Grade 9 / Operations on fractions 54 exercises (100% corrected)

a
ChingQuizz : 3 exercises available for Quizz assessment : 1. Reminders E.3382 Perform the following calculations : a 3 + 5 − 2 − 8 b 4 × 3 − 3 × 3 c 2 − 3 × 4 + 2 d 3 + 5 × 2 − 2 e 10 − (6.5 − 4) × 3 f − 1 × 2 × ( − 2) × ( − 3) E.9861 Perform the following calculations : a (+3) + ( − 2) − ( − 5) + ( − 1) − (+4) b 1 × 1 × ( − 1) × ( − 1) × 1 × ( − 1) × 1 × 1 × ( − 1) E.3381 Perform the following calculations in your head : a 49 × 6 b 21 × 13 c 5 × 3 ; 32 + 5 × 1 ; 68 d 1 ; 2 × 3 ; 3 − 0 ; 2 × 3 ; 3 Hint: Use the distributive property. 2. Addtions E.3383 Proposition : Let a , b , c be three numbers with c =0 . We have : a c + b c = a + b c This property is stated as follows : " to add two quotients with the same denominator, add the numerators and keep the same denominator ". Perform the following operations. The results must be given as simplified fractions. a 3 7 + 4 21 b 5 12 − 2 3 c 2 3 + 5 6 E.5679 1 Determine the GCD of each of the pairs of integers be-low : a GCD 4; 6 = : : : b GCD 15; 20 = : : : c GCD 12; 8 = : : : 2 Calculate and give the result in simplified fractions. a 3 4 + 2 6 b 2 15 + 3 20 c 5 12 − 9 8 E.11489 1 Determine the LCM of the integers 6 and 15 . 2 Perform the addition below and give the result as an ir-reducible fraction : 1 6 + 1 15 E.9161 Perform the following operations and express the result as an irreducible fraction : a 7 2 − 2 3 b 4 15 + 7 6 c 5 4 − 5 7 E.5724 Perform the calculations and give the result as an irreducible fraction : a 5 6 − 13 9 b 5 12 − 2 15 c 15 66 − 10 44 E.9162 Perform the calculations and give the result as an irreducible fraction : a 2 5 + 1 b − 1 3 + 1 c 5 − 8 7 E.9156 Perform the calculations and give the result as an irreducible fraction : a 1 3 − 8 9 + 5 6 b − 2 3 + 1 4 − 5 6 E.11281 Perform the calculations and give the result as an irreducible fraction : a 2 5 − 1 15 + 2 3 b 1 2 + 1 4 + 1 8 E.11280 Perform the calculations and give the result as an irreducible fraction : a 5 − 2 3 − 5 6 b 2 − 5 4 + 1 3 3. Addition and multiplication https://chingmath.fr chapExoCorrec/3382 sacados/3382 chapExoCorrec/9861 sacados/9861 chapExoCorrec/3381 sacados/3381 chapExoCorrec/3383 sacados/3383 chapExoCorrec/5679 sacados/5679 chapExoCorrec/11489 sacados/11489 chapExoCorrec/9161 sacados/9161 chapExoCorrec/5724 sacados/5724 chapExoCorrec/9162 sacados/9162 chapExoCorrec/9156 sacados/9156 chapExoCorrec/11281 sacados/11281 chapExoCorrec/11280 sacados/11280
E.9160 either a , b , c , d four numbers with b =0 and d =0 . We have the following equality: a b × c d = a × c b × d This property is stated as follows : " to multiply two quo-tients, multiply the numerators together and the denomi-nators together. " Perform the calculations and give the result in the form of an irreducible fraction a 3 4 × 2 5 b 15 49 × 21 25 c 36 64 × 24 30 d 55 32 × 24 33 E.9862 Perform the calculations and give the result as an irreducible fraction a 1 2 × 8 6 × 3 2 b − 5 2 × − 2 3 × 3 5 c ( − 2) × 5 × ( − 4) × 3 × 7 × ( − 5) ( − 10) × 6 E.612 Perform the calculations and give the result as an irreducible fraction a 1 2 − 1 3 × 5 6 b 7 3 − 5 2 × 3 7 E.11387 Perform the calculations and give the result as an irreducible fraction : a 10 9 + 5 6 × 2 5 b 2 7 × 5 8 + 1 4 E.11388 Perform the calculations and give the result as an irreducible fraction a 5 8 − 1 3 × 3 7 b 3 7 × 5 8 − 8 3 E.11358 Perform the calculations and give the result as an irreducible fraction : a 7 3 − 5 × 2 5 b 12 5 − 2 × 1 6 E.9163 Perform the calculations and give the result as an irreducible fraction : a 2 3 + 5 6 1 3 − 5 2 b 2 15 − 1 3 5 2 + 5 4 E.9164 Perform the calculations and give the result as an irreducible fraction : a 5 4 − 7 2 2 3 + 1 6 b 5 3 + 5 6 7 6 − 4 5 E.11282 Perform the calculations and give the result as an irreducible fraction : a 2 7 − 3 × 7 − 7 2 b 1 4 − 1 5 × 7 + 37 9 E.2128 Perform the calculations and give the result as an irreducible fraction : a 