Grade 6 / fractions: operations 36 exercises (including 31 corrected)

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ab 12 34 56 1. Mental Math E.11809 Compléter les pointillés: a 2 3 + 5 3 = 2 + : : : 3 b 5 4 + 8 4 = : : : + 1 4 c 4 7 + : : : 7 = 1 + 2 7 d : : : 5 + 12 5 = 3 + 1 5 2. Introduction to fractional equalities E.1321 Consider the two pavements below : 1 Using the graduated ruler, justify that the two rectangles have the same dimensions. Do the same for the hatched parts. 2 In both cases a and b , what is the proportion of hatched squares relative to all the squares making up the rectangle? 3 Justify the equality: 3 × 4 8 × 4 = 3 8 E.1623 Consider the three identical rectan-gles above, equally divided into small squares : 1 What fraction of the rectangle represents a tile? 2 Use the rectangles below to give a representation of each of the following fractions : a 1 2 b 2 5 c 2 3 3 a For each of the rectangles, indicate the number of squares used to represent each of the fractions. b Express each of the fractions in question 2 using frac-tions with 30 in the denominator. E.91 Six identical rectangles are shown be-low, but divided into distinct sections. 1 Which split represents an inequitable split of the rectan-gle? 2 In the rest of the exercise, we will only be interested in the rectangles 1 , 2 , 3 , 4 and 6 . Considering the shaded portion of rectangle 1, we’ll look at the representation of this portion on the other rectangles : a Reproduce the hatched part in rectangle 1 identically in rectangles 2 , 3 , 4 and 6 . b Complete, column by column, the following table : Rectangle n o 1 2 3 4 6 Number of tiles grisés Total number of carreaux c For each of the five rectangles, use the calculator to perform the following quotient : Nombre of tiles grisés Nombre total of tiles What do you notice? d From the previous question, we obtain the following equality sequence : https://chingmath.fr sacados/11809 chapExoCorrec/1321 sacados/1321 ab chapExoCorrec/1623 sacados/1623 chapExoCorrec/91 sacados/91 12 34 56
6121224×:::×:::36÷:::÷:::4896×:::×:::612÷:::÷::: R1R2 01A(21001B(3601C(14 1=21=31=41=51=61=81=91=101=1201ABCDE Complete the dotted lines to indicate which operation characterizes each of these operations. E.7884 Consider the two rectangles shown below : Represent on each of the rectangles the following shares : 1 a Hatch two-thirds of the rectangle R 1 . b Chop the 16 24 rectangle R 2 . 2 What can be said about fractions 2 3 and 16 24 . E.9977 For each graduated line, place the indicated point on the line, respecting the specified abscissa : 3. Equality of fractions E.7885 Justify the equalities of the following fractions : a 7 5 = 70 50 b 12 10 = 6 5 c 75 150 = 1 2 E.10529 Copy the following equations, com-pleting them with the appropriate integer: a 30 36 = : : : 6 b 28 48 = 7 : : : c 15 42 = : : : 14 E.11057 Complete the dotted lines to vali-date the equalities: a 7 3 = : : : 12 b 5 8 = 25 : : : c : : : 15 = 8 3 E.10487 Copy the following equations, fill-ing in the appropriate integer: a 15 = 3 5 b 2 3 = 8 c 21 = 3 d 2 = 10 15 E.10488 Copy the following equations, fill- ing in the appropriate integer: a 14 5 = 28 b 36 = 9 5 c 24 12 = 6 E.10515 Several unit shares are shown be-low : Give all the possibilities for writing the abscissas of the points B , C , D , E as a function of these partitions. Example: the abscissa of point A can be expressed as : A 3 5 ; A 6 10 4. Simplification of fractions E.2533 1 Which multiplication table, other than 1, includes both 15 and 24? 2 Simplify the fraction as much as possible 15 24 . E.10117 1 Which multiplication table, other than 1, includes both 13 and 39? 2 Simplify the fraction as much as possible 13 39 . https://chingmath.fr 6121224×:::×:::36÷:::÷:::4896×:::×:::612÷:::÷::: chapExoCorrec/7884 sacados/7884 R1R2 chapExoCorrec/9977 sacados/9977 01A(21001B(3601C(14 chapExoCorrec/7885 sacados/7885 chapExoCorrec/10529 sacados/10529 chapExoCorrec/11057 sacados/11057 chapExoCorrec/10487 sacados/10487 chapExoCorrec/10488 sacados/10488 chapExoCorrec/10515 sacados/10515 1=21=31=41=51=61=81=91=101=1201ABCDE chapExoCorrec/2533 sacados/2533 chapExoCorrec/10117 sacados/10117
