Grade 6 Ratio and Proportion

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1 ID : ae-6-ratio-and-proportion [1] Grade 6 Ratio and Proportion For more such worksheets visit Answer t he quest ions (1) If 15 pieces of chain can be tied together to f orm a chain that is meters long, then how many segments are needed to make a chain that is meters long (2) For the last 9 days Kamal spent the same amount every day, and has spent a total of Dhs63. If he has Dhs70 lef t with him, in how many more days will he f inish this amount? (3) The parking lot of the theater has a capacity of 1025 cars. On Monday, the ratio of the empty parking spots to occupied parking spots is 15:26. How many cars were parked there on that day? (4) In a test that Ghada wrote, the ratio of the right answers to the wrong answers that she got was 15:11. If she got 33 answers wrong, then how many right answers did she get? (5) Asma buys a car af ter taking a loan f rom a bank. The loan has to be repaid in equal installments over 2 years. If she has paid Dhs in 9 months, how much more money will she be paying back to the bank? (6) In an of f ice, the workers start their work daily at 08:30 AM and end at 05:50 PM. They get a break of 45 minutes f or eating lunch, and two cof f ee breaks of 10 minutes each. What is the simplest f orm of the ratio of the time they spend working to the time they spend on breaks? (7) Two walls of a hall have to be painted. The f irst wall is of length 19 meters and height 8 meters. The cost of the paint f or this wall is Dhs30 per square meter. The second wall is of length 19 meters and height 5 meters. The cost of the paint f or this wall is Dhs35 per square meters. What is the ratio of the costs of painting the f irst wall to the second one? Choose correct answer(s) f rom given choice (8) In the proportion 13:147::52:588, the means are: a. 52,588 b. 13,588 c. 147,52 d. 13,147 (9) The ratio of 4 hours 30 minutes to 26 hours 15 minutes is a. 7:35 b. 36:6 c. 35:6 d. 6:35

2 ID : ae-6-ratio-and-proportion [2] (10) Alim and Aisha started a competition to see who can collect the most number of stamps. At the end of one month, the ratio of the stamps Alim had to those that Aisha had was 49:57. Aisha then collected 270 stamps in one day and the ratio then became 49:66. How many stamps does Alim now have? a b c d Fill in the blanks (11) If the cost of 11 kg of corn is Dhs then kilograms of corn can be bought using Dhs (12) If the weight of 17 boxes of cookies is 18.7 kg then the weight of 35 boxes in kilograms is kg (13) Aisha is 20 years old, and her neighbor Jabir is 29 years old. In 10 years, the ratio of their ages will be : (14) The ratio of 160 g to 0.98 kg is. (15) Given the proportion 125:200::200:320, the mean proportion is 2016 Edugain ( All Rights Reserved Many more such worksheets can be generated at

3 Answers ID : ae-6-ratio-and-proportion [3] (1) 41 Number of segments needed to make meter long chain 15 or the number of segments needed to make 1 meter long chain Theref ore the number of segments needed to make meter long chain (2) 10 The number of days taken by Kamal to spent Dhs63 9 days. Since he spent same amount every day, the number of days taken by Kamal to spent Dhs1 9 1 days The number of days will be taken by Kamal to spent Dhs days. Thus, he will f inish Dhs70 lef t with him in 10 days.

4 (3) 650 ID : ae-6-ratio-and-proportion [4] The capacity of the parking in theater 1025 cars. Let the occupied parking spots has x number of cars. Theref ore, The number of empty parking spots capacity of the parking in theater - occupied parking spots x Theref ore the ratio of the empty parking spots to occupied parking spots is ( x):x x x Since it is given that the ratio of the empty parking spots to occupied parking spots is 15: x 26 x or 15x 26( x) or 15x x or 15x + 26x or 41x or x or x 650 Theref ore the number of cars parked there x 650 cars

5 (4) 45 ID : ae-6-ratio-and-proportion [5] According to the question, the ratio of the right answers to the wrong answers Ghada got 15: The number of answers Ghada got wrong 33. Let's assume Ghada got r right answers. The ratio of the right answers to the wrong answers r Theref ore, By cross multiplying both sides: 11r or, r 11 or r 45. Thus, she got 45 right answers. r 33. (5) Dhs Because the loan has to be repaid in equal installments over 2 years and we know that 1 year 12 months or 2 years months. Theref ore we can say that the loan has to be repaid in equal installments over 24 months. The Dhs paid by her in 9 months Dhs or the Dhs paid by her in 1 month or monthly installment Dhs Theref ore the Dhs will be paid by her in 24 months Dhs The remaining money will be paid by her to the bank The money will be paid by her in 24 months - The money paid by her in 9 months Dhs Dhs Dhs 78000

6 (6) 99:13 ID : ae-6-ratio-and-proportion [6] According to the question, in an of f ice, the workers start their work daily at 08:30 AM and end at 05:50 PM. T otal working time with breaks, 05:50 PM - 08:30 AM 9 hours 20 minutes 560 minutes Time f or lunch breaks 45 minutes Time f or cof f ee break 10 minutes Since their are two cof f ee breaks, the total time f or cof f ee breaks minutes Total breaks time time f or lunch break + time f or cof f ee breaks minutes Total working time without breaks minutes Now, the ratio of the time they spend on working to the time they spend on breaks, Time spend on work Time spend on breaks :13 Step 5 Theref ore, the ratio of the time spend on working to the time spend on breaks is 99:13.

