Grade 8 / Fractions: multiplication and division 108 exercises (100% corrected)

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qb7a ChingQuizz : 14 exercises available for Quizz assessment : 1. Multiplications and simplifications E.1817 Rule: To multiply two fractions together, we multiply the numer-ators together and the denominators together. For a , b , c , d four numbers, with b =0 and d =0 , we have : a b × c d = a × c b × d 1 For each row in the following table, a calculation is given and three results are proposed, but only one is correct. Determine the correct proposal: Prop.1 Prop. 2 Prop. 3 a 2 × 4 × 8 2 1 × 2 × 4 1 × 4 × 4 4 × 8 b 2 × 3 × 6 3 2 × 3 × 1 2 × 3 × 2 2 × 1 × 1 c 2 × 2 × 2 2 1 × 1 × 1 2 × 2 8 2 Complete the following sentence : To divide a product by a number, divide only one of its . . . . . . . . . 3 To simplify the fraction A = 10 × 9 15 × 22 , the following suc-cessive simplifications are performed : A = 10 × 9 15 × 22 = 10 × 9 ÷ : : : 15 × 22 ÷ : : : = 5 × 9 15 × 11 = 5 × 9 ÷ : : : 15 × 11 ÷ : : : = 1 × 9 3 × 11 = 1 × 9 ÷ : : : 3 × 11 ÷ : : : = 1 × 3 1 × 11 = 3 11 Write the missing steps. 4 Simplify, step by step, the fractions below to obtain their reduced forms : a 4 × 21 8 × 7 b 5 × 14 × 9 25 × 7 × 3 c 10 × 18 27 × 15 E.6187 Simplify each of the following frac-tions : a 12 × 5 4 × 7 b 15 × 11 3 × 4 c 7 × 3 12 × 5 E.1820 Carry out the simplifications nec-essary to obtain, by simple mental calculations, the reduced form of each of these fractions : A 8 × 12 × 15 21 × 16 × 25 = 6 35 b 6 × 15 × 28 21 × 12 × 9 = 10 9 c 45 × 12 × 18 27 × 36 × 14 = 5 7 d 5 × 24 × 35 75 × 6 = 28 3 E.8723 Simplify to the maximum the follow-ing fractions : a 5 × 21 14 × 20 b 15 × 12 9 × 25 c 24 × 28 18 × 7 E.1041 Calculate and give the result in sim-plified fractions : a 9 7 × 14 15 b 7 8 × 3 14 × 4 9 c 17 81 × 9 8 × 7 34 × 64 70 E.1042 Give the simplified form of the fol-lowing fractions : a 5 × 16 12 × 20 b 9 × 21 × 10 27 × 10 × 7 c 9 × 12 8 × 6 × 18 E.8722 Simplify each of the following frac-tions : a 3 × 2 × 5 2 × 5 × 7 b 5 × 12 × 7 7 × 12 × 3 c 3 × 4 4 × 5 × 3 E.1055 Simplify the following fractions as much as possible : a 99 × 25 22 × 125 b 9 × 12 × 10 27 × 10 × 6 c 3 × 6 × 8 16 × 12 × 18 2. Addition, subtraction and multiplication E.6220 Methods: To add two fractions, they must have the same denom-inator. To multiply two fractions, multiply the numerators to-gether and multiply the denominators together. But first, try to simplify the factors. The video opposite will show you how to perform addition and multiplication calculations. https://chingmath.fr chapExoCorrec/1817 sacados/1817 chapExoCorrec/6187 sacados/6187 chapExoCorrec/1820 sacados/1820 chapExoCorrec/8723 sacados/8723 chapExoCorrec/1041 sacados/1041 chapExoCorrec/1042 sacados/1042 chapExoCorrec/8722 sacados/8722 chapExoCorrec/1055 sacados/1055 chapExoCorrec/6220 sacados/6220 qb7a
