Grade 7 / Fractions 94 exercises (100% corrected)

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321812×:::×:::64÷:::÷:::5436×:::×::: ChingQuizz : 21 exercises available for Quizz assessment : 1. Reminders about additions E.11457 We consider the same object divided into the same number of parts. Here is an example of addition : This situation translates to : 1 5 + 2 5 = 3 5 For each of the situations below, show the corresponding sum of fractions and give the result as a fraction : a b c d 2. Equality of fractions E.2503 1 Perform the following calculations : 12 × 6 12 ; 6 × 2 × 1 2 2 What can be said about the two quotients : 6 12 and 1 2 ? E.10099 1 Perform the following calculations : 21 × 7 21 ; 7 × 3 × 1 3 2 What can be said about the two quotients : 7 21 and 1 3 ? E.1325 1 Justify that 24 and 56 are multiples of 8 by completing the blanks below : 24 = : : : × 8 ; 56 = : : : × 8 2 Justify the equality of the two numbers : 24 56 = 3 7 E.2910 Complete the dotted lines in the diagram below to check that the fractions are equal: E.2530 Justify the equations of fractions below : a 3 5 = 6 10 b 21 6 = 7 2 c 18 30 = 3 5 E.1631 Copy the following equations, com-pleting them with the appropriate integer: a 15 = 3 5 b 2 3 = 8 c 21 = 3 d 2 = 10 15 E.2564 Copy the following equations, com-pleting them with the appropriate integer: a 14 5 = 28 b 36 = 9 5 c 24 12 = 6 E.2919 Copy the following equations, com-pleting them with the appropriate integer: a 24 15 = 8 b 28 21 = 3 c 39 18 = 6 E.10071 Copy the following equations, com-pleting them with the appropriate integer: a 28 20 = 5 b 35 = 5 2 c 14 3 = 42 E.10080 Copy the following equations, com-pleting them with the appropriate integer: a 35 28 = 4 b 36 48 = 3 c 2 = 6 E.1635 Copy and complete the following equations : a 1 2 = 12 b 32 = 8 15 c 124 15 = 1.24 d 2 = 6 E.10082 Copy the following equalities, com-pleting with the appropriate integer: a 8 5 = 56 b 9 4 = 63 c 2 3 = 36 E.1632 Copy and complete with the appro-priate number to achieve quotient equality: a 1.5 12 = 120 b 32 = 3.2 15 c 124 15 = 1.24 E.10081 Copy the following equalities, com-pleting with the appropriate integer: a 4 6 = 15 b 25 35 = 21 c 16 24 = 9 Hint: several steps are required to determine the integer being searched for https://chingmath.fr chapExoCorrec/11457 sacados/11457 chapExoCorrec/2503 sacados/2503 chapExoCorrec/10099 sacados/10099 chapExoCorrec/1325 sacados/1325 chapExoCorrec/2910 sacados/2910 321812×:::×:::64÷:::÷:::5436×:::×::: chapExoCorrec/2530 sacados/2530 chapExoCorrec/1631 sacados/1631 chapExoCorrec/2564 sacados/2564 chapExoCorrec/2919 sacados/2919 chapExoCorrec/10071 sacados/10071 chapExoCorrec/10080 sacados/10080 chapExoCorrec/1635 sacados/1635 chapExoCorrec/10082 sacados/10082 chapExoCorrec/1632 sacados/1632 chapExoCorrec/10081 sacados/10081
32×13232×21632×332×4832×532×632×732×84On prend tous les entiersOn s’arrête dès qu’on retrouveun résultat précédent 3. Divisors and Criteria for Divisibility E.11496 Complete the table with crosses to indicate whether the integers shown are divisible by 2, 3, 5, or 9. Integers 450 1443 115 513 646 Divisible by 2 Divisible by 3 Divisible by 5 Divisible by 9 E.11497 Method : to determine the set of divisors of an integer: The set of divisors of the integer 32 are: 1 ; 2 ; 4 ; 8 ; 16 ; 32 Determine the set of divisors of each of these integers : a 42 b 54 c 75 E.11498 Determine the set of divisors for each of these integers : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 2 4. Quotient to simplified fractions E.1313 Write the quotients below as a sim-plified fraction : a 6.1 0.05 b 17 0.7 c 13.2 0.5 