Grade 7 / Distributivity and numerical calculation 42 exercises (100% corrected)

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R1R2abc 1. Amounts and products E.1790 Each of the following sentences contains an error. Copy the sentence and correct it: 1 In the expression ˇ 3 × 2+2 × 12 ı, 3 is the common factor of each term in this sum. 2 In the expression ˇ 2 × 7+5 × 7 ı, the term 7 is added twice. E.6708 State whether each of the statements below is true or false : a In the calculation ˇ 2+5 × 3+4 ı, there are three terms. b The calculation ˇ 1+3 × 2 ı is a product. c In the calculation ˇ 3 × (5+2) ı, the integer 2 is a factor. d In the calculation ˇ 3 × (5+2) ı, the integer 3 is a factor. e The calculation ˇ 10 × 2+2 ı can be written as a sum of 11 terms worth 2 . 2. Introduction to development E.1192 Note: we consider the calculation: A = 12 × 32 By definition of multiplication, we write: A = 32+32+32+32+32+32+32+32+32+32+32+32  12 times Putting the terms together in two ˇ packages ı, we get : A = 32+32+32+32+32+32+32+32+32+32  10 fois + 32+32  2 fois This gives : A =320+64=384 1 Consider the expression B =33 × 7 . We can write: B = 7+7+ · · · +7+7  30 fois + 7+ · · · +7  . . . fois Deduce the value of B . 2 Consider the expression C =21 × 13 . We can write: C = 13+13+ · · · +13+13  20 fois + : : : Deduce the value of B . E.1193 Note: Here is one way to calculate 17 × 15 . 17 × 15 = 15 + · · · + 15  20 fois − 15 + 15 + 15  3 fois = 300 − 45 = 255 Using reasoning similar to that in the note, find the result of the following calculations : a 19 × 15 b 28 × 7 c 9 × 22 d 999 × 130 E.10049 Using distributivity and indicating the steps in your calculation, perform the operations : a 32 × 7 b 22 × 13 c 14 × 25 d 21 × 102 E.7898 Consider a rectangle R cut into two rectangles R 1 and R 2 : Dimensions are plotted directly on the figure. 1 a Give the length and width of the rectangle R . b Give an expression for the area A R of the rectangle R . 2 Using area considerations, derive the equality: a + b × c = a × c + b × c 3. Distributivity: development E.10046 Using distributivity and indicating the steps in your calculation, perform the operations : a 11 × 17 b 21 × 24 c 12 × 52 E.1195 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : A 19 × 17 b 101 × 24 E.8800 Using distributivity and indicating the steps in your calculation, perform the operations : a 1007 × 12 b 99 × 13 E.10042 Using distributivity and indicating the steps in your calculation, perform the operations : A 103 × 25 b 99 × 12 E.10038 Using distributivity and indicating the steps in your calculation, perform the operations : A 103 × 15 b 98 × 25 c 305 × 8 E.10039 Using distributivity and indicating the steps in your calculation, perform the operations : A 999 × 9 b 990 × 5 c 7020 × 7 https://chingmath.fr chapExoCorrec/1790 sacados/1790 chapExoCorrec/6708 sacados/6708 chapExoCorrec/1192 sacados/1192 chapExoCorrec/1193 sacados/1193 chapExoCorrec/10049 sacados/10049 chapExoCorrec/7898 sacados/7898 R1R2abc chapExoCorrec/10046 sacados/10046 chapExoCorrec/1195 sacados/1195 chapExoCorrec/8800 sacados/8800 chapExoCorrec/10042 sacados/10042 chapExoCorrec/10038 sacados/10038 chapExoCorrec/10039 sacados/10039
E.1196 Using distributivity and indicating the steps in your calculation conduct, perform the operations : a 45 × 21 b 67 × 9 E.1791 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : A 102 × 14 b 99 × 17 c 98 × 13 E.1182 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : a 21 × 131 b 39 × 320 c 184 × 12 d 256 × 99 E.11218 Using distributivity and indicating the steps in your calculation conduct, perform the operations : a 101 × 12 b 98 × 25 E.1194 Using the distributive property and showing your work step by step, perform the following opera-tions : a 98 × 7 ; 5 b 12 × 37 c 32 × 11 E.6705 Using distributivity and indicating the steps in your calculation, perform the operations : a 32 × 101 c 7020 × 32 4. Introduction to factoring E.1191 Note: we consider the calculation: A = 2 × 17 + 8 × 17 Thus, the sum A can be written as : A = 17 + 17  2 fois + 17 + 17 + 17 + 17 + 17 + 17 + 17 + 17  8 fois which can be simplified as : A = 17 + 17 · · · + 17 + 17  10 fois Thus, we can adopt the calculation line: A = 2 × 17 + 8 × 17 = 2 + 8 × 17 = 10 × 17 = 170 1 The expression B =17 × 12+3 × 12 can be written as the sum of several times the number 12 . How many terms would this sum contain? 2 The expression C =7 × 4+5 × 4+8 × 4 can be written as the sum of several times the number 4 . How many terms would this sum contain? 3 Consider the expression D =4 × 1.2+6 × 1.2 . Complete the dotted lines correctly: D = : : : : : : × 1.2 E.10047 Note: here’s a way to calculate 17 × 15 . 