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Page 1 Exercise 9.1 page: 9.5 1. Express each of the following in the language of ratios: (i) In a class, the number of girls in the merit list of the board examination is two times that of boys. (ii) The number of students passing mathematics test is 2/3 of the number that appeared. Solution: (i) Ratio of the number of girls to that of boys in the merit list is 2: 1. (ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 2. Express the following ratios in language of daily life: (i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. (ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. Solution: (i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. (ii) The number of villages is 2000 times that of cities in India. 3. Express each of the following ratios in its simplest form: (i) 60: 72 (ii) 324: 144 (iii) 85: 391 (iv) 186: 403 Solution: (i) 60: 72 It can be written as 60/72 We know that the HCF of 60 and 72 is 12 By dividing the term by 12 we get (60/72) × (12/12) = 5/6 So we get 60: 72 = 5: 6 (ii) 324: 144 It can be written as 324/144 We know that the HCF of 324 and 144 is 36 By dividing the term by 36 we get (324/144) × (36/36) = 9/4 So we get 324: 144 = 9: 4 (iii) 85: 391 It can be written as 85/391 We know that the HCF of 85 and 391 is 17 By dividing the term by 17 we get (85/391) × (17/17) = 5/23 So we get 85: 391 = 5: 23 (iv) 186: 403 It can be written as 186/403 Page 2 Exercise 9.1 page: 9.5 1. Express each of the following in the language of ratios: (i) In a class, the number of girls in the merit list of the board examination is two times that of boys. (ii) The number of students passing mathematics test is 2/3 of the number that appeared. Solution: (i) Ratio of the number of girls to that of boys in the merit list is 2: 1. (ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 2. Express the following ratios in language of daily life: (i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. (ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. Solution: (i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. (ii) The number of villages is 2000 times that of cities in India. 3. Express each of the following ratios in its simplest form: (i) 60: 72 (ii) 324: 144 (iii) 85: 391 (iv) 186: 403 Solution: (i) 60: 72 It can be written as 60/72 We know that the HCF of 60 and 72 is 12 By dividing the term by 12 we get (60/72) × (12/12) = 5/6 So we get 60: 72 = 5: 6 (ii) 324: 144 It can be written as 324/144 We know that the HCF of 324 and 144 is 36 By dividing the term by 36 we get (324/144) × (36/36) = 9/4 So we get 324: 144 = 9: 4 (iii) 85: 391 It can be written as 85/391 We know that the HCF of 85 and 391 is 17 By dividing the term by 17 we get (85/391) × (17/17) = 5/23 So we get 85: 391 = 5: 23 (iv) 186: 403 It can be written as 186/403 We know that the HCF of 186 and 403 is 31 By dividing the term by 31 we get (186/403) × (31/31) = 6/13 So we get 186: 403 = 6: 13 4. Find the ratio of the following in the simplest form: (i) 75 paise to Rs 3 (ii) 35 minutes to 45 minutes (iii) 8 kg to 400 gm (iv) 48 minutes to 1 hour (v) 2 metres to 35 cm (vi) 35 minutes to 45 seconds (vii) 2 dozen to 3 scores (viii) 3 weeks to 3 days (ix) 48 min to 2 hours 40 min (x) 3 m 5 cm to 35 cm Solution: (i) 75 paise to Rs 3 It can be written as 75 paise to Rs 3 = 75 paise: Rs 3 We know that 1 Rs = 100 paise So we get 75 paise to Rs 3 = 75 paise: 300 paise Dividing the