E.6513 Write each of the quotients below as a simplified fraction : a 22 0.1 b 2.1 0.9 c 44 0.12 E.10092 Write the quotients below as a sim-plified fraction : a 0.4 0.01 b 1 6.4 c 4.9 2.8 E.10093 Write each of the quotients below as a simplified fraction : a 0.3 12 b 0.02 0.3 c 0.9 3.3 E.10098 Write the quotients below as a sim-plified fraction : a 54 1.2 b 3.18 1.8 c 0.69 0.32 d 2.7 4.05 5. Problems around simplifications E.4008 Below, three figures have been equally divided. Give, in simplified form, the fraction rep-resenting the shaded part relative to the total figure : (Show the simplifications used) E.4007 Below, three figures have been equally divided. Give, in simplified form, the fraction rep-resenting the shaded part relative to the total figure : (Show the simplifications used) https://chingmath.fr chapExoCorrec/11496 sacados/11496 chapExoCorrec/11497 sacados/11497 32×13232×21632×332×4832×532×632×732×84On prend tous les entiersOn s’arrête dès qu’on retrouveun résultat précédent chapExoCorrec/11498 sacados/11498 chapExoCorrec/1313 sacados/1313 chapExoCorrec/6513 sacados/6513 chapExoCorrec/10092 sacados/10092 chapExoCorrec/10093 sacados/10093 chapExoCorrec/10098 sacados/10098 chapExoCorrec/4008 sacados/4008 chapExoCorrec/4007 sacados/4007
10 10 10 10 10 10 10 10 10 10 10 10 10 10 E.4967 The test tubes below are designed to hold one dose of a drug. Using a simplified fraction, indicate the amount of the drug contained in each of these test tubes : a b c d E.4970 Below are 6 gasoline gauges. Indi-cate for each of them the proportion of gasoline present in the tank in the form of a simplified fraction : a b c E.10086 The test tubes below are designed to hold one dose of a drug. Using a simplified fraction, indi-cate the amount of the drug contained in each of these test tubes : a b c d E.10087 Below are 6 gasoline gauges. In-dicate for each of them the proportion of gasoline present in the tank in the form of a simplified fraction : a b c 6. Comparisons of fractions with the same denominator or numerator E.10088 Proposition: Of two fractions with the same denominator , the larger fraction is the one with the larger numerator. Of two fractions with the same numerator , the largest fraction is the one with the smallest denomi-nator. Compare the following fractions using the symbols > or < : a 3 6 . . . 5 6 b 12 5 . . . 12 3 c 16 4 . . . 20 4 d 8 6 . . . 8 10 e 11 5 . . . 15 5 f 3 8 . . . 3 12 E.1320 For each question, copy and compare the two fractions : a 2 3 . . . 1 3 b 7 12 . . . 7 11 c 5 13 . . . 2 13 E.1385 For each question, copy and compare the two fractions : a 2 3 : : : 1 3 b 7 12 : : : 7 11 c 8 13 : : : 15 13 E.1353 Compare and contrast each of the fol-lowing pairs of fractions : a 5 12 : : : 4 12 b 3 13 : : : 3 22 c 3 4 : : : 5 7 E.1359 Notation: < strictly less than less than or equal to > strictly greater than greater than or equal to 1 Two identical cakes, A and B , are divided equally: cake A is cut into 5 slices and cake B is cut into 7 slices. Which cake has the largest slices? Fill in the blanks with < or > : 1 5 . . . 1 7 2 There are two bags of candy, A and B . Bag A contains 40 red candies, and bag B contains 60 blue candies. The two bags are divided equally among 5 people. Which color is most common in each portion? Fill in the blanks with the symbols < or > : 40 5 . . . 