Perform the following calculations and give the result as a simplified fraction : a 5 3 + 5 6 b 5 7 − 1 21 c 5 2 × 4 15 d 1 + 1 2 e 5 − 4 3 f 9 2 × 4 6 E.1645 Perform the following calculations and give the result as fractions with denominators 10, 100, 1 000 etc. . . : a 3 100 × 21 10 b 45 1 000 + 3 10 c 79 100 + 1 100 E.1378 Perform the following calculations and, if possible, simplify the following fractions : a 5 2 × 9 3 b 3 7 + 1 14 c 5 2 − 3 4 d 3 4 × 5 E.6525 Perform the following calculations and give the results in simplified form : a 5 7 + 2 21 b 14 25 × 15 21 c 3 16 + 5 4 d 1 9 × 81 2 e 43 18 − 20 9 f 65 4 × 12 15 E.1355 Perform the following calculations and give the results in simplified form : a 3 8 + 3 2 b 2 − 1 3 c 32 9 × 3 8 d 1 3 × 15 2 E.1648 Perform the following calculations and give the answers as simplified fractions : a 1 3 + 4 15 b 3 5 × 15 4 c 944 3 × 2 944 E.6535 Perform the following calculations, indicating the intermediate steps and giving the result in sim-plified form : a 7 3 − 1 6 b 14 5 × 25 21 c 3 4 + 5 8 d 8 6 × 27 20 E.1649 Perform the following calculations and give the result in as simplified a form as possible : A 5 4 × 6 15 b 1 10 − 1 14 c 3 × 7 9 E.6536 Copy and complete the missing num-bers : a 1 3 + : : : 6 = 7 6 b 5 7 − : : : 14 = 9 14 c 5 6 × 2 : : : = 5 9 d : : : 7 × 14 5 = 6 5 E.1356 Copy the equalities, completing with the signs + , − , × . a 1 2 : : : : : : 1 = 3 2 b 3 2 : : : : : : 5 7 = 15 14 c 5 2 : : : : : : 1 12 = 29 12 d 3 7 : : : : : : 8 14 = 1 e 1 3 : : : : : : 1 4 = 1 12 f 3 4 : : : : : : 2 9 = 1 6 E.8727 Perform the operations below and give the result as simplified fractions : a 1 6 − 1 10 b 6 35 × 14 9 c 5 6 + 5 14 d 24 9 × 55 88 3. Priority of operations without relative numbers E.5651 We consider the two calculation pro-grams below : Calculation A Take the number 2 Add to it 2 9 Multiply it by 3 2 Make the difference of 40 3 by the previous result. Calculation B Take the number 5 2 Multiply it by 3 4 Subtract it 1 1 Without justification, give the result of these two calcu-lation programs. 2 Write each of these calculation programs in a single ex-pression. E.8648 Perform the calculations below, giv-ing the result as a simplified fraction : a 1 3 − 1 6 × 5 2 b 4 − 2 3 × 3 2 × 4 3 c 4 5 − 1 10 × 3 E.1371 Perform the following calculations without a calculator and give the results as irreducible frac-tions : a 3 4 − 1 16 × 16 5 b 1 4 + 1 3 × 2+ 1 6 c 1 3 + 1 12 × 24 5 E.8739 Perform the following calculations taking into account the priorities of the operations and giving the result as a simplified fraction : a 2 3 × 9 16 − 1 16 b 7 5 × 3 2 − 3 2 c 3 5 + 1 5 × 2 3 E.8749 Perform the following operations and give the results in simplified form : a 2 + 12 15 × 10 3 b 15 12 × 6 10 − 1 8 c 8 3 − 3 8 × 10 6 E.1361 Perform the following calculations and, if possible, simplify the following fractions : a 1 2 + 3 × 5 2 b 1 3 × 2 4 + 1 d 1 6 − 1 12 × 2 E.6221 Perform the following calculations, giving the result as a simplified fraction : a 5 3 − 2 3 1 4 + 1 2 b 5 2 − 1 × 10 3 − 7 3 https://chingmath.fr chapExoCorrec/1645 sacados/1645 chapExoCorrec/1378 sacados/1378 chapExoCorrec/6525 sacados/6525 chapExoCorrec/1355 sacados/1355 chapExoCorrec/1648 sacados/1648 chapExoCorrec/6535 sacados/6535 chapExoCorrec/1649 sacados/1649 chapExoCorrec/6536 sacados/6536 chapExoCorrec/1356 sacados/1356 chapExoCorrec/8727 sacados/8727 chapExoCorrec/5651 sacados/5651 chapExoCorrec/8648 sacados/8648 chapExoCorrec/1371 sacados/1371 chapExoCorrec/8739 sacados/8739 chapExoCorrec/8749 sacados/8749 chapExoCorrec/1361 sacados/1361 chapExoCorrec/6221 sacados/6221