two terms by HCF 75 75 paise to Rs 3 = 1: 4 (ii) 35 minutes to 45 minutes It can be written as 35 minutes to 45 minutes = 35 minutes: 45 minutes Dividing the two terms by HCF 5 35 minutes to 45 minutes = 7: 9 (iii) 8 kg to 400 gm It can be written as 8 kg to 400 gm = 8 kg: 400 gm We know that 1 kg = 1000 gm So we get 8 kg to 400 gm = 8000 gm: 400 gm Dividing the two terms by HCF 400 8 kg to 400 gm = 20: 1 (iv) 48 minutes to 1 hour It can be written as 48 minutes to 1 hour = 48 minutes: 1 hour We know that 1 hour = 60 minutes So we get 48 minutes to 1 hour = 48 minutes: 60 minutes Dividing the two terms by HCF 12 48 minutes to 1 hour = 4: 5 Page 3 Exercise 9.1 page: 9.5 1. Express each of the following in the language of ratios: (i) In a class, the number of girls in the merit list of the board examination is two times that of boys. (ii) The number of students passing mathematics test is 2/3 of the number that appeared. Solution: (i) Ratio of the number of girls to that of boys in the merit list is 2: 1. (ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 2. Express the following ratios in language of daily life: (i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. (ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. Solution: (i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. (ii) The number of villages is 2000 times that of cities in India. 3. Express each of the following ratios in its simplest form: (i) 60: 72 (ii) 324: 144 (iii) 85: 391 (iv) 186: 403 Solution: (i) 60: 72 It can be written as 60/72 We know that the HCF of 60 and 72 is 12 By dividing the term by 12 we get (60/72) × (12/12) = 5/6 So we get 60: 72 = 5: 6 (ii) 324: 144 It can be written as 324/144 We know that the HCF of 324 and 144 is 36 By dividing the term by 36 we get (324/144) × (36/36) = 9/4 So we get 324: 144 = 9: 4 (iii) 85: 391 It can be written as 85/391 We know that the HCF of 85 and 391 is 17 By dividing the term by 17 we get (85/391) × (17/17) = 5/23 So we get 85: 391 = 5: 23 (iv) 186: 403 It can be written as 186/403 We know that the HCF of 186 and 403 is 31 By dividing the term by 31 we get (186/403) × (31/31) = 6/13 So we get 186: 403 = 6: 13 4. Find the ratio of the following in the simplest form: (i) 75 paise to Rs 3 (ii) 35 minutes to 45 minutes (iii) 8 kg to 400 gm (iv) 48 minutes to 1 hour (v) 2 metres to 35 cm (vi) 35 minutes to 45 seconds (vii) 2 dozen to 3 scores (viii) 3 weeks to 3 days (ix) 48 min to 2 hours 40 min (x) 3 m 5 cm to 35 cm Solution: (i) 75 paise to Rs 3 It can be written as 75 paise to Rs 3 = 75 paise: Rs 3 We know that 1 Rs = 100 paise So we get 75 paise to Rs 3 = 75 paise: 300 paise Dividing the two terms by HCF 75 75 paise to Rs 3 = 1: 4 (ii) 35 minutes to 45 minutes It can be written as 35 minutes to 45 minutes = 35 minutes: 45 minutes Dividing the two terms by HCF 5 35 minutes to 45 minutes = 7: 9 (iii) 8 kg to 400 gm It can be written as 8 kg to 400 gm = 8 kg: 400 gm We know that 1 kg = 1000 gm So we get 8 kg to 400 gm = 8000 gm: 400 gm Dividing the two terms by HCF 400 8 kg to 400 gm = 20: 1 (iv) 48 minutes to 1 hour It can be written as 48 minutes to 1 hour = 48 minutes: 1 hour We know that 1 hour = 60 minutes So we get 48 minutes to 1 hour = 48 minutes: 60 minutes Dividing the two terms by HCF 12 48 minutes to 1 hour = 4: 5 (v) 2 metres to 35 cm It can be written as 2 metres to 35 cm = 2 metres: 35 cm We know that 1 m = 100 cm So we get 2 metres to 35 cm = 200 cm: 35 cm Dividing