60 5 3 State a rule to easily compare each pair of quotients be-low. Then, compare them using the symbols > or < : a 3 6 : : : 5 6 b 12 5 : : : 12 3 c 16 4 : : : 20 4 d 8 6 : : : 8 10 e 11 5 : : : 15 5 f 3 8 : : : 3 12 7. Comparison, Equivalence of Fractions E.1373 Copy and complete the dotted lines to compare the following fractions. Justify. a 5 3 : : : 10 8 b 12 11 : : : 1 c 56 24 : : : 7 5 E.1350 1 Complete the blanks to get two frames to the nearest unit : : : : < 54 5 <: : : ; : : : < 19 2 <: : : 2 Compare quotients : 54 5 et 19 2 https://chingmath.fr chapExoCorrec/4967 sacados/4967 10 10 10 10 chapExoCorrec/4970 sacados/4970 10 10 10 chapExoCorrec/10086 sacados/10086 10 10 10 10 chapExoCorrec/10087 sacados/10087 10 10 10 chapExoCorrec/10088 sacados/10088 chapExoCorrec/1320 sacados/1320 chapExoCorrec/1385 sacados/1385 chapExoCorrec/1353 sacados/1353 chapExoCorrec/1359 sacados/1359 chapExoCorrec/1373 sacados/1373 chapExoCorrec/1350 sacados/1350
− E.10096 For each question, complete the blanks with the appropriate comparison sign : a 58 13 : : : 5 b 12 7 : : : 1 c 0 3 : : : 7 2 E.10089 For each question, complete the blanks with the appropriate comparison sign : a 5 3 : : : 3 5 b 143 135 : : : 73 76 c 72 30 : : : 12 5 E.1352 Copy and complete the dotted lines us-ing < , > or = . a 2 7 : : : 5 7 b 2 3 : : : 5 6 c 3 7 : : : 3 5 d 2 5 : : : 8 19 e 8 20 : : : 8 19 f 9 5 : : : 2 3 E.1985 1 Transform the writing, but not their value, of the follow-ing fractions so that they have a denominator equal to 12. A = 5 6 ; B = 9 4 ; C = 12 24 2 Use the previous question to complete the dotted lines below with fractions of your choice. 12 24 <: : : < 5 6 <: : : < 9 4 E.1349 Compare the following quotients and justify : a 3.1 5 and 9.3 14 b 2.4 7 et 7.3 21 E.1384 Compare the following quotients and justify : a 2.4 2.5 et 7 7.5 b 8.2 13 et 4.1 6 E.1351 1 Without changing their values, transform each of the fol-lowing fractions so that their denominators are equal to 15 : a 4 1 ; 5 b 112 150 c 2 0 ; 5 d 1 2 e 16 16 f 2 2 Use the previous question to arrange these fractions in ascending order. 8. Comparison with 1 and 12 E.1977 1 Copy and complete the following inequalities using inte-gers : a 5 3 <: : : < 7 3 b 16 7 <: : : < 10 3 2 Copy and complete the following inequalities using frac-tions : a 1 2 < : : : 12 < 2 3 b 12 3 < : : : 12 < 50 12 9. Simplification of fractions E.10484 1 To which multiplication table, other than 1, do both 15 and 24 belong? 2 Give the simplified expression for the fraction 15 24 . 10. Addition and subtraction: same denominator E.1980 For each question : represent the result of the proposed calculation on the disc on the right ; write the calculation and its result as fractions. 1 2 3 E.1986 Perform the following calculations : a 11 5 + 2 5 b 19 2 − 4 2 c 2 7 + 17 7 E.10102 Perform the following calculations : a 7 2 − 4 2 b 5 3 + 2 3 c 3 7 + 5 7 https://chingmath.fr chapExoCorrec/10096 sacados/10096 chapExoCorrec/10089 sacados/10089 chapExoCorrec/1352 sacados/1352 chapExoCorrec/1985 sacados/1985 chapExoCorrec/1349 sacados/1349 chapExoCorrec/1384 sacados/1384 chapExoCorrec/1351 sacados/1351 chapExoCorrec/1977 sacados/1977 chapExoCorrec/10484 sacados/10484 chapExoCorrec/1980 sacados/1980 − chapExoCorrec/1986 sacados/1986 chapExoCorrec/10102 sacados/10102
− 35310−− 1214−− 51214 18324 E.10104 Carry out the calculations below, detailing the steps involved. a 13 5 − 7 5 b 19 5 − 3 5 c 9 7 − 3 7 E.10105 Perform the following additions and subtractions : a 7 3 + 5 3 b 12 5 − 7 5 E.11067 Complete the dotted lines to vali-date the equations : a 3 7 + : : : = 5 7 b 12 5 − : : : = 8 5 c 14 3 − : : : = 4 3 E.11068 Complete the dotted lines to vali-date the equations : a 2 3 + : : : = 10 3 b 25 7 − : : : = 19 7 c 18 5 − : : : = 6 5 E.6514 Perform the following calculations and give the result in simplified form : a 5 12 + 13 12 b 4 10 + 1 10 c 15 12 − 1 12 E.10100 Perform the following calculations and give the result in simplified form : a 5 3 + 7 3 b 9 4 − 7 4 c 24 13 + 2 13 E.10101 Perform the following calculations and give the result in simplified form : a 22 15 − 7 15 b 14 57 − 2 57 c 5 24 + 11 24 E.10103 Perform the following calculations : a 15 10 + 3 10 c 5 6 + 10 6 a 3 12 + 1 12 E.11582 Perform the following additions : a 15 6 + 11 6 b 33 14 + 23 14 Note: The results must be simplified fractions. 