Grade 7 Algebra-Expressions and Equations

Transcription

1 ID : ae-7-algebra-expressions-and-equations [1] Grade 7 Algebra-Expressions and Equations For more such worksheets visit Answer the questions (1) Find the sum of following polynomials: A) 8x 3-14y 3-8xy + 16y and 5y 3-5x y + xy - x - y + 14 B) 8x y - xy - xy + y - 5 and -7x 3 + 5y 3 + x y - xy - xy - y () Hamal is setting up a factory to manufacture pens. If he buys a machine that costs Dhs5058, then he can manufacture a pen for Dhs1.. On the other hand, if he buys a machine that costs Dhs4800, he can manufacture a pen for Dhs4. How many pens should he manufacture, so that total cost is the same no matter which machine he buys? (3) Faisal bought a total of 16 hens and ducks. He got a discount of Dhs0.50 for each hen and a discount of Dhs 1.40 for each duck. He saved Dhs16.10 in total. How many hens did he buy? (4) If the average of numbers 3,, 1, 0, 19 and x is 7, find the value of x. (5) The number of days left in the month of June are one fifth the number of days already passed. How many days are left in the month of June? (6) Solve the equation to find value of y. -3y = (7) Find the value of (x - 8) + ( -3x - x - 7), when x = 3. (8) The ages of Aswad and Ain are in ratio 1:5. If sum of their ages is 4 years, what is the age of Aswad? (9) The number of hours left in the day is half the number of hours already passed. How many hours have already passed in the day? (10) The number of days left in the month of June are five times the number of days already passed. How many days have already passed in the month of June?

2 ID : ae-7-algebra-expressions-and-equations [] Choose correct answer(s) from the given choices (11) Find the area of the given shape. a. ad+(a-c)b b. ab+(a-c)d c. ad+cb d. ab+cd (1) How many blocks will be there in n th figure? a. (n+1) b. n+1 c. 3n- d. n (n+1) (13) Barakah is standing in a row. If she is n th from the front and m th from the back, how many people are standing in the row? a. n + m + 1 b. n + m - 1 c. n + m d. None of these (14) If 5x + 8 = 73, what will be the value of 5x - 8? a. 61 b. 54 c. 57 d. 64 (15) If x y = 18 1, then identify the incorrect expression from the following. a x - y = 0 b. 1 y = 18 x c. 1 x= 18 y d. x - y x + y = 6 30

3 ID : ae-7-algebra-expressions-and-equations [3] 017 Edugain ( All Rights Reserved Many more such worksheets can be generated at

4 Answers ID : ae-7-algebra-expressions-and-equations [4] (1) A) 8x 3-9y 3-5x y + xy - 8xy - x + 14y + 14 In order to add the given polynomials, let us first place the like terms one below other and add as usual. +8x3-14y3-8xy +16y +5y3-5xy +xy -x -y x3-9y3-5xy +xy -8xy -x +14y +14 Sum of the polynomials 8x 3-14y 3-8xy + 16y and 5y 3-5x y + xy - x - y + 14 is 8x 3-9y 3-5x y + xy - 8xy - x + 14y B) -7x 3 + 5y x y - 4xy - 4xy - 5 In order to add the given polynomials, let us first place the like terms one below other and add as usual. +8xy -xy -xy +y -5-7x3 +5y3 +xy -xy -xy -y -7x3 +5y3 +10xy -4xy -4xy -5 Sum of the polynomials 8x y - xy - xy + y - 5 and -7x 3 + 5y 3 + x y - xy - xy - y is -7x 3 + 5y x y - 4xy - 4xy - 5.

5 () 760 ID : ae-7-algebra-expressions-and-equations [5] Let us assume x as the number of pens manufactured, so that Hamal's total cost with both the machines is the same. With first machine, which costs Dhs5058, he can manufacture 1 pen for Dhs1.. Therefore, the total cost of x pens manufactured by the first machine = x With second machine, which costs Dhs4800, he can manufacture 1 pen for Dhs4. Therefore, the total cost of x pens manufactured by the second machine = x Since, the total cost of x pens manufactured by both machines is same. Therefore, x = x 4x - 1.x = x = 778 x = 778 = Step 5 Thus, the total cost of 760 pens manufactured by both the machines is the same no matter which machine he buys.

