Grade 7 / Literal expressions: manipulation 72 exercises corrected

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ChingQuizz : 12 exercises available for Quizz assessment : 1. Simplification of literal expressions E.1054 Consider the following literal ex-pression : A = 2 × x + 3 + x + 2 + 3 + 4 × x 1 a Donner the value of the expression A pour x =10 . b How many terms does the expression A contain? Un-derline them. 2 Complete the table below following the instructions : Terme Nombre de numér. en ˇ x ı fois x 2 × x 3 x 2 3 4 × x Indication : Dans the column ˇ Terme ı, put a cross in the column to indicate the nature of the term ; In the column ˇ Number of times x ı and in the case of a term in ˇ x ı, put the coefficient of x . 3 Complete the following sentence : ˇ In total, the value x is present . . . . . . in the ex-pression A and the sum of the numerical terms has a value of . . . . . . ı 4 Justify the fact that the expression A can also be written as : A =7 × x +8 E.1234 Simplify the following expressions : a 3 × x + 2 × x + 1 + 5 × x b 2 × 5 + 2 × x − 14 Hint: two writing rules allow simplification : When a product includes a numerical factor and the factor ˇ x ı then the mulplication sign can be omitted : 2 × x 2 x ; 2 × x + 3 × 5 2 x + 15 The number 2 is called the coefficient of x . Lorque le coefficient de x est 1 , il peut être omis : 1 x x ; 5 x − 4 x x E. 1877 Simplify the following expressions : a 3 x + 4 + 8 x + 2 + x b 3 + 2 × x + 5 + 3 + x + 1 E. 11078 Simplify the following expressions : a 5 + 8 x + 3 x − 4 x + 7 b x + 20 − 15 + 3 x E.11196 Simplify the following expressions : a 5 + 4 x + 2 x − 3 − 3 x b 3 x + 5 − 4 x + 7 x − 12 E.11219 Simplify the following expressions : a 3 x + 5 + 4 x − 2 − x − 7 b 12 − 3 x + 4 x − 5 + 2 x E.10142 1 Simplify the following expressions : a A = 2 × 3 x + 2 × 4 + x × 3 b B = 3 × 2 x + 3 x + 4 × 5 2 For each of these expressions, give the coefficient of the term in x and its numerical value. E.10144 Consider the following literal ex-pression : A = 5 + 3 × x + 3 × 2 × x + 5 × 9 + x 1 Simplify the expression A . 2 Evaluate this expression for x =3.75 . 2. Simplification and x 2 term E.11104 Consider the following tiling made up of squares : https://chingmath.fr quizzChap/1155 chapExoCorrec/1054 sacados/1054 chapExoCorrec/1234 sacados/1234 chapExoCorrec/1877 sacados/1877 chapExoCorrec/11078 sacados/11078 chapExoCorrec/11196 sacados/11196 chapExoCorrec/11219 sacados/11219 chapExoCorrec/10142 sacados/10142 chapExoCorrec/10144 sacados/10144 chapExoCorrec/11104 sacados/11104 x
Which algebraic expressions represent the area of this tiling? a 10 x b 7 x × 3 x c 10 x 2 d 21 x e 3 x + 7 x f 21 x 2 E.10927 Consider the set of quadrilaterals below : 1 Give the areas of each of these quadrilaterals as a func-tion of x : Quadrilateral A B C D E F G H I Area 2 Complete the table below : Number of quadrilaterals with areas x 2 Number of quadrilaterals with areas x Number of quadrilaterals with areas 1 3 Write the expression as a function of x giving the total area of these quadrilaterals. E.1814 Consider the expression : A = 3 × x × 4 × x × 5 1 Which rule on the priority of operations, allows you to justify that the expression A is equal to the following expression B : B = 3 × 4 × 5 × x × x 2 Deduce the new writing of the expression A : A = 60 x 2 E.10146 Simplify the expressions : a 2 × 3 x × 8 b 4 x × 2 × 5 x E.1815 Consider the following literal expression : A = 3 × 2 + 2 × x + x × 3 × x + 2 x 2 + 3 × x + 1 1 Copy the expression A , then distinctly underline each of the terms in this expression. 