Grade 6 / division 74 exercises (including 73 corrected)

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1. Mental Math E.11808 Compléter les pointillés: a 24 ÷ 2 = 36 ÷ : : : b 25 ÷ 5 = : : : ÷ 3 c 49 ÷ : : : = 56 ÷ 8 d 64 ÷ 8 = : : : ÷ 2 2. Review: Euclidean division, 1-digit divisor E.11793 1 Compléter la table de multiplications suivante : × 3 41 46 51 42 47 52 43 48 53 44 49 54 45 50 55 2 a Combien de fois le nombre 3 rentre dans 139 ? Com-bien reste-t-il? b Combien de fois le nombre 3 rentre dans 155 ? Combien reste-t-il? 3 En donnant votre réponse sous la forme : Dividende = Quotient × Diviseur + Reste a Donner la division euclidienne de 137 par 3 . b Donner la division euclidienne de 163 par 3 . E.3870 Pose and perform the following Eu-clidean divisions : a 507 by 9 b 1243 by 3 3. Euclidean Division: 2-Digit Divider E.1572 1 Complete the following multiplication table : × 12 0 5 10 1 6 11 2 7 12 3 8 13 4 9 14 2 For each of the integers 75 , 143 and 166 : a Specify the maximum number of times the integer 12 fits into each. b Deduce the Euclidean divisor written as : Dividend = Quotient × 12 + Reste E.1569 1 Complete the following multiplication table : × 13 0 0 5 10 1 6 11 2 7 12 3 8 13 4 9 14 2 Perform the following Euclidean divisions : 78 by 13 ; 174 by 13 ; 168 by 13 E.9941 Pose and perform the following Eu-clidean divisions : a 1166 by 12 b 1024 by 16 4. Euclidean Division: Problems E.11455 1 Effectuer la division euclidienne de 1482 par 7 . 2 Combien de fois le nombre 7 rentre au maximum de fois dans 1482 ? https://chingmath.fr sacados/11808 chapExoCorrec/11793 sacados/11793 chapExoCorrec/3870 sacados/3870 chapExoCorrec/1572 sacados/1572 chapExoCorrec/1569 sacados/1569 chapExoCorrec/9941 sacados/9941 chapExoCorrec/11455 sacados/11455
×10÷105,3?×10÷10?84×100÷10051,4?×100÷1000,54?×1000÷1000?57,3×10÷10?0,2 E.11456 Un fermier ramasse les oeufs pondus par ses poules durant la nuit. Il en compte 748! Il compte les ranger dans des boites contenant chacune une douzaine d’oeufs. Il possède 65 boites. 1 Combien de boîtes complètes, le fermier pourra-t-il con-fectionner? 2 A-t-il suffisamment de boîtes pour ranger tous ses oeufs? E.11794 1 L’ heptagone régulier est un poly-gone à 7 sommets (donc 7 côtés) dont tous les côtés ont même longueur. Justifier qu’un heptagone, dont le périmètre à 56 cm , a tous ses côtés de longueur entière. 2 a Compléter les divisions euclidiennes ci-dessous où sont indiqués les dividendes et les diviseurs : 56 = : : : : : : × 3 + : : : : : : 56 = : : : : : : × 4 + : : : : : : 56 = : : : : : : × 5 + : : : : : : 56 = : : : : : : × 6 + : : : : : : 56 = : : : : : : × 7 + : : : : : : b Parmi les polygones réguliers ci-dessous, lesquels ont un périmètre de 56 cm et leur mesure de leurs côtés, en centimètre, est une valeur entière: Définition: Nombre de côtés Nom du polygone régulier 3 triangle équilatéral 4 carré 5 pentagone régulier 6 hexagone régulier 7 heptagone régulier E.11795 Claire, la bibliothécaire, doit accueillir les cinq classes de sixième au CDI. Elle prépare l’espace de travail pour former le maximum de groupes de 6 personnes autour d’une table. Chaque classe comporte exactement 26 élèves et chaque élève doit être à une table. Sur chaque table de travail, elle dépose 7 manuels de dif-férentes matières pour que les élèves effectuent leur recherche. Combien de manuels doit-elle préparer pour cette séance de travail? Indication : toutes traces de recherche et de prise d’initiative même incomplète seront prises en compte dans l’évaluation. 