11. Addition and Subtraction: Multiple Denominators Representation E.6515 In each case, represent the result of the proposed calculation on the left disk, then write this calculation in fractions : 1 2 E.5986 Perform the following operations, each time hatching the corresponding part of the disk : a b E.5985 Perform the following operations by hatching the corresponding part of the rectangle each time: a b 12. Addition and subtraction: multiple denominator https://chingmath.fr chapExoCorrec/10104 sacados/10104 chapExoCorrec/10105 sacados/10105 chapExoCorrec/11067 sacados/11067 chapExoCorrec/11068 sacados/11068 chapExoCorrec/6514 sacados/6514 chapExoCorrec/10100 sacados/10100 chapExoCorrec/10101 sacados/10101 chapExoCorrec/10103 sacados/10103 chapExoCorrec/11582 sacados/11582 chapExoCorrec/6515 sacados/6515 − chapExoCorrec/5986 sacados/5986 35310−− 1214−− chapExoCorrec/5985 sacados/5985 51214 18324
E.1987 Perform the following calculations : A 1 15 + 2 3 b 29 15 − 7 5 c 7 2 + 1 8 E.1644 Perform the calculations below : a 26 27 − 2 3 b 3 64 + 1 8 b 20 36 − 5 12 E.1360 Perform the following calculations : a 5 3 − 7 9 b 5 14 − 2 7 c 9 2 − 3 4 E.10108 Perform the following calculations : a 5 12 − 1 3 b 17 4 − 1 2 c 1 2 + 1 4 E.1370 Perform the following calculations : a 1 2 + 3 4 b 4 7 + 1 14 c 13 9 − 1 3 E.1641 Perform the following calculations, giving the results as simplified fractions : a 1 3 + 2 12 b 13 4 − 3 20 c 1 3 + 5 12 E.1647 Perform the following calculations, giving the results as simplified fractions : a 2 3 + 5 6 b 2 100 + 3 10 c 5 6 + 1 2 E.6520 Perform the following calculations, giving the results as simplified fractions : a 2 3 + 5 6 b 3 5 + 1 15 c 11 12 − 2 3 E.10106 Perform the following calculations, giving the results in simplified form : a 4 7 + 17 7 b 7 12 − 1 4 c 3 10 + 1 5 E.10107 Perform the following calculations, giving the results in simplified form : a 12 9 + 1 3 b 4 2 + 12 4 c 12 3 − 3 12 E.11069 Fill in the blanks to check the equa-tions : a 1 3 + : : : = 11 12 b 5 8 + : : : = 13 16 c : : : − 7 4 = 7 20 E.11070 Fill in the blanks to check the equa-tions : a 5 6 + : : : = 11 12 b 5 7 + : : : = 13 14 c : : : − 11 7 = 5 21 13. Addition and subtraction: integers and fractions E.1646 1 Give a fraction equal to 2 with a denominator of 12. 2 Perform the following calculation: 2 + 5 12 E.6521 Perform the following calculations : a 1 + 1 2 c 3 − 3 4 e 1 3 + 2 E.1366 Perform the following calculations : a 3 4 + 2 b 4 3 + 1 c 24 7 − 3 E.10109 Perform the following calculations : a 3 − 1 4 b 5 + 1 2 c 11 3 − 1 E.11071 Copy and complete the dotted lines in the following operations : a 17 4 = · · · 4 + 1 4 = · · · + 1 4 b 35 8 = · · · 8 + 3 8 = · · · + 3 8 c 42 5 = · · · 5 + 2 5 = · · · + 2 5 d 52 7 = · · · 7 + 3 7 = · · · + 3 7 E.11072 Write each of the fractions as the sum of an integer and a fraction less than 1 . a 14 9 b 27 5 c 14 3 d 51 8 e 37 4 f 15 7 14. Simplifying Fractions E.2582 From the list below, determine which quotients are equal to each other : 4 6 ; 2 2 ; 5 ; 15 30 ; 12 18 ; 28 35 ; 3 4 ; 5 ; 12 ; 2 6 ; 1 ; 20 25 E.11804 Définition: une fraction est dite simplifiée au maxi-mum si son