ABCDEFG761323 E.6217 Perform the following operations and give the results in simplified form : a 5 6 + 1 2 + 3 4 b 1 7 + 14 3 × 6 21 c 5 7 − 8 14 × 35 6 E.8740 Perform the calculations below and give the results in simplified form : a 3 − 5 3 × 5 2 + 2 b 2 3 + 1 × 1 2 + 1 4 E.1364 Give results as simplified fractions. a 8 × 9 12 + 12 8 × 9 b 6 × 6 4 × 3 − 64 − 51 8 + 4 E.8741 Perform the calculations below and give the results in simplified form : a 5 + 3 12 − 7 × 9 − 2 9 + 5 b 7 2 − 9 4 × 3 4 + 2 4. Priority of operations with relative numbers E.8744 Perform the following calculations and give the results in simplified fraction form : a 2 12 − 3 15 × 20 6 b 3 20 − 3 15 × − 5 9 e 1 6 − 5 12 − 2 3 E.8742 Give the results of the calculations below in simplified form : a 1 − − 15 7 × 14 25 b 4 15 − 24 72 × 30 20 c 3 4 × − 8 12 + 3 4 E.4762 Perform the following calculations and give the results in simplified form : a 5 2 − 24 15 × 25 8 b − 49 40 × 24 14 − 2 c 15 14 × 6 15 − 5 12 E.1037 Give the results of the calculations below in simplified form : a 3 × 5 4 − 15 14 − 3 8 b − 2 + 1 2 × 1 2 − 5 4 E.6218 Perform the following calculations and give the result in simplified form : a − 12 20 × − 15 8 + 16 6 × − 27 18 b 4 3 × − 9 7 + 1 2 × 8 3 E.1823 Give the results of the calculations below in simplified form : a 3 + − 2 3 × 3 − 4 × 4 5 × 5 − 6 b − 4 9 × 27 12 + 16 8 × − 5 4 5. Problems and multiplications of fractions E.6539 The following calculation program is considered : Multiply the chosen number by 1 3 ; Add 1 to the previous product ; Multiply the previous sum by 5 2 . 1 When the number 5 2 is chosen, what number is returned by this calculation program? 2 Translate the calculation program performed in question 1 into a single expression. E.6538 Consider the figure below composed of a rectangle ABCD and a square BEFG : The following measurements are given : AB = 7 6 ; AD = 1 3 ; EF = 2 3 1 Without justification, give the total area of this figure as a simplified fraction. 2 Write an expression with the data in the statement that yields this area. 6. Pythagorean theorem and multiplication of fractions E.8753 1 a Perform the following calculation and give the result as a simplified fraction : 2 × 2 + 8 3 × 8 3 b Give the unique fraction a b , with a> 0 and b> 0 such that : a b 2 = 100 9 2 Consider the triangle ABC right-angled C shown below and verifying: AC =2 m ; BC = 8 3 m https://chingmath.fr chapExoCorrec/6217 sacados/6217 chapExoCorrec/8740 sacados/8740 chapExoCorrec/1364 sacados/1364 chapExoCorrec/8741 sacados/8741 chapExoCorrec/8744 sacados/8744 chapExoCorrec/8742 sacados/8742 chapExoCorrec/4762 sacados/4762 chapExoCorrec/1037 sacados/1037 chapExoCorrec/6218 sacados/6218 chapExoCorrec/1823 sacados/1823 chapExoCorrec/6539 sacados/6539 chapExoCorrec/6538 sacados/6538 ABCDEFG761323 chapExoCorrec/8753 sacados/8753