the two terms by HCF 5 2 metres to 35 cm = 40: 7 (vi) 35 minutes to 45 seconds It can be written as 35 minutes to 45 seconds = 35 minutes: 45 seconds We know that 1 minute = 60 seconds So we get 35 minutes to 45 seconds = 2100 seconds: 45 seconds Dividing the two terms by HCF 15 35 minutes to 45 seconds = 140: 3 (vii) 2 dozen to 3 scores It can be written as 2 dozen to 3 scores = 2 dozen: 3 scores We know that 1 dozen = 12 score = 20 So we get 2 dozen to 3 scores = 24: 60 Dividing the two terms by HCF 12 2 dozen to 3 scores = 2: 5 (viii) 3 weeks to 3 days It can be written as 3 weeks to 3 days = 3 weeks: 3 days We know that 1 week = 7 days So we get 3 weeks to 3 days = 21 days: 3 days Dividing the two terms by HCF 3 3 weeks to 3 days = 7: 1 (ix) 48 min to 2 hours 40 min It can be written as 48 min to 2 hours 40 min = 48 min: 2 hours 40 min We know that 1 hour = 60 minutes So we get 48 min to 2 hours 40 min = 48 min: 160 min Dividing the two terms by HCF 16 48 min to 2 hours 40 min = 3: 10 (x) 3 m 5 cm to 35 cm It can be written as 3 m 5 cm to 35 cm = 3 m 5 cm: 35 cm We know that 1 m = 100 cm So we get Page 4 Exercise 9.1 page: 9.5 1. Express each of the following in the language of ratios: (i) In a class, the number of girls in the merit list of the board examination is two times that of boys. (ii) The number of students passing mathematics test is 2/3 of the number that appeared. Solution: (i) Ratio of the number of girls to that of boys in the merit list is 2: 1. (ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 2. Express the following ratios in language of daily life: (i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. (ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. Solution: (i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. (ii) The number of villages is 2000 times that of cities in India. 3. Express each of the following ratios in its simplest form: (i) 60: 72 (ii) 324: 144 (iii) 85: 391 (iv) 186: 403 Solution: (i) 60: 72 It can be written as 60/72 We know that the HCF of 60 and 72 is 12 By dividing the term by 12 we get (60/72) × (12/12) = 5/6 So we get 60: 72 = 5: 6 (ii) 324: 144 It can be written as 324/144 We know that the HCF of 324 and 144 is 36 By dividing the term by 36 we get (324/144) × (36/36) = 9/4 So we get 324: 144 = 9: 4 (iii) 85: 391 It can be written as 85/391 We know that the HCF of 85 and 391 is 17 By dividing the term by 17 we get (85/391) × (17/17) = 5/23 So we get 85: 391 = 5: 23 (iv) 186: 403 It can be written as 186/403 We know that the HCF of 186 and 403 is 31 By dividing the term by 31 we get (186/403) × (31/31) = 6/13 So we get 186: 403 = 6: 13 4. Find the ratio of the following in the simplest form: (i) 75 paise to Rs 3 (ii) 35 minutes to 45 minutes (iii) 8 kg to 400 gm (iv) 48 minutes to 1 hour (v) 2 metres to 35 cm (vi) 35 minutes to 45 seconds (vii) 2 dozen to 3 scores (viii) 3 weeks to 3 days (ix) 48 min to 2 hours 40 min (x) 3 m 5 cm to 35 cm Solution: (i) 75 paise to Rs 3 It can be written as 75 paise to Rs 3 = 75 paise: Rs 3 We know that 1 Rs = 100 paise So we get 75 paise to Rs 3 = 75 paise: 300 paise Dividing the two terms by HCF 75 75 paise to Rs 3 = 1: 4 (ii) 35 minutes to 45 minutes It can be written as 35 minutes to 45 minutes = 35 minutes: 45 minutes Dividing the two terms by HCF 5 35 minutes to 45 minutes = 7: 9 (iii) 8 kg to 400 gm It can be written as 8 kg to 400 gm = 8 kg: 400 gm We know that 1 kg = 1000 gm So we get 8 kg to 400 