014 × 2525= 25100=25% 12 × 5050= 50100=50% 34 × 2525= 75100=75% 310 × 1010= 30100=30% As Percentage0,250,50,750,3Decimal Fractions38 ×33= 924 or 38 =616= 924512 ×22= 1024 or 512=102458×33= 1524 or 58 =1016= 152412 =24= 36= 48 =510= 61223 =46= 69= 81234 =68= 912 LCM = 12 712 × 44=2848 916 × 33= 2748 1324 × 22= 2648∴ 1324; 916; 71214 × 2525= 25100=25% 12 × 5050= 50100=50% 34 × 2525= 75100=75% 310 × 1010= 30100=30% As Percentage0,250,50,750,3Decimal Fractions38 ×33= 924 or 38 =616= 924512 ×22= 1024 or 512=102458×33= 1524 or 58 =1016= 152412 =24= 36= 48 =510= 61223 =46= 69= 81234 =68= 912 LCM = 12 712 × 44=2848 916 × 33= 2748 1324 × 22= 2648∴ 1324; 916; 712 NB: Percent means per 100. Common FractionPercentageDecimal Fraction14 12 34 310 Activity 2: Rewrite each of the following as an equivalent fraction, with the denominator 24.38= 24 512= 24 1016= 24 Activity 3: Determine the lowest common multiple (LCM) of the denominators of:12; 23 and 34 __________________________________________________ Activity 4: Rewrite the following fractions with a common denominator and then arrange the original fractions in ascending order (smallest to biggest):712; 916; 1324 ________________________________________________________________________________________________________________________CLASSWORK (Suggested time: 20 minutes)Determine the lowest common multiple (LCM) of the denominators of 34, 45 and 56._________________________________________________________________________________________________________________________________________________________________ Consider the fractions 512 and plete the following statement: 512 = 24= 36 = = Complete the following statement: 718 = 36= 54 = = Write down three common fractions bigger than 718 , and smaller than 5 12.__________________________________________________________________ Circle the greatest fraction: 12; 112 ; 14; 18; 1 10 Complete the table below:Common FractionPercentageDecimal Fraction510 25 1050 1809750-32385000HOME-SCHOOLING: GRADE 8 MATHEMATICS WORKSHEETS: 19 May 2020TOPIC: COMMON FRACTIONS: Calculations using fractions and calculation techniques INTRODUCTION: Revision (Suggested time: 10 Minutes)Activity 1: Use 4 35 to show your understanding of the words below by matching the words and the number selected from the given fraction.Numerator: ___________________________________________________________________Denominator: ___________________________________________________________________Proper fractions:______________________________________________________Improper fractions: ________________________________________________________Mixed numbers: ___________________________________________________________________Equivalent fractions: ______________________Activity 2List the multiples of 3 and 6 less than 40, and then identify the common multiples and LCM. ________________________________________________________________________________________________________________________________________________________________________________________________Write down any five different fractions that are equivalent to 25.___________________________________________________________________Arrange the following fractions in ascending order (from smallest to biggest)-546100350520M (3): 3,6,9,12,15,18,21,24,27,30,33,36,39M (6): 6,12,18,24,30,36Common multiples of 3 and 6: 6; 12,18,24,30,36 The highest common multiple is 36 and the LCM is 600M (3): 3,6,9,12,15,18,21,24,27,30,33,36,39M (6): 6,12,18,24,30,36Common multiples of 3 and 6: 6; 12,18,24,30,36 The highest common multiple is 36 and the LCM is 63848100299720710; 35; 34; 1320710 × 22; 35 × 44; 34 × 55; 13201420;1220; 1520; 1320∴ 35; 1320; 710; 3400710; 35; 34; 1320710 × 22; 35 × 44; 34 × 55; 13201420;1220; 1520; 1320∴ 35; 1320; 710; 34___________________________________________________________________LESSON DEVELOPMENT (Suggested time: 30 minutes)Addition and subtraction of common fractions:Study the following calculations in each example and summarise your understanding below each example.Addition:-119380666751217 + 517 = 1717 = 1 __________________________________________________________________________________________________________________511 - 411 = 111__________________________________________________________________________________________________________________________________________78 - 34 = 78 - 34 × 22 multiples of 8 =8;16;24;32 = 78 - 68 multiples of 4 = 4;8;12;16;20 = 18 LCM = 8____________________________________________________________________________________________________________________________________________________________________________________Example 3: 215+ 36 = 115+ 36Multiples of 5 =5;10;15;20;25;30;35;Multiples of 6 = 6;12;18;24;30;36 LCM = 30:115 × 66+ 36 × 55= 6630 + 1530= 8130= 2 2130= 2 710OR: 215+ 36 = 2(15 + 36)= 215 × 66+ 36 × 55= 2 630+ 1530= 2 2130= 2710OR: 215+ 36 = 115+ 36 = 66 + 1530 = 8130 = 2 2130= 27101217 + 517 = 1717 = 1 __________________________________________________________________________________________________________________511 - 411 = 111__________________________________________________________________________________________________________________________________________78 - 34 = 78 - 34 × 22 multiples of 8 =8;16;24;32 = 78 - 68 multiples of 4 = 4;8;12;16;20 = 18 LCM = 8____________________________________________________________________________________________________________________________________________________________________________________Example 3: 215+ 36 = 115+ 36Multiples of 5 =5;10;15;20;25;30;35;Multiples of 6 = 6;12;18;24;30;36 LCM = 30:115 × 66+ 36 × 55= 6630 + 1530= 8130= 2 2130= 2 710OR: 215+ 36 = 2(15 + 36)= 215 × 66+ 36 × 55= 2 630+ 1530= 2 2130= 2710OR: 215+ 36 = 115+ 36 = 66 + 1530 = 8130 = 2 2130= 2710Example 1: (same denominators)Example 2: (different denominators) Note: 2130 and 710 are equivalent fractions.