ABC2m83m ABC56m12m ABC256m52m ABC53m54m 83cm2cm103cmABC 34cm1cm54cmABC 43cm83cm3cmABC Determine the measurement of the [ AB ] side. E.8752 1 a Perform the following calculation and give the result as a simplified fraction : 5 6 × 5 6 − 1 2 × 1 2 b Give the unique fraction a b , with a> 0 and b> 0 , veri-fying : a b 2 = 4 9 2 Consider the triangle ABC right-angled C shown below and verifying: AB = 5 6 m ; BC = 1 2 m Determine the measurement of the [ AC ] side. E.8751 Consider the triangle ABC right- angled C shown below and verifying: AB = 25 6 m ; BC = 5 2 m Determine the measurement of the [ AC ] side. E.8750 Consider the triangle ABC right-angled C shown below and verifying: AC = 5 3 m ; BC = 5 4 m Determine the measurement of the [ AB ] side. 7. Pythagorean theorem and fraction multiplication E.4757 Consider the triangle ABC shown below : Show that the triangle ABC is right-angled A . E.4758 Consider the triangle ABC shown below : Show that the triangle ABC is right-angled C . E.4759 Consider the triangle ABC shown opposite : Show that the triangle ABC is not a right-angled triangle. 8. Inverses https://chingmath.fr ABC2m83m chapExoCorrec/8752 sacados/8752 ABC56m12m chapExoCorrec/8751 sacados/8751 ABC256m52m chapExoCorrec/8750 sacados/8750 ABC53m54m chapExoCorrec/4757 sacados/4757 83cm2cm103cmABC chapExoCorrec/4758 sacados/4758 34cm1cm54cmABC chapExoCorrec/4759 sacados/4759 43cm83cm3cmABC
×2÷2?53×7÷7?94 ×12÷12?35×-35÷-35?74 E.1832 1 Complete the dotted lines below with a number in frac-tional writing to verify the equalities: a 4 × : : : = 5 b 7 × : : : = 3 c 3 × : : : = 1 2 For each line, determine, among the four proposals, the one that will give with the proposed number a product equal to 1 Prop. 1 Prop. 2 Prop. 3 Prop. 4 a 2 3 2 3 5 2 3 2 3 b 3 15 5 1 5 2 5 15 2 c 2 3 1.5 0.66 3 4 2 3 d 2 3 + 1 4 7 3 3 2 + 4 1 12 11 1.1 Definition: Two numbers are said to be opposés if the sum of these two numbers is 0 . Example: 5 and − 5 because 5 + ( − 5) = 0 Two numbers are said to be inverses of each other if their product is equal to 1. Example: 3 × 1 3 = 1 ; 5 4 × 4 5 = 1 3 Determine the inverses of the following numbers : a 3 b − 3 c 0.25 d 2 7 e − 11 3 f 1 + 0.5 E.4701 Note: if a is non-zero, the inverse of the quotient a b is b a If possible, give the decimal form of the inverse of the follow-ing numbers : a 1 2 b 5 4 c 2 7 d 3 5 e − 1 f 1.5 g 0.2 h 0.75 j 0.1 k 3.25 9. Divisions E.1833 1 The following MCQ offers you a product to complete, with only one of the proposed answers, so as to verify equality: Prop. 1 Prop. 2 Prop. 3 a 2 × ? = 5 3 10 6 10 3 5 6 b 7 × ? = 9 4 9 28 2 4 63 4 c 1 2 × ? = 3 5 6 5 3 10 6 10 d − 3 5 × ? = 7 4 35 12 − 35 12 − 21 20 2 Complete the following diagrams using the previous ques-tion : 3 Using the diagrams above, determine the simplified form of each of the following quotients : a 5 3 2 b 9 