5. Division by 10, 100, 1000 E.9943 1 Complete the diagrams below : 2 Using the previous question, copy and complete the fol-lowing calculations : a : : : : : : ÷ 10 = 5.3 b 84 ÷ 10 = : : : : : : c : : : : : : ÷ 100 = 51.4 d : : : : : : ÷ 100 = 0.54 e 57.3 ÷ 1 000 = : : : : : : f 0.2 ÷ 10 = : : : : : : E.6696 Using mental arithmetic, perform the following operations : a 546 ÷ 10 b 0.345 ÷ 10 c 24.5 ÷ 100 d 1035 ÷ 100 e 1000 ÷ 1000 f 547.1 ÷ 100 E.9916 Using mental arithmetic, perform the following calculations : a 2.4 ÷ 100 b 34.15 ÷ 1000 c 754.1 ÷ 10000 d 7 ÷ 100 E.2319 Using mental arithmetic, complete the following calculations : a 4.213 ÷ = 0.04213 b 721 ÷ = 7.21 c 917.4 ÷ = 0.9174 d 5.41 ÷ = 0.541 E.6326 We consider the following two cal-culation programs : Program A Choose a number. Multiply it by 10 . Divide the result by 10 Display the result Program B Choose a number. Multiply it by 100 . Divide the result by 100 Display the result 1 If we choose the number 15 , what is the number returned by each of these calculation programs? 2 If we choose the number 4 , what is the number returned by each of these calculation programs? 3 What can we say about these two calculation programs? https://chingmath.fr chapExoCorrec/11456 sacados/11456 chapExoCorrec/11794 sacados/11794 chapExoCorrec/11795 sacados/11795 chapExoCorrec/9943 sacados/9943 ×10÷105,3?×10÷10?84×100÷10051,4?×100÷1000,54?×1000÷1000?57,3×10÷10?0,2 chapExoCorrec/6696 sacados/6696 chapExoCorrec/9916 sacados/9916 chapExoCorrec/2319 sacados/2319 chapExoCorrec/6326 sacados/6326
E.9944 Complete the following sentences : Dividing a number by 10 is equivalent to shifting the decimal point from . . . . . . . . . to . . . . . . . . . Dividing a number by 100 is equivalent to shifting the decimal point from . . . . . . . . . to . . . . . . . . . 6. Multiplication and division by 10, 100, 1000 E.1492 Using mental arithmetic, perform the following calculations : a 1.5 × 1 000 b 25.143 ÷ 100 c 0.0012 × 10 d 0.87 ÷ 100 e 1.324 ÷ 100 f 0.3 × 100 E.1495 Using mental arithmetic, perform the following calculations : a 2.7 × 10 000 b 354.89 ÷ 1 000 c 0.005 × 10 d 0.064 ÷ 100 e 25.79 ÷ 1 000 f 0.214 ÷ 10 E.6579 Using mental arithmetic, perform the following operations : a 54.3 × 100 b 0.86 × 1000 c 49 × 10 d 748 ÷ 1000 e 0.45 ÷ 100 f 91.6 ÷ 10 E.1496 Using mental arithmetic, perform the following calculations : a 12.541 × 10 000 b 0.12 ÷ 1 000 c 2.243 × 10 d 21.245 ÷ 100 E.1472 Using mental arithmetic, perform the following calculations : a 2.56 ÷ 10 b 1.5 + 100 c 3.1 × 1 000 d 12 ÷ 1 000 e 1841 − 100 f 3.54 × 10 000 E.1469 Using mental arithmetic, perform the following calculations : a 354 ÷ 10 b 27 + 100 c 0.564 × 100 d 25 ÷ 1 000 e 1946 − 100 f 2.5 × 10 000 E.3513 Using mental arithmetic, perform the following calculations : a 35.14 × 100 b 0.024 ÷ 10 c 98.75 ÷ 1 000 d 0.03524 × 10 000 E.1499 Using mental arithmetic, complete the following calculations : a 51 + : : : = 151 b 51 ÷ : : : = 0.51 c 12.3 × : : : = 123 d 25.143 ÷ : : : = 0.25143 e 13 × : : : = 13 000 f 75 ÷ : : : = 0.075 E.9973 Using mental arithmetic, complete the blanks below : a : : : : : : × 1 000 = 95.4 b : : : : : : × 100 = 0.54 c : : : : : : ÷ 10 = 54 d : : : : : : ÷ 1 000 = 3.51 E.6580 Using