2 The table below represents the six terms of the expres-sion A . In the right-hand column, give the simplified form of each term : Simplified expression Expression term 3 × 2 2 × x x × 3 × x 2 x 2 3 × x 1 3 In view of the previous table, complete the following sen-tence : In the literal expression A : there are . . . . . . times the term x 2 , there are a . . . . . . times the term x , the sum of the numerical terms has a value de . . . . . . 4 Justify that the literal expression A admits as simplified writing: A = 5 x 2 + 5 x + 7 E. 10931 Simplify the expressions below : a 3 d 2 + 7 d 2 + d + 3 d + 9 + 3 d 2 + 4 b 2 s + 4 + 2 s + s 2 + 3 s + 3 s 2 + 4 E. 10932 Simplify the expressions below : a 4 r + 8 r + r 2 + 4 r 2 + 7 + 3 + 7 r b 1 + 6 p 2 + 7 p + p 2 + 4 p + 2 p + 9 E.10143 Simplify the following expressions : a 3 x + 7 x 2 + 5 + 2 + 2 × x × 3 + 7 × 2 b 3 × x + 2 x + 4 × 2 + 3 + x × x + x E.1931 Simplify the following expressions : a 2 x 2 + 2 + 3 × x + x 2 + 6 × 2 b 2 x 2 + 3 × x + x 2 + 3 x + 2 E. 11197 Simplify the expressions : a 3 x − x 2 + 5 x − 7 + 3 x + 5 + 3 x 2 + 10 x − 12 b − 15 x + 12 x 2 − 5 x 2 + 14 + 32 x − 7 + 5 x E. 11220 Simplify the expressions : a 4 x 2 + 5 x − 12 + 2 x + 3 x 2 + 5 − 4 x 2 b − 7 x + 5 x 2 − 10 + 3 x + 2 x 2 + 8 E.11079 Simplify the following expressions : a 9 x 2 +5 x − 6 x 2 +4+3 x − 2 b 5 + 8 x − 3 + 3 x + 2 x 2 + x 2 E.10933 Simplify the expressions below : a − 5 c 2 + c 2 + 2 c − 5 c − 2 − 3 c 2 b 2 k 2 + k 2 − 2 k − 5 k − 1 + 3 k − 5 E.10934 Simplify the expressions : a 2 ‘ 2 − 3 + 4 ‘ + ‘ − 3 − ‘ 2 + 2 ‘ 2 b 3 w 2 − 2 w + 4 w + 2 − 5 + w 2 + 2 w 2 E. 10935 Simplify the expressions : a 6 x 2 + 8 y 2 − 6 y − 3 + 4 x 2 − 6 y − 8 x + 4 x b − 1 + 4 x 2 + 8 x − 2 x − 2 − 3 y − 2 y − 2 y 2 E.10936 Simplify the expressions : a − 5 y 2 − 5 y 2 + 4 y + 1 + 3 − 3 x − 7 x 2 − 6 y b 8 y + 4 x + 2 − 8 y 2 − 5 − 2 x 2 + 3 y − 7 x https://chingmath.fr chapExoCorrec/10927 sacados/10927 xxAxB3C4D4E3F4GxH3I chapExoCorrec/1814 sacados/1814 chapExoCorrec/10146 sacados/10146 chapExoCorrec/1815 sacados/1815 chapExoCorrec/10931 sacados/10931 chapExoCorrec/10932 sacados/10932 chapExoCorrec/10143 sacados/10143 chapExoCorrec/1931 sacados/1931 chapExoCorrec/11197 sacados/11197 chapExoCorrec/11220 sacados/11220 chapExoCorrec/11079 sacados/11079 chapExoCorrec/10933 sacados/10933 chapExoCorrec/10934 sacados/10934 chapExoCorrec/10935 sacados/10935 chapExoCorrec/10936 sacados/10936