3 − 3 + 5 6 2 + − 9 2 4. Addition, multiplication and priority of operations E.620 Perform the calculations and give the result as an irreducible fraction : a 1 3 × 2 5 + 2 5 b 7 3 − 5 2 × 7 3 E.2127 Perform the calculations and give the result as an irreducible fraction : a 7 3 × 5 4 + 1 6 b 10 9 × 12 5 − 4 3 E.5052 Perform the calculations and give the result as an irreducible fraction : a 8 5 − 5 7 × 14 4 b 15 9 × 12 25 − 7 4 E.3347 Perform the calculations and give the result as an irreducible fraction : a 21 26 × 13 7 − 13 7 b 3 7 − 2 7 × 21 8 E.11364 Perform the calculations and give the result as an irreducible fraction : a 3 4 + 5 6 × 3 2 b 5 2 − 15 6 × 21 25 E.11363 Perform the calculations and give the result as an irreducible fraction : a 9 28 × 7 5 + 10 3 × 6 25 b E.5005 Perform the calculations and give the result as an irreducible fraction : a 5 7 + 1 7 × 5 + 1 2 b 42 15 2 3 − 1 3 × 9 7 E.5006 Perform the calculations and give the result as an irreducible fraction : a 6 5 × 16 9 × 6 32 − 15 12 b 5 2 − 6 25 × 15 12 × 6 22 − 3 15 E.9159 Perform the calculations and give the result as an irreducible fraction : a 3 + 5 6 2 b 5 3 − 3 2 2 − 5 4 E.11365 Perform the calculations and give the result as an irreducible fraction : a 4 3 2 − 5 − 9 2 2 b 1 3 − 1 2 1 3 + 1 2 2 E.9165 Perform the calculations and give the result as an irreducible fraction : a − 2 − 9 × − 3 8 + 3 − 36 https://chingmath.fr chapExoCorrec/9160 sacados/9160 chapExoCorrec/9862 sacados/9862 chapExoCorrec/612 sacados/612 chapExoCorrec/11387 sacados/11387 chapExoCorrec/11388 sacados/11388 chapExoCorrec/11358 sacados/11358 chapExoCorrec/9163 sacados/9163 chapExoCorrec/9164 sacados/9164 chapExoCorrec/11282 sacados/11282 chapExoCorrec/2128 sacados/2128 chapExoCorrec/620 sacados/620 chapExoCorrec/2127 sacados/2127 chapExoCorrec/5052 sacados/5052 chapExoCorrec/3347 sacados/3347 chapExoCorrec/11364 sacados/11364 chapExoCorrec/11363 sacados/11363 chapExoCorrec/5005 sacados/5005 chapExoCorrec/5006 sacados/5006 chapExoCorrec/9159 sacados/9159 chapExoCorrec/11365 sacados/11365 chapExoCorrec/9165 sacados/9165
5. Quotients E.5007 Proposition: Let a , b , c , d be four non-zero numbers. We have the following equal-ity: This property can be stated as follows : ˇ di-viding by a quotient is equivalent to multi-plying by its inverse ı a b c d = a b × d c Perform the calculations and give the result in the form of an irreducible fraction : a 3 4 9 16 b 5 4 25 c 21 14 15 d 3 5 2 5 E.2174 Perform the calculations and give the result as an irreducible fraction : a 2 7 − 15 7 ÷ 5 4 b 2 13 − 5 13 ÷ 10 16 E.9166 Perform the calculations and give the result as an irreducible fraction : a 4 3 − 1 7 6 − 2 b 2 3 + 1 2 17 9 − 1 3 E.9157 Perform the calculations and give the result as an irreducible fraction : a 3 4 + 5 4 ÷ 4 3 − 1 2 b 3 − 5 1 + 1 3 E.9158 Perform the calculations and give the result as an irreducible fraction : a 4 3 − 5 6 1 2 + 1 b 2 − 5 12 1 3 − 8 5 E.9168 Perform the calculations and give the result as an irreducible fraction : a 4 3 + 3 10 5 2 − 2 5 b 5 3 − 7 4 1 + 1 6 E.9155 Perform the calculations and give the result as an irreducible fraction : a 3 2 − 10 6 2 7 + 1 3 b 1 − 11 6 10 9 + 5 6 E.4985 Perform the calculations and give the result as an irreducible fraction : a 7 8 − 7 8 × 3 7 3 × 2 − 2 = 1 8 b 25 2 5 4 2 2 = 64 E.11366 Perform the calculations and give the result as an irreducible fraction : a 25 2 5 4 2 2 b 3 − 9 5 2 1 − 1 5 E.9167 Perform the calculations and give the result as an irreducible fraction : a 1 + 1 2 2 3 5 + 3 4 = 5 3 b E.11367 Perform the calculations and give the result as an irreducible fraction : a 1 2 + 2 1 − 5 3 b 2 1 + 3 2 + 5 2 6. Problems and fractions E.604 1 Perform the calculation below and give the result as an irreducible fraction : 1 − 1 4 + 3 4 × 4 5 2 A landowner sold a quarter of his property in 2001 and four-fifths of the remainder in 2002 . a What total fraction of the property was sold between 2001 and 2002 ? b What fraction of the property remains unsold at the end of the two years? c What was the area of the property knowing that the portion unsold at the end of the two years represents six hectares? E.2130 Four children share a bar of chocolate. The first takes a third of the bar and the second takes a quar-ter. The third takes the 2 5 of what is left after the first and second have helped themselves. 