4 7 c 3 5 1 2 d 7 4 − 3 5 E.1047 Proposition: For a divide a fraction by a number, multiply that frac-tion by the inverse of that number: a b c = a b × 1 c Examples: 5 4 3 = 5 4 × 1 3 = 5 × 1 4 × 3 = 5 12 5 4 3 = 5 × 3 4 = 15 4 Perform the following calculations and give the result as irre-ducible fractions : a 3 4 7 b 3 2 3 c 2 3 5 3 E.1048 Perform the following calculations and give the results as simplified fractions as possible : a 8 3 ÷ 12 3 b 18 3 ÷ 9 c 3 ÷ 4 6 https://chingmath.fr chapExoCorrec/1832 sacados/1832 chapExoCorrec/4701 sacados/4701 chapExoCorrec/1833 sacados/1833 ×2÷2?53×7÷7?94 ×12÷12?35×-35÷-35?74 chapExoCorrec/1047 sacados/1047 chapExoCorrec/1048 sacados/1048
5m210=3m40=7m25m AB1=33=2C E.1058 Perform the following calculations and give the results as simplified fractions : a 7 3 ÷ 14 3 b 15 3 ÷ 5 c 15 6 ÷ 100 18 E.8943 Perform the following calculations and give the result as irreducible fractions : a 2 3 ÷ 7 4 b 8 5 ÷ 3 c 2 5 ÷ 4 15 E.8947 Perform the following calculations and give the results as maximally simplified fractions : a 4 12 20 3 b 14 26 28 39 c 25 16 15 E.4763 Perform the following operations : a 3 6 5 b − 5 9 15 c − 5 9 27 − 15 E.8948 For each question, determine the in-teger x verifying the equality: a 16 x 5 = 20 3 b 15 8 x = 3 40 c x 14 9 4 = 10 21 E.8773 For each of the rectangles below, their length and area measurements are given : Determine the measure of the width of these two rectangles. 10. Priority of operations with the division E.1049 Perform the calculations below and give the results as simplified fractions : a 5 3 + 4 3 ÷ 3 5 − 3 7 b 14 5 ÷ 8 5 + 4 E.1051 Perform the following calculations and give the results as simplified fractions : a − 2.5 26 + 2 13 ÷ 8 13 a 1 3 − 2 ÷ 4 15 − 13 12 E.8769 Perform the following calculations, giving the results as simplified fractions : a 2 + 4 ÷ − 4 3 b 3 + 2 3 ÷ 1 3 E.1846 Perform the following calculations and give the results as simplified fractions : a 3 − 1 4 − 3 + 1 8 b 5 6 − 1 3 2 7 + 3 14 c 1 2 + 2 1 3 + 4 3 E.8766 Perform the following calculations and give the results as simplified fractions : a 2 + 1 3 − 3 + 1 3 b 3 − 1 4 − 3 + 1 8 E.1053 Perform the calculations below and give the results as a simplified fraction : a − 3 × 5 4 15 6 + 5 1 2 b 5 2 + 3 8 15 12 E.5652 We consider the two calculation pro-grams below : Calculation A Take the number 4 5 Subtract it 2 3 Divide it by 2 5 Calculation B Take 1 3 Divide it by 2 7 Subtract from it 1 Multiply it by 5 2 1 Without justification, give the result of each of these two calculation programs. 2 Translate each of the calculation programs into a single expression. E.8775 Consider the graduated line below where the graduations are regular and the points A 1 3 and B 3 2 are represented : Determine the abscissa of the point C . E.8767 Perform the following calculations and give the results as simplified fractions : a 1 1 + 1 1 + 1 2 b 1 + 1 1 + 1 1 + 1 1 + 1 2 https://chingmath.fr chapExoCorrec/1058 sacados/1058 chapExoCorrec/8943 sacados/8943 chapExoCorrec/8947 sacados/8947 chapExoCorrec/4763 sacados/4763 chapExoCorrec/8948 sacados/8948 chapExoCorrec/8773 sacados/8773 5m210=3m40=7m25m chapExoCorrec/1049 sacados/1049 chapExoCorrec/1051 sacados/1051 chapExoCorrec/8769 sacados/8769 chapExoCorrec/1846 sacados/1846 chapExoCorrec/8766 sacados/8766 chapExoCorrec/1053 sacados/1053 chapExoCorrec/5652 sacados/5652 chapExoCorrec/8775 sacados/8775 AB1=33=2C chapExoCorrec/8767 sacados/8767