6 (3) 7 ID : ae-7-algebra-expressions-and-equations [6] Let us assume that Faisal bought x number of hens. Since, Faisal bought a total of 16 hens and ducks. Therefore, the number of ducks bought by Faisal = 16 - x Faisal got a discount of Dhs 0.50 for each hen. So, the total saving on x hens = 0.50x Faisal got a discount of Dhs 1.40 for each duck. So, the total saving on (16 - x) ducks = 1.40(16 - x) Since, Faisal saved Dhs16.10 in total, therefore 0.50x (16 - x) = x x = x x = ( )x = x = -6.3 x = x = 7 Step 5 Thus, the number of hens bought by Faisal are 7

7 (4) 57 ID : ae-7-algebra-expressions-and-equations [7] If we look at the question carefully, we notice that the average of the numbers 3,, 1, 0, 19 and x is 7. We have to find out the value of x from the numbers. Total numbers (3,, 1, 0, 19, and x) = x So, the average of the numbers = 6 numbers is 7] x = x = 7 6 x = x = 57 = 7 [Since, the average of Therefore the value of x is 57.

8 (5) 5 days ID : ae-7-algebra-expressions-and-equations [8] According to the question, Number of days left in the month of June = already passed Let the number of days already passed be. 1 5 Number of days So, the number of days left in the month of June = 5 We know that the total number of days in the month of June are 30 So, + 5 = 30 Or, 6 5 = 30 Or, = = 5 Step 5 Therefore, the number of days are left in the month of June = 5 5 = 5 days (6) y = 0.5 Let us solve the given equation by following the given steps: -3y = y = y = -1.5 y = Thus, y = 0.5

9 (7) -39 ID : ae-7-algebra-expressions-and-equations [9] The given expression is: (x - 8) + ( -3x - x - 7), where x = 3. Let us first simplify the given expression. (x - 8) + ( -3x - x - 7) = -x - x - 15 Now, let us put the value x = 3 in the simplified expression -x - x = -(3) - (3) - 15 = (-6) + (-15) = (-6) + (-15) = -39 Hence, the value of the expression (x - 8) + ( -3x - x - 7), when x = 3 is -39. (8) 7 years If we look at the question carefully, we notice that the ratio of Aswad's and Ain's ages is 1:5. Let us suppose that the age of Aswad is 1x, then the age of Ain is 5x. Since, the sum of their ages is 4 years, therefore 1x + 5x = 4 6x = 4 x = 4 6 x = 7 Thus, the age of Ain = 1x = 1 7 [Put x = 7] = 7 years

10 (9) 16 hours ID : ae-7-algebra-expressions-and-equations [10] According to the question number of hours left in the day = passed Let the number of hours already passed be. 1 Number of hours already So, the number of hours left in the day = We know that the total number of hours in a day = 4 So, + = 4 or, 3 = 4 or, = 4 3 = 16 Step 5 Therefore, the number of hours already passed in the day = 16 hours.

11 (10) 5 days ID : ae-7-algebra-expressions-and-equations [11] According to the question, the number of days left in the month of June = 5 Number of days already passed Let the number of days already passed be. So, the number of days left in the month of June = We know that the total number of days in the month of June are 30 So, = 30 Or, = 30 6 = 5 Step 5 Therefore, the number of days have already passed in the month of June = 5 days

12 (11) b. ab+(a-c)d ID : ae-7-algebra-expressions-and-equations [1] If we look at the given shape carefully, we notice that it is a combination of following shapes: Since, both the shapes are rectangular, sum of the area of both the shapes = ab+(a-c)d. This area is also equal to the area of the given shape. So, the area of the given shape is ab+(a-c)d. Hence, option b is the correct answer.

13 ID : ae-7-algebra-expressions-and-equations [13] (1) d. n (n+1) Number of block in 1 st figure = 1 Number of blocks in nd figure = 3 We can observe that the number of blocks in 3 rd figure = 3 (3 + 1) = 6 Now, we can say that the number of blocks in n th figure will be = n(n+1) Hence, option d is the correct answer. (13) b. n + m - 1 Since, Barakah is n th from the front, there are (n - 1) people who are standing in front of her. Similarly, since she is m th from the back, there are (m - 1) people who are standing behind her. Total number of people in the row = Number of people standing in front of Barakah + 1 (Barakah herself) + Number of people standing behind Barakah = (n - 1) (m - 1) = n + m - 1 Hence, option b is the correct answer.

14 (14) c. 57 ID : ae-7-algebra-expressions-and-equations [14] If we look at the question carefully, we notice that we have to find out the value of 5 x - 8. Firstly, we have to find the value of x from the expression 5x + 8 = 73. 5x = 73-8 x = 65 5 x = 13 Let us now place the value of x as 13, in the expression 5x x - 8 = (5 13) - 8 = 65-8 = 57 Thus, the correct answer is option c. (15) b. 1 y = 18 x If you look at the question carefully, you will notice that x y = by cross multiplying both sides x y = 18 1 can be written as: 1x = 18y If you observe all of options carefully, you will notice that if 1x = 18y, then 1 y is never equal to 18 x and hence the incorrect answer is 1 y = 18 x. Hence, option b is the correct answer.