ID : in-6-full-year-6th-grade-review [1] Class 6 Full Year 6th Grade Review For more such worksheets visit www.edugain.com Answer the questions (1) Parallelogram ABCD is given below, what is the ratio of the area of the triangle ABC to the area of the parallelogram ABCD? (2) If the number in the center is the sum of the rest of the numbers, find the value of z. 2 4 106 5z 5z (3) 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? (4) The table below shows the number of books read by five children in one month. Name Number of books Lovleen? Sanjana 9 Ajoy 13 Ismail 8 Akshiti 25 If Lovleen read 6 books more than 1 5 of the total number of books read by the other four children, then how many books did Lovleen read in a month? (5) The sum of two numbers is 13527. If one of the addends is twice the other addend, then what is the value of the smaller addend? (6) The side of an equilateral triangle is shown as b. Find the perimeter of the equilateral triangle using b. (7) Convert the following fractions into percent: (Write the answers upto 3 decimal places) A) 8 2 B) 20 4 C) 27 9
D) 8 64 E) 72 36 F) 35 ID : in-6-full-year-6th-grade-review [2] 10 (8) Rajesh bought the following things from his first salary: A gaming system for Rs. 1410.65 Some clothes for Rs. 4966.15 A television for Rs. 15779.60 If his salary is Rs. 50000, how much money is he left with after all the shopping? (9) A survey was done in all schools of Pune, where each student was asked for their favorite colour. Result of survey is shown in the circle chart. Which is the most liked colour among students in Pune? (10) If we have to divide Rs. 1080 into three proportional shares with the ratio of 7:5:6, then what will be the value of the largest share? (11) The sum of 4 consecutive odd numbers is 56. Find the numbers. (12) Alisha has 1200 toffees that she wants to distribute on her birthday. She distributes 7 15 of these in the class. Out of the remaining toffees, she distributes 2 5 to her teachers. How many toffees are left with her? (13) What is the area of the shaded region in the given figure? Choose correct answer(s) from the given choices (14) If e and f are two whole numbers, the commutative property is applicable for their subtraction if and only if : a. e = f b. e f c. e < f d. e > f
(15) Harsh drew a rectangle as shown below. Then he cuts along the line and slide the triangle to the opposite side. Which figure did he get after this move? ID : in-6-full-year-6th-grade-review [3] a. A pentagon b. A square c. A parallelogram d. A triangle 2017 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : in-6-full-year-6th-grade-review [4] (1) 1:2 We know that the opposite sides of a parallelogram are equal in length. So in triangles BCA and DCA: AD = BC (Opposite sides of a parallelogram) BA = CD (Opposite sides of a parallelogram) AC = AC (Common side) We may say that all the sides of these two triangles are equal. This also means that the area of both the triangles is equal which is equal to half the area of the parallelogram. This means the ratio of the area of triangle ABC to the parallelogram ABCD will be 1:2. (2) 10 It is given that 106 is the sum of 2, 4, 5z, and 5z Therefore, 2 + 4 + 5z + 5z = 106 10z + 6 = 106 10z = 106-6 z = 100 10 z = 10 Thus, the value of z is 10.
(3) 16 hours ID : in-6-full-year-6th-grade-review [5] According to the question number of hours left in the day = passed Let the number of hours already passed be. 1 2 Number of hours already So, the number of hours left in the day = 2 Step 4 We know that the total number of hours in a day = 24 So, + 2 = 24 or, 3 2 = 24 or, = 24 2 3 = 16 Step 5 Therefore, the number of hours already passed in the day = 16 hours. (4) 17 Total number of books read by Sanjana, Ajoy, Ismail and Akshiti, = 9 + 13 + 8 + 25 = 55 It is given that Lovleen reads 6 books more than 1 5 of total number of books read by other four children, that is, 6 more than 1 5 of 55. Therefore, number of books read by Lovleen = = 11 + 6 = 17 books 1 5 55 + 6
(5) 4509 ID : in-6-full-year-6th-grade-review [6] It is given that one of the numbers is twice the other number. Therefore, their sum should be thrice the other number. We know, sum of the given numbers = 3 the other number Therefore, the other number = 13527 3 = 4509 (6) 3b The perimeter of a shape (polygon) is equal to the sum of length of all its sides. A triangle has 3 sides and in the case of an equilateral triangle, all sides are of equal length. Therefore, the perimeter is equal to three times the length of a side. = 3 b = 3b (7) A) 400.000 % To convert any fraction into percent, we have to multiply it with 100. Therefore, the fraction 8 2 can be converted into percent as: 8 2 = 8 2 100 = 400.000 % Hence, the percent of fraction 8 2 is 400.000 %.
B) 500.000 % ID : in-6-full-year-6th-grade-review [7] To convert any fraction into percent, we have to multiply it with 100. Therefore, the fraction 20 4 can be converted into percent as: 20 4 = 20 4 100 = 500.000 % Hence, the percent of fraction 20 4 is 500.000 %. C) 300.000 % To convert any fraction into percent, we have to multiply it with 100. Therefore, the fraction 27 9 can be converted into percent as: 27 9 = 27 9 100 = 300.000 % Hence, the percent of fraction 27 9 is 300.000 %.
D) 12.500 % ID : in-6-full-year-6th-grade-review [8] To convert any fraction into percent, we have to multiply it with 100. Therefore, the fraction 8 64 can be converted into percent as: 8 64 = 8 64 100 = 12.500 % Hence, the percent of fraction 8 64 is 12.500 %. E) 200.000 % To convert any fraction into percent, we have to multiply it with 100. Therefore, the fraction 72 36 can be converted into percent as: 72 36 = 72 36 100 = 200.000 % Hence, the percent of fraction 72 36 is 200.000 %.
