Grade 8 / Fractions: addition and subtraction 41 exercises corrected

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ChingQuizz : 9 exercises available for Quizz assessment : 1. Reminders: multiples, divisors, fractions E.6193 1 Complete the blanks with the words ˇ factors ı and ˇ mul-tiples ı : a 25 admits the integer 5 as . . . . . . . . . . . . . . . . b 21 is a . . . . . . . . . . . . . . . of the integer 7 . c 24 is not a . . . . . . . . . . . . . . . of the integer 8 . d 8 is a . . . . . . . . . . . . . . . of the integer 24 . 2 For each question, circle the correct answers from the suggestions : a The integer 32 admits as factors : 2 4 8 12 b The integers 16 and 24 admit as common factors : 2 4 8 12 c The integer 6 admits for multiples : 6 12 26 36 d The integers 8 and 12 admit as common multiples : 8 12 24 96 E.5725 In this exercise, any evidence of even incomplete research or even unsuccessful initiative will be considered in the assessment. We consider the six identical test tubes but filled to different levels. 1 For each of the test tubes, give the fraction of the speci-men shown in gray. 2 Which test tubes must be combined to obtain a new test tube filled to unity? E.5696 In middle school, Lise eats 1 4 from the package of cakes she just opened. Back from college, her sister Agathe eats the 2 3 of the cakes remaining in the package Lise started. This leaves 5 cakes. What was the original number of cakes in the package? If the work is not completed, still leave a search record. It will be considered in the assessment. E.2915 Fill in the blanks with the appropri-ate fraction simplified : a 3 × = 5 b 15 × = 35 c 2 × = 9 d 18 × = 27 e 16 × = 2 f 77 × = 7 2. Reminders: simplification E.1633 Simplify each of the following frac-tions as far as possible : a 18 30 b 45 63 c 24 36 d 10 5 Indication : we will follow a wording identical to that pre-sented below : E.1634 Simplify the following fractions as much as possible : a 14 42 b 120 180 c 18 42 d 224 84 E.4666 Which of the following are simplifi-cations of fractions? a 30 20 = 3 2 b 12 21 = 4 7 c 24 18 = 8 9 d 19 20 = 18 19 e 18 32 = 9 16 f 49 21 = 7 3 3. Reminders: addition, subtraction with the same denominator E.8716 Addition and subtraction rule : For any integer a , b , c , with c =0 , we have : a c + b c = a + b c ; a c − b c = a − b c Note: so adding or subtracting two fractions requires the same denominator. https://chingmath.fr quizzChap/1026 chapExoCorrec/6193 sacados/6193 chapExoCorrec/5725 sacados/5725 10A 10B 10C 10D 10E 10F chapExoCorrec/5696 sacados/5696 chapExoCorrec/2915 sacados/2915 chapExoCorrec/1633 sacados/1633 chapExoCorrec/1634 sacados/1634 chapExoCorrec/4666 sacados/4666 chapExoCorrec/8716 sacados/8716
Translate each of the graphs below by a calculation on frac-tional numbers : 1 2 3 E.4661 Perform the calculations below : a 2 3 + 8 3 b 7 5 + 9 5 c 13 7 + 3 7 d 12 5 − 6 5 e 13 7 − 5 7 f 17 15 − 3 15 E.8717 Perform the following calculations and give the result as a simplified fraction : a 5 12 + 13 12 b 2 7 + 17 7 c 4 10 + 1 10 d 15 12 − 1 12 e 7 2 − 4 2 f 22 15 − 7 15 E.8725 Perform the following calculations and give the results as simplified fractions : a 2 10 + 3 10 b 5 3 + 12 3 c 15 4 − 11 4 E.8726 Perform the calculations below and give their result as a simplified fraction : a 5 6 + 11 6 b 54 3 − 27 3 c 3 15 + 7 15 4. Reminders: addition, subtraction with the denominator multiple of each other E.8718 Note: To add two fractions, both denominators must be equal. In the questions below, we transform one of the fractions into an equal fraction but with a denominator identical to the other fraction. Thus, we can apply the rules previously given Each of the graphs below represents an addition of fractions. Copy and complete the blanks to obtain the desired equality: 1 1 : : : + 3 : : : = : : : : : : + : : : : : : = : : : + : : : : : : = 5 8 2 5 : : : − 1 : : : = : : : : : : − : : : : : : = : : : − : : : : : : = 3 10 E.8728 Perform the calculations below and give the results as simplified fractions : A 3 10 + 2 100 b 2 10 + 7 100 c 0.25 + 1 10 E.1040 Perform the following operations : a 3 100 + 7 10 b 1 10 + 27 100 c 5 10 − 2 10 d 3 10 − 7 100 e 17 10 − 19 100 f 1 10 − 1 1000 E.4662 Perform the calculations below. The results will be given as a simplified fraction. a 4 7 − 3 14 b 19 12 − 5 4 c 37 16 − 9 4 d 13 10 + 6 5 e 6 21 + 1 7 f 5 6 + 7 24 E.1354 1 Simplify the following fractions : 12 60 ; 30 60 2 Perform the following operation: 1 5 + 1 2 And give the result as a maximally simplified fraction. E.8724 Perform the following calculations. The results will be given as a simplified fraction. a 1 + 5 6 + 3 10 b 2 + 5 12 − 7 15 c 1 5 + 3 10 − 3 14 5. Finding the common denominator and comparing fractions https://chingmath.fr − chapExoCorrec/4661 sacados/4661 chapExoCorrec/8717 sacados/8717 chapExoCorrec/8725 sacados/8725 chapExoCorrec/8726 sacados/8726 chapExoCorrec/8718 sacados/8718 − chapExoCorrec/8728 sacados/8728 chapExoCorrec/1040 sacados/1040 chapExoCorrec/4662 sacados/4662 chapExoCorrec/1354 sacados/1354 chapExoCorrec/8724 sacados/8724
E.8719 Proposition: Let a , b , c be three strictly positive integers : If two fractions have the same denominator then the largest fraction is the one with the largest numerator : if a<b then a c < b c Example: for comparison 3 5 < 4 5 If two fractions have the same numerator then the largest fraction is the one with the smallest denomina-tor: if b<c then a b > a c Example: are compared to 2 5 < 2 7 1 a Give all multiples of 6 that are strictly less than 30 . b Complete the dotted lines : 5 6 = : : : 12 = : : : 18 = : : : 24 2 Complete the dotted lines : 3 4 = : : : 8 = : : : 12 = : : : 16 = : : : 20 = : : : 24 = : : : 28 3 Compare the two fractions of 5 6 and 3 4 . E.4700 1 Determine the least common multiple of 4 and 6 . 2 Compare the two fractions : 7 4 and 11 6 6. Addition and subtraction E.2542 Consider the two numbers written as fractions : A = 5 6 ; B = 1 4 . 1 Give the least common multiple of the denominators of these two fractions. 2 Write the two numbers A and B in fractional writing so that they have the same denominator. 3 Add the numbers A and B E.2544 Copy and perform the following ad-ditions, completing the intermediate step beforehand : a 1 3 + 1 2 = : : : 6 + : : : 6 = : : : + : : : 6 = : : : 6 b 3 5 + 7 10 = : : : 10 + : : : 10 = : : : + : : : 10 = : : : 10 c 5 6 + 3 4 = : : : 12 + : : : 12 = : : : + : : : 12 = : : : 12 d 8 7 + 8 3 = : : : 21 + : : : 21 = : : : + : : : 21 = : : : 21 e 2 15 + 1 10 = : : : 30 + : : : 30 = : : : + : : : 30 = : : : 30 f 5 6 + 10 9 = : : : 18 + : : : 18 = : : : + : : : 18 = : : : 18 E.8736 Perform the following sums : a 1 6 + 1 9 b 3 10 − 1 4 c 3 4 − 1 6 d 5 9 + 1 12 e 5 8 − 1 10 f 1 10 + 5 12 Hint: To perform these sums, we will focus on the smallest common denominator and use a similar format : E.8720 Perform the following operations and give the result in simplified form : a 7 6 + 9 10 b 3 20 + 7 12 c 7 15 + 7 10 Note: Use a format similar to the one be-low : E.8721 1 a Complete the blanks : 120 = 12 × : : : ; 120 = 15 × : : : b Determine the least common multiple of the numbers 12 and 15 . 2 Perform the following sum : 1 12 + 1 15 . Give the simplified form of the result. https://chingmath.fr chapExoCorrec/8719 sacados/8719 et et chapExoCorrec/4700 sacados/4700 chapExoCorrec/2542 sacados/2542 chapExoCorrec/2544 sacados/2544 chapExoCorrec/8736 sacados/8736 chapExoCorrec/8720 sacados/8720 chapExoCorrec/8721 sacados/8721