gm = 8000 gm: 400 gm Dividing the two terms by HCF 400 8 kg to 400 gm = 20: 1 (iv) 48 minutes to 1 hour It can be written as 48 minutes to 1 hour = 48 minutes: 1 hour We know that 1 hour = 60 minutes So we get 48 minutes to 1 hour = 48 minutes: 60 minutes Dividing the two terms by HCF 12 48 minutes to 1 hour = 4: 5 (v) 2 metres to 35 cm It can be written as 2 metres to 35 cm = 2 metres: 35 cm We know that 1 m = 100 cm So we get 2 metres to 35 cm = 200 cm: 35 cm Dividing the two terms by HCF 5 2 metres to 35 cm = 40: 7 (vi) 35 minutes to 45 seconds It can be written as 35 minutes to 45 seconds = 35 minutes: 45 seconds We know that 1 minute = 60 seconds So we get 35 minutes to 45 seconds = 2100 seconds: 45 seconds Dividing the two terms by HCF 15 35 minutes to 45 seconds = 140: 3 (vii) 2 dozen to 3 scores It can be written as 2 dozen to 3 scores = 2 dozen: 3 scores We know that 1 dozen = 12 score = 20 So we get 2 dozen to 3 scores = 24: 60 Dividing the two terms by HCF 12 2 dozen to 3 scores = 2: 5 (viii) 3 weeks to 3 days It can be written as 3 weeks to 3 days = 3 weeks: 3 days We know that 1 week = 7 days So we get 3 weeks to 3 days = 21 days: 3 days Dividing the two terms by HCF 3 3 weeks to 3 days = 7: 1 (ix) 48 min to 2 hours 40 min It can be written as 48 min to 2 hours 40 min = 48 min: 2 hours 40 min We know that 1 hour = 60 minutes So we get 48 min to 2 hours 40 min = 48 min: 160 min Dividing the two terms by HCF 16 48 min to 2 hours 40 min = 3: 10 (x) 3 m 5 cm to 35 cm It can be written as 3 m 5 cm to 35 cm = 3 m 5 cm: 35 cm We know that 1 m = 100 cm So we get 3 m 5 cm to 35 cm = 305 cm: 35 cm Dividing the two terms by HCF 5 3 m 5 cm to 35 cm = 61: 7 5. Find the ratio of (i) 3.2 metres to 56 metres (ii) 10 metres to 25 cm (iii) 25 paise to Rs 60 (iv) 10 litres to 0.25 litre Solution: (i) 3.2 metres to 56 metres It can be written as 3.2 metres to 56 metres = 3.2 metres: 56 metres Dividing the two terms by HCF 1.6 3.2 metres to 56 metres = 2: 35 (ii) 10 metres to 25 cm It can be written as 10 metres to 25 cm = 10 m: 25 cm We know that 1 m = 100 cm 10 metres to 25 cm = 1000 cm: 25 cm Dividing the two terms by HCF 25 10 metres to 25 cm = 40: 1 (iii) 25 paise to Rs 60 It can be written as 25 paise to Rs 60 = 25 paise: Rs 60 We know that 1 Rs = 100 paise 25 paise to Rs 60 = 25 paise: 6000 paise Dividing the two terms by HCF 25 25 paise to Rs 60 = 1: 240 (iv) 10 litres to 0.25 litre It can be written as 10 litres to 0.25 litre = 10 litres: 0.25 litre Dividing the two terms by HCF 0.25 10 litres to 0.25 litre = 40: 1 6. The number of boys and girls in a school are 1168 and 1095 respectively. Express the ratio of the number of boys to that of the girls in the simplest form. Solution: No. of boys = 1168 No. of girls = 1095 So the ratio of the number of boys to that of the girls = 1168: 1095 Dividing the two terms by HCF 73 Ratio of number of boys to that of the girls = 16: 15 Hence, the ratio of the number of boys to that of girls in simplest form is 16: 15. Page 5 Exercise 9.1 page: 9.5 1. Express each of the following in the language of ratios: (i) In a class, the number of girls in the merit list of the board examination is two times that of boys. (ii) The number of students passing mathematics test is 2/3 of the number that appeared. Solution: (i) Ratio of the number of girls to that of boys in the merit list is 2: 1. (ii) Ratio of the number of students passing a mathematics test to that of total students appearing in the test is 2: 3. 