Outside the middle school program / Fractions 33 exercises (100% corrected)

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1. Addition, subtraction and relative numbers E.1044 Perform the following calculations and give the result in simplified form : a − 3 5 + 4 15 b 3 4 + 5 − 6 c − 2 3 − − 3 4 d 2 − 8 + − 1 − 16 e 5 2 − − 9 10 f 1 − 3 − − 1 − 3 E.1045 Give the results of the following calcula-tions in their simplified forms : a 2 − 7 + 6 14 b − 5 8 + 2 c 8 75 − 4 100 d − 2 16 − − 5 12 e 7 4 + 5 − 6 f − 3 14 + − 5 21 E.1043 Calculate and give the result in simpli-fied fractions. a 3 4 + 2 6 b 2 15 + 3 20 c 5 12 − 9 8 d 5 6 − 13 9 e 5 12 − 2 15 f 15 66 − 10 44 2. Product E.8745 Perform the following calculations and give the result in simplified form : a − 7 15 × 9 21 × 20 − 3 b − 8 5 × − 24 − 27 × 9 − 12 E.4665 Give the sign of the following products : a 5 − 3 × − 4 7 b 12 − 5 × − 4 − 3 c − 5 − 14 × − 4 15 d − 11 − 5 × − 10 11 e 7 − 6 × − 36 − 17 f − − 9 − 7 × − 25 27 3. Priorities for operations with relative numbers E.1857 Perform the following calculations and give the results in simplified form : a − − 3 4 + 4 − 27 × − 3 8 b − 3 8 − − 2 4 + 1 2 c 2 − 12 25 × 15 8 E.8748 Perform the following calculations and give the results in the simplest form possible : a 1 + 1 − 2 × 1 2 b 5 9 × 27 4 + 5 6 c 3 7 + 8 4 × − 1 2 E.1057 Carry out the following calculations and give the result as simplified fractions as possible : a − 7 15 × − 5 21 − − 4 3 b − 3 + 9 5 × 3 c 5 2 − − 2 7 × 14 5 E.8747 Perform the following calculations and give the results in the simplest form possible : a − 7 15 × − 5 21 − − 4 3 b − 3 + 9 5 × 3 c 3 − − 6 7 × 21 12 E.8746 Perform the following calculations and give their results in simplified form : a 15 4 × − 12 18 + 27 18 × 6 5 b 1 2 × 16 14 − 21 16 × 8 3 E.11790 1 Calculer A = − 2 7 + 3 7 × 59 9 ÷ 25 3 et donner le résultat sous la forme d’une fraction irréductible. 2 Le nombre A obtenu est-il un nombre entier? décimal? rationnel? Justifier la réponse. 4. With square roots E.11771 Effectuer les calculs suivants et donner les résultats sous formes simplifiées : a √ 12 + √ 12 7 √ 3 + √ 75 b 5 3 27 + 12 5. Simplifying Fractions: Using the Greatest Common Divisor https://chingmath.fr chapExoCorrec/1044 sacados/1044 chapExoCorrec/1045 sacados/1045 chapExoCorrec/1043 sacados/1043 chapExoCorrec/8745 sacados/8745 chapExoCorrec/4665 sacados/4665 chapExoCorrec/1857 sacados/1857 chapExoCorrec/8748 sacados/8748 chapExoCorrec/1057 sacados/1057 chapExoCorrec/8747 sacados/8747 chapExoCorrec/8746 sacados/8746 chapExoCorrec/11790 sacados/11790 chapExoCorrec/11771 sacados/11771
4532=××45××32==LCMa 7456=××74××56==LCMb 314121=××314××121==LCMa 512415=××512××415==LCMb E.11495 1 a Give the 8 divisors of 70 . b Give the 8 divisors of 42 . c What are the common divisors of 70 and 42 ? 2 Simplify the fraction 70 42 as much as possible. E.10083 Method : To make a fraction irreducible, simplify it (Di-vide the numerator and denominator by the same number) by the greatest common divisor . Example: Divisors of 18 : 1 , 2 , 3 , 6 , 9 , 18 ; divisors of 27 : 1 , 3 , 9 , 27 . By simplifying using the greatest common divisor of the nu-merator and denominator, the fraction will be simplified to the maximum : 18 27 = 18 ÷ 9 27 ÷ 9 = 2 3 1 a Give all the divisors of 12 . b Give all the divisors of 16 . c Give all the common divisors of 12 and 16 . 