11. Addition, subtraction, products E.1357 Perform the calculations and give the results as simplified fraction : a 5 2 + 13 4 b 3 + 5 4 c 10 2 × 6 5 E.1380 Calculate the following operations and give the result as a simplified fraction : a 2 5 + 3 b 2 7 + 3 14 c 18 5 × 7 6 E.8743 Perform the following calculations and give their results in simplified form : a 5 3 − 7 4 b 1 2 + 1 − 4 12. Priorities for operations without relative numbers E.6540 Perform the calculations below, leav-ing the intermediate calculations and giving the result as a simplified fraction : a 7 3 − 5 6 × 2 3 b 5 2 − 1 4 × 7 3 c 4 5 − 1 10 × 3 E.1375 Perform the following calculations and give the results in simplified form : a 3 7 + 5 14 b 33 4 − 2 × 5 2 c 3 7 × 14 6 + 1 2 E.1368 Perform operations. Be careful to respect the priority of operations : a 5 3 × 2 − 2 b 3 × 5 6 + 1 3 c 5 3 − 2 5 × 15 6 E.1381 Calculate the following operations and give the result as a simplified fraction : a 0.5 3 + 4 5 × 2 3 b 2 3 + 1 6 × 12 5 c 3 + 2 5 × 3 4 E.6526 Perform the following calculations, taking into account the order of operations and giving the result as a simplified fraction : a 3 7 + 2 3 × 5 14 b 7 4 − 3 2 × 8 3 c 1 + 5 3 × 5 2 − 3 4 E.1379 1 Calculate and give the result as irreducible fractions : a 3 × 1 2 + 3 8 b 2 5 × 2 3 + 29 30 c 7 4 − 1 2 × 1 7 + 3 7 2 Perform the following calculations using distributivity. The results will be given in simplified form : a 7 8 × 14 9 + 7 8 × 4 9 b 12 × 12 3 − 5 4 E.1382 Calculate and give the result in simpli-fied form : 7 4 − 1 2 × 1 7 + 3 7 E.1050 Perform the following calculations : a 2 3 × 5 − 5 9 b 5 12 + 1 3 × 9 4 E.1046 Perform the following calculations and give the result as fractions : a 3 2 − 15 8 × 12 30 b 1 2 + 2 3 × 5 4 − 1 4 c 3 − 3 4 − 1 2 13. Quotient E.280 Perform the following calculations and give the result as a simplified fraction : a 1 1 + 1 1 + 1 1 + 1 6 b 1 2 − 5 6 2 1 9 + 1 12 E.1781 Perform the following calculations and give the various results in simplified fraction form : a 1 1 + 1 2 − 1 3 + 2 7 b 2 − 1 3 2 7 4 − 6 2 18 https://chingmath.fr chapExoCorrec/1357 sacados/1357 chapExoCorrec/1380 sacados/1380 chapExoCorrec/8743 sacados/8743 chapExoCorrec/6540 sacados/6540 chapExoCorrec/1375 sacados/1375 chapExoCorrec/1368 sacados/1368 chapExoCorrec/1381 sacados/1381 chapExoCorrec/6526 sacados/6526 chapExoCorrec/1379 sacados/1379 chapExoCorrec/1382 sacados/1382 chapExoCorrec/1050 sacados/1050 chapExoCorrec/1046 sacados/1046 chapExoCorrec/280 sacados/280 chapExoCorrec/1781 sacados/1781