2. Express the following ratios in language of daily life: (i) The ratio of the number of bad pencils to that of good pencils produced in a factory is 1: 9. (ii) In India, the ratio of the number of villages to that of cities is about 2000: 1. Solution: (i) The number of bad pencils produced in a factory is 1/9 of the number of good pencils produced in the factory. (ii) The number of villages is 2000 times that of cities in India. 3. Express each of the following ratios in its simplest form: (i) 60: 72 (ii) 324: 144 (iii) 85: 391 (iv) 186: 403 Solution: (i) 60: 72 It can be written as 60/72 We know that the HCF of 60 and 72 is 12 By dividing the term by 12 we get (60/72) × (12/12) = 5/6 So we get 60: 72 = 5: 6 (ii) 324: 144 It can be written as 324/144 We know that the HCF of 324 and 144 is 36 By dividing the term by 36 we get (324/144) × (36/36) = 9/4 So we get 324: 144 = 9: 4 (iii) 85: 391 It can be written as 85/391 We know that the HCF of 85 and 391 is 17 By dividing the term by 17 we get (85/391) × (17/17) = 5/23 So we get 85: 391 = 5: 23 (iv) 186: 403 It can be written as 186/403 We know that the HCF of 186 and 403 is 31 By dividing the term by 31 we get (186/403) × (31/31) = 6/13 So we get 186: 403 = 6: 13 4. Find the ratio of the following in the simplest form: (i) 75 paise to Rs 3 (ii) 35 minutes to 45 minutes (iii) 8 kg to 400 gm (iv) 48 minutes to 1 hour (v) 2 metres to 35 cm (vi) 35 minutes to 45 seconds (vii) 2 dozen to 3 scores (viii) 3 weeks to 3 days (ix) 48 min to 2 hours 40 min (x) 3 m 5 cm to 35 cm Solution: (i) 75 paise to Rs 3 It can be written as 75 paise to Rs 3 = 75 paise: Rs 3 We know that 1 Rs = 100 paise So we get 75 paise to Rs 3 = 75 paise: 300 paise Dividing the two terms by HCF 75 75 paise to Rs 3 = 1: 4 (ii) 35 minutes to 45 minutes It can be written as 35 minutes to 45 minutes = 35 minutes: 45 minutes Dividing the two terms by HCF 5 35 minutes to 45 minutes = 7: 9 (iii) 8 kg to 400 gm It can be written as 8 kg to 400 gm = 8 kg: 400 gm We know that 1 kg = 1000 gm So we get 8 kg to 400 gm = 8000 gm: 400 gm Dividing the two terms by HCF 400 8 kg to 400 gm = 20: 1 (iv) 48 minutes to 1 hour It can be written as 48 minutes to 1 hour = 48 minutes: 1 hour We know that 1 hour = 60 minutes So we get 48 minutes to 1 hour = 48 minutes: 60 minutes Dividing the two terms by HCF 12 48 minutes to 1 hour = 4: 5 (v) 2 metres to 35 cm It can be written as 2 metres to 35 cm = 2 metres: 35 cm We know that 1 m = 100 cm So we get 2 metres to 35 cm = 200 cm: 35 cm Dividing the two terms by HCF 5 2 metres to 35 cm = 40: 7 (vi) 35 minutes to 45 seconds It can be written as 35 minutes to 45 seconds = 35 minutes: 45 seconds We know that 1 minute = 60 seconds So we get 35 minutes to 45 seconds = 2100 seconds: 45 seconds Dividing the two terms by HCF 15 35 minutes to 45 seconds = 140: 3 (vii) 2 dozen to 3 scores It can be written as 2 dozen to 3 scores = 2 dozen: 3 scores We know that 1 dozen = 12 score = 20 So we get 2 dozen to 3 scores = 24: 60 Dividing the two terms by HCF 12 2 dozen to 3 scores = 2: 5 (viii) 3 weeks to 3 days It can be written as 3 weeks to 3 days = 3 weeks: 3 days We know that 1 week = 7 days So we get 3 weeks to 3 days = 21 days: 3 days Dividing the two terms by HCF 3 3 weeks to 3 days = 7: 1 (ix) 48 min to 2 hours 40 min It can be written as 48 min to 2 hours 40 min = 48 min: 2 hours 40 min We know that 1 hour = 60 minutes So we get 48 min to 2 hours 