35310−− 1214−− 51214 18324 E.10118 1 Which multiplication table, other than 1, includes both 12 and 28? 2 Simplify the fraction as much as possible 28 12 . E.10485 Simplify each of the fractions be-low : a 24 18 b 10 15 c 28 36 d 40 56 Hint: we will divide the numerator and denominator by a common factor other than 1 E.10486 Simplify each of the fractions be-low : a 21 12 b 60 66 c 63 27 d 55 40 Hint: we will divide the numerator and denominator by a common factor other than 1 E.11494 Definition: A fraction is said to be simplified to the greatest extent possible if its numerator and denomina-tor have only the integer 1 as a common divisor 1 Justify that each of the fractions below is not simplified to the maximum extent possible : a 8 6 b 21 12 c 15 35 2 Justify that each of the fractions below is simplified to the maximum extent possible : a 7 5 b 15 8 E.1369 Leaving the steps of your calculations, simplify the following fractions as much as possible : a 15 20 b 18 12 c 16 24 E.1383 From the list below, determine the quotients that are equal to each other : 24 14 ; 7 2 ; 60 35 ; 21 6 ; 12 7 ; 5 7 Hint: Three groups of equal quotients can be formed E.11805 L’exercice n’existe pas. 5. Adding Fractions: Common Denominators E.11748 Effectuer les opérations suivantes en hachurant à chaque fois la partie correspondante du disque : a b E.11749 Effectuer les opérations suivantes en hachurant à chaque fois la partie correspondante du rectan-gle: a b E.11750 Effectuer les calculs suivants : a 1 15 + 2 3 b 29 15 − 7 5 c 7 2 + 1 8 E.11756 Effectuer les calculs ci-dessous : a 26 27 − 2 3 b 3 64 + 1 8 b 20 36 − 5 12 E.11757 Effectuer les calculs suivants en don-nant les résultats sous la forme de fractions simplifiées : a 1 3 + 2 12 b 13 4 − 3 20 c 1 3 + 5 12 E.11758 Effectuer les calculs suivants en don-nant les résultats sous la forme de fractions simplifiées : a 2 3 + 5 6 b 2 100 + 3 10 c 5 6 + 1 2 https://chingmath.fr chapExoCorrec/10118 sacados/10118 chapExoCorrec/10485 sacados/10485 chapExoCorrec/10486 sacados/10486 chapExoCorrec/11494 sacados/11494 chapExoCorrec/1369 sacados/1369 chapExoCorrec/1383 sacados/1383 sacados/11805 chapExoCorrec/11748 sacados/11748 35310−− 1214−− chapExoCorrec/11749 sacados/11749 51214 18324 chapExoCorrec/11750 sacados/11750 chapExoCorrec/11756 sacados/11756 chapExoCorrec/11757 sacados/11757 chapExoCorrec/11758 sacados/11758
6036÷:::÷:::÷:::÷:::÷:::÷::: 4860÷:::÷:::÷:::÷:::÷:::÷::: 6. Addition and Subtraction of Integers and Fractions E.11751 1 Donner une fraction égale à 2 ayant un dénominateur de 12. 2 Effectuer le calcul suivant : 2 + 5 12 E.11752 Effectuer les calculs suivants : a 1 + 1 2 c 3 − 3 4 e 1 3 + 2 E.11759 Recopier et compléter les pointillés dans les opérations ci-dessous : 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 7. Adding Fractions: Different Denominators E.11753 L’exercice n’existe pas. E.11754 L’exercice n’existe pas. E.11755 L’exercice n’existe pas. 8. Unclassified exercises E.4346 Consider the four figures below : 1 For the first three figures, determine the value of the quotient : nombre of squares noires nombre of squares 2 In the fourth figure, there is the same proportion of black squares as in the first three figures. Knowing that this figure contains 100 squares, how many squares are black? E.1372 Gold at ˇ18 caratsı is a metal containing 18 = 24 pure gold. How much pure gold does a ring weighing 63 grams contain? E.10122 Complete the diagrams below to obtain at the end a simplified fraction (you don’t fi t have to use all the proposed steps) : 1 2 https://chingmath.fr chapExoCorrec/11751 sacados/11751 chapExoCorrec/11752 sacados/11752 chapExoCorrec/11759 sacados/11759 sacados/11753 sacados/11754 sacados/11755 chapExoCorrec/4346 sacados/4346 chapExoCorrec/1372 sacados/1372 chapExoCorrec/10122 sacados/10122 6036÷:::÷:::÷:::÷:::÷:::÷::: 4860÷:::÷:::÷:::÷:::÷:::÷:::