73×92(7×÷(3×7×93×2(7÷×(9÷87×134(8÷×(1÷8×137×4(8×÷(7× E.274 Perform the following calculations and give the result in simplified fraction form : a 1 1 6 + 4 3 3 + 5 2 + 2 7 b 1 4 − 5 6 2 5 9 + 1 E.8772 Perform the following calculations and give the results as simplified fractions : a − 2.5 26 + 2 13 ÷ 8 13 b − 2.5 7 + 2 14 ÷ 8 7 E.8770 Perform the following calculations and give the results as simplified fractions : a 1 + 1 2 1 − 1 2 b 2 + 5 3 2 − 5 3 c 1 4 + 5 2 × 3 45 5 6 + 5 4 E.4764 Perform the following calculations and give the results as simplified fractions : a 3 + 2 5 3 − 4 10 b 3 2 − 15 8 × 6 27 5 12 + 66 12 × 4 33 14. Operations on fractions E.10498 Perform the following calculations with-out a calculator and give the results as irreducible fractions : a 3 5 + 1 5 × 10 6 b 2 3 + 5 3 × 6 14 c 2 7 + 1 7 × 14 3 E.10499 Perform the following operations : a 3 10 + 2 5 × 7 6 b 5 3 × 3 2 + 5 12 c 3 4 + 5 6 × 3 2 E.10500 Perform the following calculations : a 5 7 × 5 4 − 5 14 b 8 9 × 5 2 − 7 6 c 3 5 + 1 5 × 2 3 15. Us-math: multiplication E.9645 With American notations: when multiplying a ˇ mixed fractions ı with a ˇ proper fractions ı, distributivity can be used : 8 1 2 × 1 5 = 8 + 1 2 × 1 5 = 8 × 1 5 + 1 2 × 1 5 = 8 5 + 1 × 1 2 × 5 = 8 5 + 1 10 = 8 5 + 1 10 = 16 10 + 1 10 = 16 + 1 10 = 17 10 = 10 10 + 7 10 = 1 + 7 10 = 1 7 10 Calculate the following products and express the results as a ˇ mixed fractions ı : a 5 3 5 × 1 4 b 2 3 × 7 3 8 c 5 3 7 × 1 4 d 7 9 × 4 1 5 E.9644 With American notations: several techniques are used to multiply ˇ mixed fractions ı. Here’s one of them, it involves going through the ˇ improper fractions ı : 2 1 2 × 5 1 3 = 2 + 1 2 5 + 1 3 = 4 2 + 1 2 15 3 + 1 3 = 5 2 × 16 3 = 5 × 16 6 = 5 × 8 3 = 40 3 = 39 3 + 1 3 = 13 + 1 3 = 13 1 3 Calculate the following products and express in the form of ˇ mixed fractions ı simplified : a 3 1 5 × 3 2 3 b 1 2 3 × 2 5 7 c 4 1 3 × 1 1 4 d 1 2 8 × 1 1 7 16. Multiplications E.10110 1 Connect each calculation with its corresponding online operation: 2 Using your calculator, compare each of the calculation pairs : https://chingmath.fr chapExoCorrec/274 sacados/274 chapExoCorrec/8772 sacados/8772 chapExoCorrec/8770 sacados/8770 chapExoCorrec/4764 sacados/4764 chapExoCorrec/10498 sacados/10498 chapExoCorrec/10499 sacados/10499 chapExoCorrec/10500 sacados/10500 chapExoCorrec/9645 sacados/9645 chapExoCorrec/9644 sacados/9644 chapExoCorrec/10110 sacados/10110 73×92(7×÷(3×7×93×2(7÷×(9÷87×134(8÷×(1÷8×137×4(8×÷(7×
69m116m 615×532112×2768×591223512 ABCD12m35m 7 3 × 9 2 and 7 × 9 3 × 2 ; 8 7 × 13 4 and 8 × 13 7 × 4 E.1376 Consider the rectangle below : 1 a What does the number 116 × 69 represent for this rectangle? b For this figure, what does the number 12 correspond to? c Color in blue a part of this rectangle with an area of 116 × 69 4 × 3 m 2 . 2 a Locate two segments on this figure with lengths 116 4 m and 69 3 m respectively. b Color in red a rectangle having 116 4 m and 69 3 m as the measure of its sides. 