mental arithmetic, complete the following blanks : a 5.54 × : : : : : : = 554 b : : : : : : × 0.015 = 1.5 c 12.1 × : : : : : : = 12 100 d 0.45 ÷ : : : : : : = 0.045 e 978 ÷ : : : : : : = 0.978 f 45.54 ÷ : : : : : : = 0.004 545 7. Numbers of tenths, hundredths, thousandths E.2147 The number 32.45 can be written in several ways : Fractional decomposition : 32.45=32+ 4 10 + 5 100 Fractional writing: 32.45 = 3245 100 From the two previous entries, determine the answer to the following questions : 1 What is the hundredths digit of this number? 2 How many hundredths does this number include? E.9888 Consider the number A =63.5491 : 1 Copy and complete the blanks : 63.5491 = : : : 100 + 9 1 000 + 1 10 000 ; 63.5491 = : : : 1 000 + 1 10 000 2 How many hundredths does the number A contain? How many thousandths does the number A contain? E.9893 Consider the number A =27.06 . 1 Give the decimal fraction decomposition of the number A . 2 Give the number of hundredths of the number A . Deter-mine the number of hundredths contained in A . https://chingmath.fr chapExoCorrec/9944 sacados/9944 chapExoCorrec/1492 sacados/1492 chapExoCorrec/1495 sacados/1495 chapExoCorrec/6579 sacados/6579 chapExoCorrec/1496 sacados/1496 chapExoCorrec/1472 sacados/1472 chapExoCorrec/1469 sacados/1469 chapExoCorrec/3513 sacados/3513 chapExoCorrec/1499 sacados/1499 chapExoCorrec/9973 sacados/9973 chapExoCorrec/6580 sacados/6580 chapExoCorrec/2147 sacados/2147 chapExoCorrec/9888 sacados/9888 chapExoCorrec/9893 sacados/9893
50012 3301 191 79105 9785 E.9965 Consider the number A =0.91 . 1 Give the decimal fraction decomposition of the number A . 2 Give the number of hundredths of the number A . Deter-mine the number of hundredths contained in A . E.3389 On each of the tables below, the la-bels (tenfold D , unit U , tenth d . . . ) have been erased ; using the indications given, replace the decimal point in the deci-mal writing of the numbers and correctly complete the first line of the table with the missing labels : 1 This number has fifty tens. 2 The hundredths digit of this number is zero. 3 The number of thousandths of this number is one hun-dred and ninety-one. 4 This number has seventy nine hundreds. 5 The hundredths digit of this number is nine. 8. Exact decimal division E.2375 Place the following divisions to de-termine the exact value of their quotients. A 35.12 ÷ 4 b 35.1 ÷ 6 E.3871 Place the following divisions to de-termine the exact value of their quotients. a 129 ÷ 4 b 88.48 ÷ 7 E.2854 Place the following divisions to de-termine the exact value of their quotients. A 60.08 ÷ 8 b 213.9 ÷ 6 E.10428 Pose the following divisions to de-termine the exact value of their quotients : a 142.3 ÷ 4 b 606.9 ÷ 7 E.11059 Pose the following divisions to de-termine the exact value of their quotients : a 705 ÷ 6 b 337 ÷ 8 E.1579 1 Construct the multiplication table for the integer 14. (from 14 to 140) 2 Place the following divisions to determine the exact value of their quotients. a 732.2 ÷ 14 b 436.8 ÷ 14 E.9946 Place the following divisions to de-termine the exact value of their quotients. a 17457 ÷ 12 b 945 ÷ 12 E.9945 Place the following divisions to de-termine the exact value of their quotients. a 2046 ÷ 12 b 843 ÷ 12 E.2374 Place the following divisions to de-termine the exact value of their quotients. A 567 ÷ 14 b 531 ÷ 18 E.6652 Place the following divisions to de-termine the exact value of their quotients. A 8.16 ÷ 12 b 84.56 ÷ 7 E.10512 The following decimal divisions have been performed, but some information has been erased. Only remainders, quotients and factors are still displayed : a . . . 