3. Simplification, x terms and fractions E.10937 Simplify expressions : a 2 3 × x + 5 4 + 1 2 + 7 3 × x b 7 2 − 5 8 + 7 3 × x − 7 6 × x E.11080 Simplify the expressions : a 5 4 × x + 3 4 × x + 1 3 + 2 3 b 8 5 × x + 7 5 × x + 9 7 − 2 7 E.10938 Consider the figure below, which is composed of rectangles and squares : Express the area of the shaded region in terms of x . 4. Introduction to distributivity E.11102 The two figures below are composed of rectangles : 1 Let A 1 be the area of rectangle AEFD . Express this area as a product, then as a sum. 2 Let A 2 be the area of rectangle GHIJ . Express this area as a product, then as a difference. E.11103 The two figures below are composed of rectangles : 1 Let A 1 be the area of rectangle AEFD . Express this area as a product, then as a sum. 2 Let A 2 be the area of rectangle GHIJ . Express this area as a product, then as a difference. E.11302 do an exercise where the perimeter is 4 × ( n + 4) ou 4 × n + 16 E.11741 Un enfant possède les trois urnes ci-dessous : 1 Que peut-on dire de ces trois urnes? 2 a Il vide ses trois urnes sur son bureau. Décrire ce qu’il possède. b Compléter l’égalité des expressions algébriques : 3 × x + 2 = : : : × x + : : : https://chingmath.fr chapExoCorrec/10937 sacados/10937 chapExoCorrec/11080 sacados/11080 chapExoCorrec/10938 sacados/10938 3cm2cmx chapExoCorrec/11102 sacados/11102 ABCDEFx23GHIJKL4x2 chapExoCorrec/11103 sacados/11103 ABCDEFx3GHIJKLxy5 sacados/11302 E2E3E4E5 sacados/11741 222
5. Distributivity - Development E. 1242 Develop and simplify expressions : a 4 × ( x + 5) b (2 x + 1) × 5 E.1244 Develop and simplify expressions : a 6 × (2 x + 3) b 4 × (2 x + 4) E.11332 Expand and simplify expressions : a 4 × ( x − 5) b 3 × (5 x − 3) E. 1243 Develop and simplify expressions : a 3 × ( x + 2) b 5 × (2 x − 1) e 3 × (4 x − 1) E. 11198 Expand and simplify the expres-sions : a 3 × 2 x + 3 b x × 3 x − 4 E.11221 Expand and simplify the expres-sions : a 4 × 3 x + 7 b x × 4 x − 2 6. Distributivite - Development, reduction E. 10133 Expand and simplify the expres-sions : a (2 x + 1) × 5 + 2 c 2 × (4 + x + 5) E.10135 Expand and simplify the expres-sions : a 2 × (6 + x + 2) b 3 × 5 + 2 x + 3 x E.1245 Expand and simplify the expres-sions : a 5 × (2 + x ) + 2 × (2 x − 1) b 3 × ( x + 2) + 2 × (3 x − 1) E.10132 Expand and simplify the expres-sions : a 2 × ( x − 1) + 8 × (3 x + 4) b 3 × ( x + 2) + 2 × (3 x − 1) E.10134 Expand and simplify the expres-sions : a 3( x + 2) + 2 x + 1 b 2(5 − x ) + x × ( x + 3) − 7 E.11199 Expand and simplify the expres-sions : a 5 x − 2 + 3 × 4 x − 4 b 2 x − 4 + x 5 + x E.11222 Expand and simplify the expres-sions : a 3 x + 5 + 4 × 3 x − 7 b 4 2 x + 1 + x 3 + 2 x 7. Distributivity, Reduction, and Computation E.1235 Consider the expression : A =3 ; 2 x + 5( x +1)+1 ; 8 x +4 . 1 Expand and simplify the literal expression A . 2 Evaluate the expression A for x =2154 ; 45 . E.1237 1 Simplify the expression : A =3 × ( x +2)+7 x +2 . 2 Evaluate the expression A for x =12 ; 5 . E.1236 Evaluate the expression A for x = 8541 ; 554 : A = 3 x + x + 5 × ( x + 2) + x E.10136 Evaluate the expression B for x =0.45684 : B = 12 × (3 x + 4) + 7 × (2 x + 6) + 10 E.10137 Evaluate the expression B for x =12.1 où : B = 3 × (7 x + 2) + 5 − 21 × x 8. Distributivity - Factoring E.1250 Using distributivity, factor the ex-pressions : a 3 x + 2 × 3 b 6 × 2 − 6 × x c 2 x + 2 × 3 E.1246 Using distributivity, factor the ex-pressions : a 4 x + 4 × 3 b 3 x + 3 × 1 c 5 x + 5 × 1 https://chingmath.fr chapExoCorrec/1242 sacados/1242 chapExoCorrec/1244 sacados/1244 chapExoCorrec/11332 sacados/11332 chapExoCorrec/1243 sacados/1243 chapExoCorrec/11198 sacados/11198 chapExoCorrec/11221 sacados/11221 chapExoCorrec/10133 sacados/10133 chapExoCorrec/10135 sacados/10135 chapExoCorrec/1245 sacados/1245 chapExoCorrec/10132 sacados/10132 chapExoCorrec/10134 sacados/10134 chapExoCorrec/11199 sacados/11199 chapExoCorrec/11222 sacados/11222 chapExoCorrec/1235 sacados/1235 chapExoCorrec/1237 sacados/1237 chapExoCorrec/1236 sacados/1236 chapExoCorrec/10136 sacados/10136 chapExoCorrec/10137 sacados/10137 chapExoCorrec/1250 sacados/1250 chapExoCorrec/1246 sacados/1246