numérateur et dénominateur n’ont que l’entier 1 pour diviseur commun 1 Justifier que chacune des fractions ci-dessous n’est pas simplifiée au maximum : a 8 6 b 21 12 c 15 35 2 Justifier que chacune des fractions ci-dessous est simpli- https://chingmath.fr chapExoCorrec/1987 sacados/1987 chapExoCorrec/1644 sacados/1644 chapExoCorrec/1360 sacados/1360 chapExoCorrec/10108 sacados/10108 chapExoCorrec/1370 sacados/1370 chapExoCorrec/1641 sacados/1641 chapExoCorrec/1647 sacados/1647 chapExoCorrec/6520 sacados/6520 chapExoCorrec/10106 sacados/10106 chapExoCorrec/10107 sacados/10107 chapExoCorrec/11069 sacados/11069 chapExoCorrec/11070 sacados/11070 chapExoCorrec/1646 sacados/1646 chapExoCorrec/6521 sacados/6521 chapExoCorrec/1366 sacados/1366 chapExoCorrec/10109 sacados/10109 chapExoCorrec/11071 sacados/11071 chapExoCorrec/11072 sacados/11072 chapExoCorrec/2582 sacados/2582 chapExoCorrec/11804 sacados/11804
96364818=÷2÷2249=÷2÷283=÷3÷3 6020÷:::÷:::÷:::÷:::÷:::÷::: 1842÷:::÷:::÷:::÷:::÷:::÷::: fiée au maximum : a 7 5 b 15 8 E.10530 Simplify the following fractions as much as possible : a 54 36 b 168 120 E.2563 Leaving the steps of your calculations, simplify the following fractions as much as possible : a 9 12 b 55 33 c 16 36 d 25 45 E.9636 Leaving the steps of your calculations visible, simplify the following fractions as much as possible : a 42 27 b 35 49 c 27 36 15. Simplifying fractions: in several steps E.2531 Method : To simplify a fraction as much as possible, it is sometimes necessary to simplify several times by a common factor in the numerator and denominator, as shown below : Complete the diagrams below to obtain a simplified fraction at the end. (You do not have to use all the steps suggested.) : 1 2 E.2578 By leaving out steps in your calculations, simplify the frac-tions below as much as possible : a 42 70 b 20 56 E.2532 By leaving out steps in your calculations, simplify the frac-tions below as much as possible : a 54 36 b 48 132 c 54 186 E.10119 By leaving out steps in your calculations, simplify the frac- tions below as much as possible : a 42 63 b 120 180 c 18 168 E.1374 By leaving out steps in your calculations, simplify the frac-tions below as much as possible : a 135 90 b 98 28 c 224 84 E.1377 Leaving the steps of your calculations visible, simplify the following fractions as much as possible : a 100 80 b 70 14 c 66 110 E.1365 Leaving the steps of your calculations visible, simplify the following fractions as much as possible : a 108 198 b 60 150 c 84 36 E.10095 Leaving the steps of your calculations, simplify the following fractions as much as possible : a 840 560 b 120 64 c 390 546 E.10123 Leaving the steps of your calculations visible, simplify the following fractions as much as possible : a 350 1 400 b 525 210 c 168 126 E.10124 Leaving the steps of your calculations visible, simplify the following fractions as much as possible : a 84 126 b 120 168 c 210 315 16. Unclassified exercises https://chingmath.fr chapExoCorrec/10530 sacados/10530 chapExoCorrec/2563 sacados/2563 chapExoCorrec/9636 sacados/9636 chapExoCorrec/2531 sacados/2531 96364818=÷2÷2249=÷2÷283=÷3÷3 6020÷:::÷:::÷:::÷:::÷:::÷::: 1842÷:::÷:::÷:::÷:::÷:::÷::: chapExoCorrec/2578 sacados/2578 chapExoCorrec/2532 sacados/2532 chapExoCorrec/10119 sacados/10119 chapExoCorrec/1374 sacados/1374 chapExoCorrec/1377 sacados/1377 chapExoCorrec/1365 sacados/1365 chapExoCorrec/10095 sacados/10095 chapExoCorrec/10123 sacados/10123 chapExoCorrec/10124 sacados/10124
E.10120 Write each of the decimal numbers be-low as a simplified fraction : a 0.54 b 0.08 c 0.125 https://chingmath.fr chapExoCorrec/10120 sacados/10120