2 Simplify the fraction 16 12 as much as possible. E.10085 Leaving out the steps in your calculations, simplify the fol-lowing fractions as much as possible : a 4 12 b 12 14 c 24 56 Hint: For each fraction, find the greatest common divisor of the numerator and denominator among 2 , 4 , or 8 . E.10084 Leaving out the steps in your calculations, simplify the fol-lowing fractions as much as possible : a 12 15 b 15 36 c 14 35 Hint: For each fraction, find the greatest common divisor of the numerator and denominator among 3 , 7 , or 9 . E.9635 Leaving out the steps in your calculations, simplify the fol-lowing fractions as much as possible : a 20 12 b 16 40 c 38 20 Hint: For each fraction, find the greatest common divisor of the numerator and denominator among 2 , 4 , or 8 . E.10121 Leaving the steps of your calculations, simplify the following fractions as much as possible : a 27 36 b 36 30 c 30 54 d 30 120 Hint: For each fraction, simplify using the greatest com-mon divisor of the numerator and denominator. 6. Us-math: addition and subtraction E.9641 With American notations: the ˇ least common multiple ı (LCM) of two integers is the greatest common multiple. For example: first multiples of 12 : 12 , 24 36 , 48 , 60 , 72 first multiples of 15 : 15 , 30 , 45 , 60 , 75 Ainsi, le LCM de 12 et 15 est 60 . For each question, complete the blanks : E.10113 For each question, complete the blanks : E.9639 Calculate the sums below and give their results as ˇ mixed fractions ı : a 3 1 4 + 2 5 8 b 2 1 6 + 29 12 c 3 2 3 + 9 3 12 E.10111 Calculate the sums below and give their results as ˇ mixed fractions ı : a 5 2 5 + 6 3 10 b 3 1 2 + 3 1 8 c 6 1 4 + 8 5 16 E.9640 Calculate the sums below and give their results as ˇ mixed fractions ı : a 3 4 5 + 2 3 10 b 1 7 15 + 3 4 5 c 5 5 8 + 2 3 4 https://chingmath.fr chapExoCorrec/11495 sacados/11495 chapExoCorrec/10083 sacados/10083 chapExoCorrec/10085 sacados/10085 chapExoCorrec/10084 sacados/10084 chapExoCorrec/9635 sacados/9635 chapExoCorrec/10121 sacados/10121 chapExoCorrec/9641 sacados/9641 4532=××45××32==LCMa 7456=××74××56==LCMb chapExoCorrec/10113 sacados/10113 314121=××314××121==LCMa 512415=××512××415==LCMb chapExoCorrec/9639 sacados/9639 chapExoCorrec/10111 sacados/10111 chapExoCorrec/9640 sacados/9640
E.10114 Calculate the sums below and give their results as ˇ mixed fractions ı : a 4 1 3 + 2 1 4 b 2 5 12 + 1 7 15 c 7 1 2 + 4 4 9 E.10112 Calculate the differences be-low and give their results as ˇ mixed fractions ı : a 9 2 3 − 3 1 5 b 7 5 6 − 2 1 5 c 8 2 3 − 2 3 7 E.9642 Calculate the sums below and express the result as ˇ mixed fractions ı : a 4 3 8 + 2 5 12 b 3 + 2 3 8 c 5 2 21 + 1 1 28 E.9643 Calculate the differences below and give their results as ˇ mixed fractions ı : a 7 2 3 − 3 1 4 b 4 3 10 − 2 1 4 c 5 5 8 − 3 1 7 E.10115 Perform the calculations be-low and express their results as ˇ mixed fractions ı : a 2 5 4 + 1 3 b 3 7 4 − 1 6 c 5 1 2 − 3 3 5 E.10116 Perform the calculations be-low and express their results as ˇ mixed fractions ı : a 23 6 + 3 5 12 b 2 7 10 + 3 3 4 c 5 1 7 − 3 3 5 7. Us-math: mixed fractions E.9638 With American notations: there are two ways to name fractions : the ˇ proper fractions ı : if the numerator is less than the numerator as 2 9 , 1 3 the ˇ improper fractions ı : if the numerator is greater than the numerator like 7 2 , 11 7 For the ˇ improper fractions ı, the notation ˇ mixed fraction ı allows this number to be written as an integer and a ˇ proper fractions ı : 7 2 = 6 + 1 2 = 6 2 + 1 2 = 3 + 1 2 = 3 1 2 Write each of the fractions in the form of ˇ mixed fractions ı where the ˇ proper fractions ı is given in its simplified form. a 30 9 b 3 3 12 c 5 17 15 d 1 22 12 e 3 1 3 E.9633 Compare the following fractions : a 43 12 et 3 5 12 a 7 5 7 et 7 2 7 a 3 2 5 et 28 3 E.9634 Compare the following frac-tions : a 3 2 7 et 3 5 7 b 2 3 7 et 2 3 8 c 4 3 4 et 4 7 12 E.10094 Compare the following fractions : a 25 7 et 3 5 7 b 6 2 3 et 16 3 c 25 9 et 3 2 9 https://chingmath.fr chapExoCorrec/10114 sacados/10114 chapExoCorrec/10112 sacados/10112 chapExoCorrec/9642 sacados/9642 chapExoCorrec/9643 sacados/9643 chapExoCorrec/10115 sacados/10115 chapExoCorrec/10116 sacados/10116 chapExoCorrec/9638 sacados/9638 chapExoCorrec/9633 sacados/9633 chapExoCorrec/9634 sacados/9634 chapExoCorrec/10094 sacados/10094