40 min = 48 min: 160 min Dividing the two terms by HCF 16 48 min to 2 hours 40 min = 3: 10 (x) 3 m 5 cm to 35 cm It can be written as 3 m 5 cm to 35 cm = 3 m 5 cm: 35 cm We know that 1 m = 100 cm So we get 3 m 5 cm to 35 cm = 305 cm: 35 cm Dividing the two terms by HCF 5 3 m 5 cm to 35 cm = 61: 7 5. Find the ratio of (i) 3.2 metres to 56 metres (ii) 10 metres to 25 cm (iii) 25 paise to Rs 60 (iv) 10 litres to 0.25 litre Solution: (i) 3.2 metres to 56 metres It can be written as 3.2 metres to 56 metres = 3.2 metres: 56 metres Dividing the two terms by HCF 1.6 3.2 metres to 56 metres = 2: 35 (ii) 10 metres to 25 cm It can be written as 10 metres to 25 cm = 10 m: 25 cm We know that 1 m = 100 cm 10 metres to 25 cm = 1000 cm: 25 cm Dividing the two terms by HCF 25 10 metres to 25 cm = 40: 1 (iii) 25 paise to Rs 60 It can be written as 25 paise to Rs 60 = 25 paise: Rs 60 We know that 1 Rs = 100 paise 25 paise to Rs 60 = 25 paise: 6000 paise Dividing the two terms by HCF 25 25 paise to Rs 60 = 1: 240 (iv) 10 litres to 0.25 litre It can be written as 10 litres to 0.25 litre = 10 litres: 0.25 litre Dividing the two terms by HCF 0.25 10 litres to 0.25 litre = 40: 1 6. The number of boys and girls in a school are 1168 and 1095 respectively. Express the ratio of the number of boys to that of the girls in the simplest form. Solution: No. of boys = 1168 No. of girls = 1095 So the ratio of the number of boys to that of the girls = 1168: 1095 Dividing the two terms by HCF 73 Ratio of number of boys to that of the girls = 16: 15 Hence, the ratio of the number of boys to that of girls in simplest form is 16: 15. 7. Avinash works as a lecturer and earns Rs 12000 per month. His wife who is a doctor earns Rs 15000 per month. Find the following ratios: (i) Avinash’s income to the income of his wife. (ii) Avinash’s income to their total income. Solution: Avinash salary earned per month = Rs 12000 Avinash wife salary per month = Rs 15000 (i) Avinash’s income to the income of his wife = 12000/15000 = 4: 5 (ii) Avinash’s income to their total income = 12000/ (12000 + 15000) = 4: 9 8. Of the 72 persons working in an office, 28 are men and the remaining are women. Find the ratio of the number of: (i) men to that of women, (ii) men to the total number of persons (iii) persons to that of women. Solution: No. of persons working in an office = 72 No. of men = 28 So the number of women = 72 – 28 = 44 (i) men to that of women = 28: 44 Multiplying and dividing the equation by HCF 4 Men to that of women = (28/44) × (4/4) = 7: 11 (ii) men to the total number of persons = 28: 72 Multiplying and dividing the equation by HCF 4 Men to the total number of persons = (28/72) × (4/4) = 7: 18 (iii) persons to that of women = 72: 44 Multiplying and dividing the equation by HCF 4 Persons to that of women = (72/44) × (4/4) = 18: 11 9. The length of a steel tape for measurements of buildings is 10 m and its width is 2.4 cm. What is the ratio of its length to width? Solution: It is given that Length of a steel tape = 10 m Width of steel tape = 2.4 cm So the ratio of its length to width = 10 m/ 2.4 cm We know that 1 m = 100 cm Ratio of its length to width = 1000 cm/ 2.4 cm Dividing the two terms by HCF 0.8 cm Ratio of its length to width = 1250: 3 Hence, the ratio of its length to width is 1250: 3.Read More
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1. What is the concept of ratio in mathematics? 
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