3 4 13.74 b . . . 1 6 15.2 Determine the dividend of each of these divisions. 9. Problems with exact decimal divisions https://chingmath.fr chapExoCorrec/9965 sacados/9965 chapExoCorrec/3389 sacados/3389 50012 3301 191 79105 9785 chapExoCorrec/2375 sacados/2375 chapExoCorrec/3871 sacados/3871 chapExoCorrec/2854 sacados/2854 chapExoCorrec/10428 sacados/10428 chapExoCorrec/11059 sacados/11059 chapExoCorrec/1579 sacados/1579 chapExoCorrec/9946 sacados/9946 chapExoCorrec/9945 sacados/9945 chapExoCorrec/2374 sacados/2374 chapExoCorrec/6652 sacados/6652 chapExoCorrec/10512 sacados/10512
E.1593 1 On division-quotient: A school has 892 pupils. The school takes all its students on a field trip. Each rented bus has 42 seats. How many buses will be full? How many free seats will be left on the last bus? 2 On division-sharing: Three sisters go to the market and buy a silk fabric 11.4 meters long. They divide the purchase into three equal parts. How much will each sister’s fabric measure? E.1602 John rides his bike 5 times a week to school. At the beginning of the week his meter reads 202 km while at the end of the same week it reads 228.5 km . Calculate the distance from John’s house to his school. E.9975 1 On the division-quotient: for Raphael’s birthday, his mother buys bottles of Champougny at the market and champagne flutes to serve the guests : A bottle of Champougny has a capacity of 1.65 ‘ . Each flute has a capacity of 15 c‘ (0.15 ‘ ) . a How many people will Raphael’s mother be able to serve with one bottle? b Knowing that there will be 30 guests, how many bot-tles will she need to provide? 2 On the division-share: At the end of a meal at a restaurant, eight friends find themselves paying a bill of 66.80 e . Dividing the price of the meal equally, help them figure out how much each of them should pay. E.1603 1 Claire bought a large 1.6 kilogram chicken at 36 pesos. What is the price per kilogram of chicken? 2 At the same merchant, how much would a 2.2 kilogram chicken cost? E.6651 Hadéja wants to know the length of her bedroom. To do this, she needs the following information : She takes 13 steps to cover the length of her room. Her width is exactly 5.2 m and she travels it taking ex-actly 8 steps. We’ll assume that the steps taken by Hadéja are all the same length. Determine the length of Hadéja’s chamber. (we’ll leave the reasoning steps as well as the associated posed calculations) All traces of research or initiative will be taken into account in the assessment. E.10419 Consider the figure below composed of a regular pentagon on which two squares have been leaned : Knowing that the perimeter of the shaded figure has measure 21.6 cm , determine the measure of one side of the pentagon. E.10420 The figure below is composed of a regular hexagon and two squares of the same length. Knowing that the shaded figure has a perimeter of 56.5 cm , determine the measurement of one side. E.10476 Consider the figure below : where : the rectangle has a length measuring twice its width. two regular hexagons whose sides measure the width of the rectangle. Knowing that the perimeter of the shaded figure has measure 50.4 cm , determine the length of each side of the hexagon. 