E.10145 Using distributivity, factor the ex-pressions : a 4 x + 6 b 14 x + 21 c 18 x + 12 E.1247 Using distributivity, factor the ex-pressions : a 3 x + 15 b 6 x + 12 c 12 x + 4 E.10139 Using distributivity, factor the ex-pressions : a 5 x + 25 b 4 x + 20 c 3 x + 18 E.10138 Using distributivity, factor the ex-pressions : a 2 x 2 + 3 x b 4 x 2 + 2 x c 15 x 2 + 9 x E.11200 Using distributivity, factor the ex-pressions : a 10 x + 6 b 5 x 2 + 3 x c x × y + 3 x 2 E.11223 Using distributivity, factor the ex-pressions : a 9 x + 24 b 7 x 2 + 2 x c 3 x × y + 2 y 2 9. Distributivity - Development and factoring E.11201 Consider the expressions : A = 3 3 x − 2 + 5 x + 2 1 Expand and simplify the expression A . 2 Using the expression obtained in question 1 , , factor the expression A . E.11202 Consider the expressions : A = 3 4 x + 2 + 2 x − 5 1 Expand and simplify the expression A . 2 Using the expression obtained in question 1 , , factor the expression A . E.11203 Consider the expressions : A = 2 5 x − 4 + 5 x − 5 1 Expand and simplify the expression A . 2 Using the expression obtained in question 1 , , factor the expression A . E.11204 Consider the expressions : A = 5 5 x 2 + x + x (5 x + 3) 1 Expand and simplify the expression A . 2 Using the expression obtained in question 1 , , factor the expression A . E.11205 Consider the expressions : A = 3 5 x 2 + 5 x + x ( x + 3) 1 Expand and simplify the expression A . 2 Using the expression obtained in question 1 , , factor the expression A . E.11206 Consider the expressions : A = 2 2 x 2 − x + x (3 x − 3) 1 Expand and simplify the expression A . 2 Using the expression obtained in question 1 , , factor the expression A . 10. Modeling problem E.6356 We want to make frames with small tiles. Below are three such frames : 1 Keeping in mind the look of these frames, how many tiles will it take to build a frame that has 8 tiles on each of these sides? 2 Of the formulas below, only one determines the number of tiles needed to make a frame having x tiles on each of these sides. a 6 n b 6 n − 8 c 6 n − 16 Find the correct formula. 3 Give the characteristics of the largest frame that can be constructed using 94 tiles. https://chingmath.fr chapExoCorrec/10145 sacados/10145 chapExoCorrec/1247 sacados/1247 chapExoCorrec/10139 sacados/10139 chapExoCorrec/10138 sacados/10138 chapExoCorrec/11200 sacados/11200 chapExoCorrec/11223 sacados/11223 chapExoCorrec/11201 sacados/11201 chapExoCorrec/11202 sacados/11202 chapExoCorrec/11203 sacados/11203 chapExoCorrec/11204 sacados/11204 chapExoCorrec/11205 sacados/11205 chapExoCorrec/11206 sacados/11206 chapExoCorrec/6356 sacados/6356