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________CLASSWORK (Suggested time: 20 minutes)1. Calculate: 413 + 56________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________734 - 1112________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________8 37 – 4 57________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________2. Which improper fraction is equal to 2310? 3310 ; 1610; 2110 ; 2310 ___________________________________________________________________________3. Circle the mixed number that is equivalent to 11812. 123; 212; 112; 3144. Change these mixed numbers to improper fractions or whole numbers. Reduce to lowest terms if necessary. a) 5 95 = ________________b) 22 147 = ________________ c) 32 710 = ________________ 5. Circle a proper fraction whose numerator is a composite number. 3 86 ; 4 35 ; 713; 1213996950-635000HOME-SCHOOLING: GRADE 8 MATHEMATICS WORKSHEETS: 21 May 2020TOPIC: COMMON FRACTIONS: Calculations using fractions and calculation techniques4787900203200 13+ 14 - 12 = 4+3 -612 = 11200 13+ 14 - 12 = 4+3 -612 = 112INTRODUCTION: Revision (Suggested time: 10 Minutes)Simplify 13+ 14 - 12 _______________________________________________________________________________________________________________________________________________________________________________________LESSON DEVELOPMENT (Suggested time: 30 minutes)Note: consider the following steps when simplifying fractions with multiple operations:Separate the terms using brackets guided by the “+” and the “-“ signsimplify within the bracketwork from left to rightActivity Simplify each of the following expressions as far as possible: Study the calculations below and summarise your understanding of each step below:16 - 12 × 13 = 16- 12 × 13 (2 terms) = 16 - 16 =0__________________________________________________________________________________________________________________________________________________________________________________________________________________________2 13 + 25 – 3 = 73 + 25 – 31 = 35+6-4515 = -415____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________12+ 23 ÷14 × 16 + 13 × 16 = 12+ 23 ÷ 14 × 16+13 × 16 (3 terms) = 12+23 × 41 × 16+ 118 = 12+ 818 + 118 = 12 × 99 + 818+ 118 = 918+ 818+ 118 = 1818 = 1______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ CLASSWORK (Suggested time: 20 minutes)Simplify the following expressions as far as possible:14 ÷ 15 - 12 × 13____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________2 14+ 112 - 12________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________214+ 312 ×123- 5 1 12______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________1473200-45720000HOME-SCHOOLING: GRADE 8 MATHEMATICS WORKSHEETS: 22 May 2020TOPIC: COMMON FRACTIONS: Calculations using fractionsINTRODUCTION: Revision (Suggested time: 10 Minutes)Simplify each of the following expressions as far as possible:169 _________________________________________________________________________________________________________________________________________________________________________________________________________________3216 __________________________________________________________________________________________________________________________________________________________________________________________________________________23 ____________________________________________________________________________________________________________________________________________42 __________________________________________________________________________________________________________________________________________________________________________________________________________________153482600445770169 = 13 ×13 = 133216 = 36 ×6 ×6 = 6OR 3216 = 2 ×2 ×2 ×3×3 ×3 = 2 ×3 = 623 = 2 × 2 × 2 = 842 = 4 × 4 = 16153 = 15× 15 ×15 = 112500169 = 13 ×13 = 133216 = 36 ×6 ×6 = 6OR 3216 = 2 ×2 ×2 ×3×3 ×3 = 2 ×3 = 623 = 2 × 2 × 2 = 842 = 4 × 4 = 16153 = 15× 15 ×15 = 1125____________________________________________________________________________________________________________________________________________LESSON DEVELOPMENT (Suggested time: 30 minutes)Study the following calculations and summarise them.233 = 23 × 23 × 23 = 827__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________11 19 × 3102 = 1009 × 9100 = 1___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________232 ÷ 4 12 = 49 ÷ 92 = 49 × 29 = 881__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 1232 ÷21232= 532 ÷2 532 = 259 ÷2 259 Note: 2 259 = 21 × 259 = 509 = 259 × 950 = 12___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________43 × 92 = 23 × 32 =1____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________916 ÷ 14 = 34 ÷ 12 = 34 × 21 = 32 ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________225 - 901000 = 25 - 9100 = 25 - 310 = 4 -310 = 110__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________3278 - 94 = 32 - 34 = 6 -34 = 34________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Note: when adding or subtracting fractions, any method demonstrated in lesson two can be used to make the denominators the same.CLASSWORK (Suggested time: 20 minutes)Simplify each of the following expressions without using a calculator:1232÷559________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________259 - 259______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 279 - 3338_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ................
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