3 What can you say about the fractions 116 4 × 69 3 and 116 × 69 4 × 3 E.1642 Perform the following calculations : a 6 4 × 2 3 b 32 40 × 120 E.1367 Relate each calculation to its own result : E.6537 Consider the rectangle below with dimensions : AB = 32 m ; AD = 15 m Establish that the hatched portion has area 20 m 2 . Any trace of research, even if incomplete, will be con-sidered in the scoring 17. Share E.8789 Perform the calculations, detailing the steps and giving the results as simplified fractions : a 5 24 + 1 8 b 4 15 − 7 6 c 1 2 × 5 3 − 2 3 d 1 4 − 5 3 × 6 5 E.8790 Perform the following calculations, de-tailing your steps and giving the answer as a simplified frac-tion : a 5 3 − 8 6 ÷ 5 6 b 11 1 3 × 5 − 1 5 E.8834 Perform the following calculations and give the result as a simplified fraction : a 2 7 − 8 21 b 3 7 + 5 7 × 2 15 c 5 4 3 d 3 1 6 + 3 15 E.8926 Perform the following calculations and give the result as a simplified fraction : a 5 3 − 10 9 b 1 3 − 2 3 × 1 8 c 3 9 5 d 4 1 3 + 1 2 18. Unclassified exercises E.270 Perform the calculations below (look for little tricks to simplify your approach) : a 8 × 3 4 + 5 8 b 8 3 × 6 − 3 4 c 1 2 × 2 3 × 3 4 × 4 5 × 5 6 × 6 7 × 7 8 E.1358 Perform the calculations and give the results as simplified fraction : a 2 − 5 4 b 24 5 × 5 6 c 3 7 + 2 d 1 3 + 4 9 https://chingmath.fr chapExoCorrec/1376 sacados/1376 69m116m chapExoCorrec/1642 sacados/1642 chapExoCorrec/1367 sacados/1367 615×532112×2768×591223512 chapExoCorrec/6537 sacados/6537 ABCD12m35m chapExoCorrec/8789 sacados/8789 chapExoCorrec/8790 sacados/8790 chapExoCorrec/8834 sacados/8834 chapExoCorrec/8926 sacados/8926 chapExoCorrec/270 sacados/270 chapExoCorrec/1358 sacados/1358
E.8771 Perform the following calculations : a − 2 + 49 20 × 5 14 b 5 3 − − 7 6 + 12 5 E.8765 Perform the following calculations : a − 3 + 40 15 × 5 4 b 3 7 − − 4 9 + 5 7 E.8768 Perform the following calculations, re-specting the priority of operations and the use of relative num-bers. a − 3 + 7 3 × 9 b − 2 3 + 1 3 × 9 4 c 2 − 2 3 + 5 6 E.1059 Perform the following calculations : a 1 7 − 1 6 × 2 + 1 3 b − 3 75 + 2 50 × 2 E.1021 Perform the following calculations and give the results in simplified form : a 7 × 81 × 15 10 × 9 × 14 b 2 + 11 × 2 2 + 19 × 2 c d 5 + 3 × 5 12 1 + 1 2 e 2 + 3 3 − 5 + 2 × 6 3 + 1 f 1 1 + 1 1 + 1 3 E.4377 Perform the following calculations and give the results in simplified form : a 77 × 16 × 36 18 × 49 × 8 b 4 + 3 × 5 2 − 4 × 5 c 5 3 27 + 12 d 1 − 5 3 × 4 2 + 7 9 e 2 1 + 1 3 − 1 f 2 1 + 3 1 + 3 2 E.8763 Perform the following calculations and give the results as simplified fractions : a 8 ÷ 4 3 b 3 5 6 c 32 15 8 E.8764 Perform the following calculations and give the results as simplified fractions : a 5 12 15 4 b − − 5 6 − 5 4 c 1 2 5 3 E.11776 On considère l’expression : A = 2 3 +3 1 3 +5 Écrire A sous la forme d’une fraction irréductible. https://chingmath.fr chapExoCorrec/8771 sacados/8771 chapExoCorrec/8765 sacados/8765 chapExoCorrec/8768 sacados/8768 chapExoCorrec/1059 sacados/1059 chapExoCorrec/1021 sacados/1021 chapExoCorrec/4377 sacados/4377 chapExoCorrec/8763 sacados/8763 chapExoCorrec/8764 sacados/8764 chapExoCorrec/11776 sacados/11776 Extrait Centres Etrangers - Juin 2004 - 4 points