E.6358 The image below shows the footprints of a man walking. The step length P is the distance between the back of two consecutive footprints. Paul asked some of his friends to participate in a study. Here is the information he noted : Longueur of a step en mètres Nombre of pas par minutes Emilie 0.64 90 Ahmed 0.75 105 Pascal 0.73 102 Which of the following proposed formulas most closely ap-proximates the observations made by Paul : a 7.5 × n − 1000 × P = 35 b n ÷ P = 140 c 10 × P × 190 − n = 640 où we use the following notations : n : steps per minute ; P : step length in meters. E.6474 Diariatou reviews her movie releases over the past three weeks : The first week, she went 2 times to the movies and bought a drink from 3 e and popcorn from 2 e . The second week, she went 1 times to the movies and bought popcorn at 2 e . The third week she went 1 times to the movies and bought nothing. Noting x the price of a movie ticket, give an expression giving Diaratou’s total spending over the three weeks. 11. Usmath E.9649 With American notations: to perform operations on al-gebraic expressions, we can lay them out in lines by aligning terms of the same kind. Examples: Here are the two operations posed : (5 x + 2) + (3 x + 1) ; (9 x + 7) − (5 x + 2) Perform the operations below by laying them out in lines : a 8 x + 3 + 2 x + 1 b 5 x + 7 − x + 1 E.10140 Perform the operations below by laying them out in lines : a x + 4 + 3 x + 1 b 8 x + 4 − 3 x + 2 E.9650 With American notations: to perform operations on al-gebraic expressions, we can lay them out in lines by aligning terms of the same kind. Examples: Here are the two operations posed : (4 x − 2) + ( − 2 x + 1) ; (5 x + 2) − ( − x − 1) Perform the operations below by laying them out in lines : a 8 x − 3 + − 2 x − 5 b − 5 x + 7 − − x + 1 E.10141 Perform the operations below by laying them out in lines : a x − 4 + − 3 x − 1 b 5 x + 1 − − 3 x − 2 E.9651 With American notations: to perform operations on al-gebraic expressions, we can lay them out in lines by aligning terms of the same kind. Examples: Here are the two operations posed : (2 x 2 + x − 2)+(5 x 2 − 3 x +1) ; ( x 2 +9 x +7) − (3 x 2 − 2) Perform the operations below by laying them out in lines : a x 2 − 3 + 5 x 2 − 2 x + 5 b x 2 + x − 4 − − 3 x 2 + 5 x − 1 c 3 x 2 + 7 − − x 2 − 5 x + 1 12. Unclassified exercises E.11207 Consider the two polygons ABCDEF and GHIJKL shown below and composed of rectangles : https://chingmath.fr chapExoCorrec/6358 sacados/6358 chapExoCorrec/6474 sacados/6474 chapExoCorrec/9649 sacados/9649 chapExoCorrec/10140 sacados/10140 chapExoCorrec/9650 sacados/9650 chapExoCorrec/10141 sacados/10141 chapExoCorrec/9651 sacados/9651 chapExoCorrec/11207 sacados/11207 x463ABCDEFx23GHIJKL
1 a Express the area of the polygon ABCDEF as a func-tion of x . b Propose the expression of this area as a product. 2 a Express the area of the polygon GHIJKL as a func-tion of x . b Propose the expression of this area as a product. E.11224 Consider the two polygons ABCDEF and GHIJKL shown below and composed of rectangles : 1 a Express the area of the polygon ABCDEF as a func-tion of x . b Propose the expression of this area as a product. 2 a Express the area of the polygon GHIJKL as a func-tion of x . b Propose the expression of this area as a product. https://chingmath.fr chapExoCorrec/11224 sacados/11224 x6.9.3ABCDEFx23GHIJKL