10. First steps towards equations E.1340 In Paris in 2005 , Alain bought 14 metro tickets for 19.6 e . We note x the price of a ticket. 1 Which equality is verified by x among? a 19.6 + x = 14 b 14 + x = 19.6 c 14 × x = 19.6 d 19.6 × x = 14 2 Determine the value of x . E.1605 In this exercise, ˇ x ı represents a number which checks the equality below : (6 × x ) + 12 = 27 What is the value of this number? https://chingmath.fr chapExoCorrec/1593 sacados/1593 chapExoCorrec/1602 sacados/1602 chapExoCorrec/9975 sacados/9975 chapExoCorrec/1603 sacados/1603 chapExoCorrec/6651 sacados/6651 chapExoCorrec/10419 sacados/10419 chapExoCorrec/10420 sacados/10420 chapExoCorrec/10476 sacados/10476 chapExoCorrec/1340 sacados/1340 chapExoCorrec/1605 sacados/1605
6,266,276,286,296,36,31 E.9974 nelise went to the market to buy three kilos of orange and a salad for a total of 5.7 e . The salad cost 1.2 e . We note x the price of a kilo of oranges. 1 What is the equality verified by x among? a 1.2 × x + 3 = 5.7 b 3 × x + 1.2 = 5.7 c 5.7 × x + 1.2 = 3 d 1.2 × x + 5.7 = 3 2 Determine the value of x . 11. Rounded decimal division E.11093 1 Divide 227 by 7 to obtain the quotient to the thousandth. 2 Give the frame to the nearest hundredth of this quotient. 3 Give the quotient of 227 by 7 , rounded to the nearest hundredth. E.11094 Perform the following divisions to obtain the quotients below, rounded to two decimal places : a 105.5 ÷ 7 b 94 ÷ 3 E.1583 Perform the following divisions to obtain the values of their quotients, rounded to the nearest tenth : A 146 ÷ 7 b 158 ÷ 7 E.11061 Place the following divisions in or-der to obtain the value, rounded to the nearest thousandth, of their quotients : a 148 ÷ 7 b 51.25 ÷ 6 E.9949 Form the following divisions and give the values, rounded to the nearest hundredth, of their quotients : a 124 ÷ 6 b 0.152 ÷ 8 E.10429 1 Complete the table below to obtain the multiplication table for 13 : × 13 0 4 8 1 5 9 2 6 10 3 7 2 Determine the value rounded to the nearest hundredth of 140 ÷ 13 . E.11060 1 Complete the table below to obtain the multiplication table for 14 : × 14 0 4 8 1 5 9 2 6 10 3 7 2 Determine the value rounded to the nearest thousandth of 524 ÷ 14 . E.1599 Perform the following divisions to obtain the value rounded to two decimal places of their quo-tients : a 32.7 ÷ 16 b 0.2464 ÷ 16 E.9950 Place the following divisions in order to obtain their quotients rounded to the hundredth : A 927 ÷ 13 b 467 ÷ 13 E.11095 Place the divisions to obtain the quotients below, rounded to the nearest hundredth : a 128.1 ÷ 16 b 80.97 ÷ 16 E.11140 Perform the following divisions to obtain the value rounded to two decimal places of their quo-tients : a 8.44 ÷ 21 b 53.1 ÷ 21 E.10401 We wish to perform the approxi-mate division of 44 by 7 . 1 Copy and complete the division shown opposite : 2 a Complete the blanks below to frame the division of 44 by 7 to the nearest hundredth : : : : < 44 ÷ 7 <: : : 4 4 - . . . . - . . . . - . . . . - . . . 7 . , . . . b Place the point A of abscissa A 44 ÷ 7 on the scaled line below : c Give the rounded value of the decimal division of 44 by 7 to the nearest hundredth. https://chingmath.fr chapExoCorrec/9974 sacados/9974 chapExoCorrec/11093 sacados/11093 chapExoCorrec/11094 sacados/11094 chapExoCorrec/1583 sacados/1583 chapExoCorrec/11061 sacados/11061 chapExoCorrec/9949 sacados/9949 chapExoCorrec/10429 sacados/10429 chapExoCorrec/11060 sacados/11060 chapExoCorrec/1599 sacados/1599 chapExoCorrec/9950 sacados/9950 chapExoCorrec/11095 sacados/11095 chapExoCorrec/11140 sacados/11140 chapExoCorrec/10401 sacados/10401 6,266,276,286,296,36,31