7 × 15+3 × 15 = 15 + ... + 15  7 fois + 15 + ... + 15  3 fois = 10 × 15 = 150 a 17 × 12 + 3 × 12 b 6 × 3 + 3 × 14 c 3 × 4 + 4 × 3 5. Distributivity: factoring E.10036 Using distributivity and indicating the steps in your calculation, perform the operations : a 97 × 2 + 3 × 2 c 4 × 3 + 3 × 36 e 32 × 12 − 2 × 12 E.10000 Using distributivity and indicating the steps in your calculation, perform the operations : A 51 × 5 − 11 × 5 b 7 × 102 − 2 × 7 E.10037 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : a 6 × 104 − 4 × 6 b 8 × 87 + 2 × 87 c 24 × 1006 − 6 × 24 E.10041 Using distributivity and indicating the steps in your calculation, perform the operations : e 8 × 87 + 87 × 2 f 25 × 34 − 25 × 4 g 13 × 7 + 7 × 7 E.1177 Calculate using distributivity and showing your work: a 24 × 34 − 24 × 14 b 24 × 6 + 26 × 6 E.6711 Using distributivity, perform the op-erations in the easiest way without using the calculator: a 3 × 5 + 17 × 5 b 12 × 15 + 18 × 15 c 7 × 24 + 3 × 24 E.10044 Using distributivity and indicating the steps in your calculation, perform the operations : a 12 × 13 + 12 × 7 b 52 × 13 − 13 × 2 E.1180 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : a 87 × 8 + 3 × 8 b 9 × 12 + 8 × 9 c 7 × 105 − 5 × 7 E.11217 Calculate using distributivity and detailing your calculations : a 7 × 102 − 2 × 7 b 11 × 13 + 11 × 7 E.10035 Using distributivity and indicating the steps in your calculation, perform the operations : a 2.35 × 13 + 2.35 × 87 b 64 × 5.2 + 36 × 5.2 https://chingmath.fr chapExoCorrec/1196 sacados/1196 chapExoCorrec/1791 sacados/1791 chapExoCorrec/1182 sacados/1182 chapExoCorrec/11218 sacados/11218 chapExoCorrec/1194 sacados/1194 chapExoCorrec/6705 sacados/6705 chapExoCorrec/1191 sacados/1191 chapExoCorrec/10047 sacados/10047 chapExoCorrec/10036 sacados/10036 chapExoCorrec/10000 sacados/10000 chapExoCorrec/10037 sacados/10037 chapExoCorrec/10041 sacados/10041 chapExoCorrec/1177 sacados/1177 chapExoCorrec/6711 sacados/6711 chapExoCorrec/10044 sacados/10044 chapExoCorrec/1180 sacados/1180 chapExoCorrec/11217 sacados/11217 chapExoCorrec/10035 sacados/10035
E.1176 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : a 48.8 × 2 + 1.2 × 2 b 36 × 0.34 + 36 × 1.66 E.10043 Using distributivity and indicating the steps in your calculation, perform the operations : A 48.8 × 2 + 1.2 × 2 b 1.33 × 2 + 0.67 × 2 E.1197 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : A 7.87 × 3 + 2.13 × 3 b 12.12 × 12.5 − 2.12 × 12.5 E.1181 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : a 22 × 5 + 13 × 5 b 52 × 23 − 23 × 2 c 26 × 33 + 34 × 33 E.10045 Using distributivity and indicating the steps in your calculation, perform the operations : a 22 × 4 + 13 × 4 b 8 × 18 − 3 × 8 E.1179 Using distributivity and indicating the steps in your calculation, perform the following opera-tions : a 3.2 × 1.6 + 3.2 × 0.4 b 34 × 5.3 − 1.3 × 34 E.10040 Using distributivity and indicating the steps in your calculation, perform the operations : a 12 × 3 + 1.2 × 70 b 3.2 × 60 + 32 × 4 E.10048 Using distributivity and indicating the steps in your calculation, perform the operations : a 7 × 4+5 × 4+8 × 4 b 4 × 1.2+6 × 1.2 c 6 × 15+40 × 1.5 6. Distributivity E.1178 For his child’s birthday, M r A invites 24 of his friends. He buys each of the children a 33 peso slice of cake and a 7 peso soda. 1 Which of the expressions below represents the purchases made by M r A for this birthday: a 25 × 33 + 25 × 7 b 33 × (25 + 7) c 25 + 33 + 25 + 7 d 25 × (33 + 7) 2 Give the value of all these purchases. 7. A little further on E.10050 Each of the following sentences con-tains an error. Copy the sentence and correct it: 1 Distributivity allows us to state that the calculation of ˇ (10+1) × 8 ı is equal to the calculation of ˇ 10 × 8+1 ı. 2 Distributability allows us to say that the calculation of ˇ 7 × 3+7 × 7 ı is equal to the calculation of ˇ 14 × 10 ı. E.1169 Despite their complex form, these calculations can be done in your head ; find the trick and give the result : A 13 × (2 × 124 + 5) × (13 × 2 − 26) b 3.12 + 4 × 3.12 + 9 × 3.12 + 6 × 3.12 c (13 × 52 − 3) ÷ (13 × 52 − 3) E.1170 Despite their complex form, these calculations can be performed in your head ; find the trick and give your result : a 3 × (121 × 50 − 31 × 4) ÷ (121 × 50 − 31 × 4) b 37 × 2.2458 + 63 × 2.2458 c 3.75 × 100+10 × (9 ÷ 3+7)+12 × 3.75 × 12 × 100 − 12 × 375 https://chingmath.fr chapExoCorrec/1176 sacados/1176 chapExoCorrec/10043 sacados/10043 chapExoCorrec/1197 sacados/1197 chapExoCorrec/1181 sacados/1181 chapExoCorrec/10045 sacados/10045 chapExoCorrec/1179 sacados/1179 chapExoCorrec/10040 sacados/10040 chapExoCorrec/10048 sacados/10048 chapExoCorrec/1178 sacados/1178 chapExoCorrec/10050 sacados/10050 chapExoCorrec/1169 sacados/1169 chapExoCorrec/1170 sacados/1170