E.8774 Below is shown a segment [ AB ] where two points M and N are placed such that : segment [ AM ] is one-third of segment [ AB ] ; segment [ BN ] represents two-sevenths of segment [ AB ] . Determine the fraction of segment [ AB ] that separates points M and N . E.2132 Three points A , B and C of a graduated line have abscissa : 1 4 ; 1 3 ; 5 12 Are these three points evenly spaced on the graduated line? E.8755 The Egyptians used only 1 numerator fractions, with the exception of the 2 3 fraction. To find the double of their numerator fractions 1 , tables were available, one of which is shown below : whose use of the first row of the table tells us : The double 1 5 is the sum of 1 3 and 1 15 1 Complete the table with the correct values replacing the blanks. 2 Check the relationship induced by the last row of this table. E.8714 Consider the square shown oppo-site, which has been decomposed into 4 equal squares. Some of these squares have been subdivided into squares of the same dimension. What fraction of the square ABCD is shaded? 7. Relative numbers: simplification of fractions E.4663 Complete the blanks to verify the following equations : a 5 : : : = − 5 7 b − 3 4 = 3 : : : c − 3 : : : = 3 4 d 12 − 15 = − : : : 5 e 27 : : : = − 3 − 2 f 36 24 = − 15 : : : E.4664 Complete the blanks below to verify the equalities: a 8 − 5 = : : : 20 b − 15 : : : = − 3 7 c − 4 11 = − 16 : : : d 36 81 = − : : : 9 e − 7 − 10 = : : : 40 f 12 20 = − 15 : : : 8. Relative numbers: addition and subtraction E.1056 Perform the following additions and subtractions, giving the result as a fraction simplified as far as possible : a 2 4 + 2 − 4 b 5 3 + − 17 6 c − 5 12 − − 2 3 d 2 + − 3 2 E.8737 Perform the following additions and subtractions, giving the result as a fraction simplified to the maximum : a 2 7 + 3 11 b 5 8 + 2 c − 3 11 + − 4 5 E.4761 Perform the following operations. The result will be given as a simplified fraction : a − 1 6 + 1 − 14 b 3 10 − 7 15 c − 3 15 − − 4 25 d 5 6 + 9 − 10 E.8738 Perform the following additions and subtractions, giving the result as a fraction simplified to the maximum : a − 7 10 + 5 6 b − 1 15 + − 1 12 9. Problem https://chingmath.fr chapExoCorrec/8774 sacados/8774 ABMN chapExoCorrec/2132 sacados/2132 chapExoCorrec/8755 sacados/8755 53157428...61811666138521041510...17125168 chapExoCorrec/8714 sacados/8714 ABCD chapExoCorrec/4663 sacados/4663 chapExoCorrec/4664 sacados/4664 chapExoCorrec/1056 sacados/1056 chapExoCorrec/8737 sacados/8737 chapExoCorrec/4761 sacados/4761 chapExoCorrec/8738 sacados/8738
E.4630 Successive figures are constructed by adding a new square ; more precisely, the new square added to a side measuring half of the previous square : It is assumed that the first square had a side measuring 1 cm . 1 Show that the area of the figure in step 2 measures : A 2 = 5 4 2 Determine as an irreducible fraction, the area A 3 of this figure made in step 3 . 3 Determine the area A 4 of this figure in step four. E.4765 1 Test the identity below for integers between 1 and 9 : 1 n ( n + 1) = 1 n − 1 n + 1 2 Use the previous question to easily determine the value of A où : A = 1 + 1 2 + 1 6 + 1 12 + 1 20 + 1 30 + 1 42 + 1 56 + 1 72 + 1 90 10. Share E.8778 Perform the following calculations and give the results as simplified fractions : a 5 3 + 2 9 b 2 3 − 5 4 c 3 10 − 7 6 d 15 16 × 24 75 E.8779 Perform the calculations below and give their results as simplified fractions : a 2 3 − 3 2 × 4 9 b 10 9 × 6 25 + 1 3 × 1 5 c 1 3 1 − 5 2 E.8780 Perform the following calculations and give the results as simplified fractions : a 1 2 3 a 1 + 3 ÷ 3 2 × 5 − 5 11. Unclassified exercises E.3326 Simplify the fraction 1404 3465 by 3. Is the resulting fraction irreducible? https://chingmath.fr chapExoCorrec/4630 sacados/4630 Etape no1 Etape no2 Etape no3 chapExoCorrec/4765 sacados/4765 chapExoCorrec/8778 sacados/8778 chapExoCorrec/8779 sacados/8779 chapExoCorrec/8780 sacados/8780 chapExoCorrec/3326 sacados/3326