F) 350.000 % ID : in-6-full-year-6th-grade-review [9] To convert any fraction into percent, we have to multiply it with 100. Therefore, the fraction 35 10 can be converted into percent as: 35 10 = 35 10 100 = 350.000 % Hence, the percent of fraction 35 10 is 350.000 %.
(8) Rs. 27843.60 ID : in-6-full-year-6th-grade-review [10] Amount received by Rajesh as his salary = Rs. 50000 Let us add the money spent by Rajesh: Ten Thousands Thousands Hundreds Tens Ones. Tenth Hundredth A gaming system 1 4 1 0. 6 5 Some clothes 4 9 6 6. 1 5 A television 1 5 7 7 9. 6 0 Total Expense 2 2 1 5 6. 4 0 Hence, Rajesh's total expense is Rs. 22156.40. In order to find the amount left with Rajesh, let us subtract his total expense from his salary : Amount left with Rajesh = Rajesh's salary - Rajesh's total expense = 50000-22156.40 = 50000.00-22156.40...(Writing 50000 in decimal form 50000.00 so that the two numbers are Like Decimals) Step 4 Now, let us subtract 22156.40 from 50000.00 by placing the digits of the two decimal numbers according to their place values: Ten Thousands Thousands Hundreds Tens Ones. Tenth Hundredth 5 0 0 0 0. 0 0-2 2 1 5 6. 4 0 2 7 8 4 3. 6 0 Step 5 Hence, Rajesh is left with Rs. 27843.60 after all his shopping.
(9) Red ID : in-6-full-year-6th-grade-review [11] If you look at the circle chart carefully, you will notice that the colour which has most survey in circle chart is Red. The colour which has most survey in circle chart, is the most liked colour among students in Pune, therefore the most liked colour among students in Pune is Red. (10) Rs. 420 Let us assume x as the proportionality constant. Rs. 1080 is divided into three shares of 7x, 5x, and 6x. So, 7x + 5x + 6x = Rs. 1080 18x = Rs. 1080 Rs. 1080 x = 18 x = Rs. 60 Therefore, all the three shares: 7x = 7 Rs. 60 = Rs. 420 5x = 5 Rs. 60 = Rs. 300 6x = 6 Rs. 60 = Rs. 360 Step 4 Now, if we compare all the three shares, we notice that the value of the largest share is Rs. 420.
(11) 11, 13, 15 and 17 ID : in-6-full-year-6th-grade-review [12] Let x be an odd number, therefore 4 consecutive odd numbers are x, x + 2, x + 4 and x + 6. The sum of 4 consecutive odd numbers is 56. x + x + 2 + x + 4 + x + 6 = 56 4x + 12 = 56 4x = 56-12 4x = 44 x = 44 4 x = 11 Therefore, the 4 consecutive odd numbers are 11, 13, 15 and 17.
(12) 384 ID : in-6-full-year-6th-grade-review [13] The given problem has a whole number and a few fraction numbers. A fraction is a number representing a part of a whole. The total number of toffees Alisha has = 1200...(a whole number) The number of toffees Alisha distributes in the class = 7 15 of 1200 = 1200 7 15 = 8400 15 = 560 Step 4 We just found that Alisha distributes 560 out of 1200 toffees in the class. Thus, the number of toffees Alisha is now left with = 1200-560 = 640 toffees Step 5 Alisha distributes 2 5 of the remaining toffees to the teachers: 2 5 of 640 = 2 5 640 = 1280 5 = 256 Thus the number of toffees Alisha distributes to the teachers = 256. Step 6 The total number of toffees Alisha distributed = The number of toffees she distributed in the class + The number of toffees she distributed to her teachers = 560 + 256 = 816 Step 7 In order to find the number of toffees now left with Alisha, let us subtract the total number of toffees she initially had with the total number of toffees she distributed: 1200-816 = 384 Step 8 The number of toffees left with Alisha are 384.
ID : in-6-full-year-6th-grade-review [14] (13) 112 m 2 The given figure is a rectangle, where the length is 16m and the breadth is 14m. There are 4 rectangles unshaded at the corners of the figure. If we find their area and subtract from the area of whole rectangle, we'll get the area of the shaded portion. The shaded length is 2m, therefore the length of the unshaded area will be 16-2 = 14m. Since the shaded length lies at the center, we can say that the length of the rectangles at the corners is 14 2 = 7m each. Step 4 The shaded breadth is 6m, therefore the unshaded breadth will be 14-6 = 8m. Again, since the breadth lies at the center, we can say that the breadth of the corner rectangles will be 8 2 = 4m Step 5 We now have four unshaded rectangles of length 7m and breadth 4m. The area of one such rectangle will be 7 4 = 28 sq. m. Step 6 Therefore the area of four such rectangles will be 4 28 = 112 sq. m. Step 7 The area of the big rectangle = 16 14 = 224 sq. m. Step 8 Therefore the area of the shaded portion = 224-112 = 112 sq. m. (14) a. e = f The Commutative Property is applicable to an algebraic operation if the order of the operands does not matter. For example, a + b = b + a and a b = b a. For the Commutative Property to be applied for the subtraction of two whole numbers e and f, the numbers should be equal. Hence, the values e - f and f - e will be equal only if e = f, in which case the value would become 0.
(15) c. A parallelogram ID : in-6-full-year-6th-grade-review [15] According to the question, Harsh cuts the given parallelogram along the line and slide the triangle to the opposite side. The figure we get after this move is: Therefore, we can say that Harsh gets a parallelogram. Step 4 Hence, option c is the correct answer.