100mh Profondeur totale400cmHauteurtotale252cmPalier50cm Côté forméde3carreauxCôté forméde4carreauxCôté forméde5carreaux 12. Problems E.6377 A shopkeeper sells a box of water for 0.50 e while a pack of 6 bottles for 2.73 What is the cost price of a bottle when it was purchased from a pack? E.1535 The supermarkets Croisemment of-fer on its promotional magazine a bag of 120 g dry sausage from Auvergne whose price is unfortunately not indicated. Only the price of this sausage per kilogram is indicated : 19.08 e = kg 1 a What is the price of 12 kg of sausage? b How many bags of 120 g can be designed with 12 kg of sausage? c Deduce the price of a bag of sausage? 2 Justify, without calculation, that the price of a bag of sausage can also be obtained by calculation: 0.12 × 19.08 E.11062 Adrien buys 6 kilograms of rice for 8.04 e . Iris would like to buy 3.5 kilograms of the same rice. How much will this cost? E.6613 A farmers’ association buys 15 kilograms of fertilizer at 7.34 e per kilogram. Then, they share this fertilizer among the 10 member of the association. How much do each member have to contribute to make this purchase? 13. Open problems E.5762 To build a complete shelf, a car-penter needs the following ma-terials: 4 long boards ; 6 short boards ; 12 small squares ; 2 large brackets ; 14 screws. The joiner has a stock of 26 long boards, 33 short boards, 200 small squares, 20 large squares and 510 screws. How many complete shelves can the carpenter build? E.6371 An alley is 100 m long. We wish to plant 16 trees whose width is 4 m regularly spaced along the alley: Determine the space ( h ) separating two trees. E.5761 Below is given a profile view of a staircase with 14 steps. A carpenter needs to cover these steps with wood ; to do this, he needs to know the length formed by the steps : this length is represented on the drawing by the broken line connecting the two points. Give the measure of this length. E.5763 In a grocery store, the shopkeeper wants to sell the remaining 125 packs of ˇ choco-bon ı as soon as possible. To do this, he creates as many batches as possible, each con-taining 7 packets of cookies. A promotion is made on these batches : the 7 e packages of the batch are free. The other packages will be sold individually. Knowing that a pack of ˇ choco-bon ı is sold at the price of 1.2 e , determine the sum obtained by the sale of these 125 packs. E.6357 We wish to construct a frame using small tiles. Here is a representation of three such frames : 1 How many tiles to build a frame : a where each side is made of 6 tiles? b each side of which is formed of 7 tiles? 2 What is the largest frame that can be constructed with 100 tiles? https://chingmath.fr chapExoCorrec/6377 sacados/6377 chapExoCorrec/1535 sacados/1535 chapExoCorrec/11062 sacados/11062 chapExoCorrec/6613 sacados/6613 chapExoCorrec/5762 sacados/5762 Extrait de Pisa chapExoCorrec/6371 sacados/6371 100mh chapExoCorrec/5761 sacados/5761 Profondeur totale400cmHauteurtotale252cmPalier50cm chapExoCorrec/5763 sacados/5763 chapExoCorrec/6357 sacados/6357 Côté forméde3carreauxCôté forméde4carreauxCôté forméde5carreaux