1 Which of the calculations below finds the share taken by the third child? A = 1 − 1 3 − 1 4 × 2 5 ; B = 1 − 1 3 − 1 4 × 2 5 C = 1 − 1 3 − 1 4 ÷ 2 5 ; D = 1 − 1 3 + 1 4 × 2 5 2 Perform the selected calculation. https://chingmath.fr chapExoCorrec/5007 sacados/5007 chapExoCorrec/2174 sacados/2174 Extrait brevet 2008 - 4,5 points chapExoCorrec/9166 sacados/9166 chapExoCorrec/9157 sacados/9157 chapExoCorrec/9158 sacados/9158 chapExoCorrec/9168 sacados/9168 chapExoCorrec/9155 sacados/9155 chapExoCorrec/4985 sacados/4985 chapExoCorrec/11366 sacados/11366 chapExoCorrec/9167 sacados/9167 chapExoCorrec/11367 sacados/11367 chapExoCorrec/604 sacados/604 Groupe Ouest - Juin 2003 - 3 points chapExoCorrec/2130 sacados/2130 Grenoble - 3 points - Juin 1996
GarçonsFillesGarçonsFillesGarçonsFillesGarçonsFillesDiagramme 1GarçonsFillesGarçonsFillesGarçonsFillesGarçonsFillesDiagramme 1Diagramme 2 GarçonsFillesGarçonsFillesGarçonsFillesGarçonsFilles E.3375 In question 1 of this exer-cise, any record of research, even if incomplete, or initiative, even if unsuccessful, will be considered in the evaluation . 1 A landowner sold one-quarter of his property in 2006 and then one-third of the rest in 2007. What fraction of his property does he have left today? 2 What is the current size of his property knowing that it was originally 40 hectares? E.7633 In a class of 24 students, there are 16 girls. 1 Can either of the two diagrams below correctly represent the distribution of students in this class? 2 The distribution of students in this class was represented by a pie chart. Write the calculation first to determine the measure of the angle of the sector that represents the girls. E.5022 1 Jacques, Jean and Emilie buy together a 72 hectare farm-land which they divide up as follows : John takes one-third of the field. Of the part left by John, James takes two-fifths. Emily takes the remaining part. Determine the area of Emily’s land. 2 With the number 1 and the numbers present in the state-ment, write a calculation that directly gives the area taken up by Emile. 7. Share E.613 A = 5 4 + 11 4 × 20 33 ; B = 1 12 ÷ 2 − 7 3 Calculate A and B , giving details of the calculations. Give the result as a simplified fraction. E.2135 In this section, calculations will need to be detailed. Consider the three numbers A , B and C : A = − 5 3 + 7 5 ; B = 7 4 ÷ 21 9 C = − 2 × 60 − 5 × 4 2 − (8 − 15) 1 Determine the value of the expressions A and B in sim-plified fraction form. 2 Calculate the value of the expression C . E.606 Perform the following calculations, detailing the calculations and giving the results as irreducible fractions : A = 2 3 + 5 3 × 1 15 ; B = 1 − 3 7 ÷ 12 5 C = 9 2 3 ; D = 3 4 + 3 1 2 + 2 E.11542 Perform the calculations and give the result as a simplified fraction : a 4 7 5 3 − 1 6 b 9 7 − 1 7 × 20 3 8. Unclassified exercises E.645 A = 1 − 2 3 + 1 4 ; B = 3 − 5 2 1 + 1 5 1 Showing the various calculation steps, write A and B as an irreducible fraction. 2 Calculate the four-fifths of 35 8 . We’ll call C the result given as an irreducible fraction. 3 Show that the sum A + B + C is an integer. https://chingmath.fr chapExoCorrec/3375 sacados/3375 chapExoCorrec/7633 sacados/7633 GarçonsFillesGarçonsFillesGarçonsFillesGarçonsFillesDiagramme 1GarçonsFillesGarçonsFillesGarçonsFillesGarçonsFillesDiagramme 1Diagramme 2 GarçonsFillesGarçonsFillesGarçonsFillesGarçonsFilles chapExoCorrec/5022 sacados/5022 chapExoCorrec/613 sacados/613 chapExoCorrec/2135 sacados/2135 chapExoCorrec/606 sacados/606 chapExoCorrec/11542 sacados/11542 chapExoCorrec/645 sacados/645