7 (7) 48:35 ID : ae-6-ratio-and-proportion [7] The length of f irst wall 19 meters The height of f irst wall 8 meters The area of f irst wall length of f irst wall height of f irst wall 19 8 m 2 The cost of the paint f or f irst wall is Dhs30 per square meter. Theref ore the cost of painting the f irst wall Dhs The length of second wall 19 meters The height of second wall 5 meters The area of second wall length of second wall height of second wall 19 5 m 2 The cost of the paint f or second wall is Dhs35 per square meter. Theref ore the cost of painting the second wall Dhs Step 5 The f raction of the costs of painting the f irst wall to the second one Step 6 Dhs Dhs Theref ore the ratio of the costs of painting the f irst wall to the second one 48:35 (8) c. 147,52 13:147::52:588 can be written as The f our parts of the proportion are separated into two groups, the means and the extremes, based on their arrangement in the proportion. Reading f rom lef t-to-right and topto-bottom, the means are the second and third numbers. Remembering that mean is a type of average may help you remember that the means of a proportion are in the middle when reading lef t-to-right, top-to-bottom. Theref ore the means of the proportion are 147,52

8 (9) d. 6:35 ID : ae-6-ratio-and-proportion [8] If you look at the question caref ully, you will notice that, you have to f ind out the ratio of 4 hours 30 minutes to 26 hours 15 minutes. First of all we have to change each value in the same unit. Since we know that 1 hour 60 minutes. 4 hours minutes. 26 hours minutes. theref ore 4 hours 30 minutes 240 minutes + 30 minutes 270 minutes. 26 hours 15 minutes 1560 minutes + 15 minutes 1575 minutes. Now the ratio of 270 minutes to 1575 minutes :35 Theref ore the ratio of 4 hours 30 minutes to 26 hours 15 minutes is 6:35.

9 (10) a ID : ae-6-ratio-and-proportion [9] The ratio of the stamps collected by Kazuhito and Hinata at the end of the month was 49:57. Let the number of total stamps collected by Kazuhito and Hinata by the end of the month be 49x and 57x respectively. Now, additional stamps collected by Aisha in one day 270. This means, the new number of Hinata s stamps 57x On equating new ratios, 49x 49 57x x 57x x 1 57x x 57x x - 57x 270 (66-57)x 270 9x 270 x x 30 Stamps collected by Alim 49x Step 5 Theref ore, the total number of stamps collected by the Alim is (11) 26 Number of kgs can be purchased using Dhs kg 11 or the number of kgs can be purchased using Dhs kg Theref ore the number of kgs can be purchased using Dhs kg

10 (12) 38.5 ID : ae-6-ratio-and-proportion [10] The weight of 17 boxes of cookies 18.7 kg or, the weight of 1 box of cookies kg 17 Theref ore, the weight of 35 boxes of cookies kg (13) The present age of Aisha is 20 years, theref ore the age of Aisha af ter 10 years years The present age of Jabir is 29 years, theref ore the age of Jabir af ter 10 years years The f raction of their ages af ter 10 years Theref ore the ratio of their ages af ter 10 years 10:13 (14) 8:49 If we look at the question caref ully, we will notice that the unit of the numbers 160 g and 0.98 kg are dif f erent. We have to f irst convert both numbers into same unit. Since we know that, 1kg 1000g, 0.98 kg 980 g. Now we have to f ind the ratio of 160 g and 980 g. The ratio of 160 g to 980 g Theref ore, the ratio of 160 g to 0.98 kg 8:49.

11 (15) 200 ID : ae-6-ratio-and-proportion [11] 125:200::200:320 can be written as The f our parts of the proportion are separated into two groups, the means and the extremes, based on their arrangement in the proportion. Reading f rom lef t-to-right, the mean terms are the second and third numbers. For cases where second and third terms are same, the middle terms are called the mean proportion between f irst and f ourth terms. Theref ore the mean proportion is 200

Class 4 Unitary Method

ID : in-4-unitary-method [1] Class 4 Unitary Method For more such worksheets visit www.edugain.com Answer t he quest ions (1) 96 baskets of guavas weigh 40.992 kilograms. What will be the weight of 61