Page 1 Exercise 6.7 page: 6.24 1. Write each fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions: Solution: Page 2 Exercise 6.7 page: 6.24 1. Write each fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions: Solution: 2. Mark 2/6, 4/6, 8/6 and 6/6 on the number line and put appropriate signs between fractions given below: (i) 5/6 …….. 2/6 (ii) 3/6 ……. 0/6 (iii) 1/6 …… 6/6 (iv) 8/6 …… 5/6 Solution: (i) We know that 5/6 > 2/6 as 5 > 2 and the denominator is same. (ii) We know that 3/6 > 0/6 as 3 > 0 and the denominator is same. (iii) We know that 1/6 < 6/6 as 6 > 1 and the denominator is same. (iv) We know that 8/6 > 5/6 as 8 > 5 and the denominator is same. 3. Compare the following fractions and put an appropriate sign: (i) 3/6 …… 5/6 (ii) 4/5 …… 0/5 (iii) 3/20 …… 4/20 (iv) 1/7 ……. 1/4 Solution: (i) We know that 3/6 < 5/6 as 3 < 5 and the denominator is same. (ii) We know that 4/5 > 0/5 as 4 > 0 and the denominator is same. Page 3 Exercise 6.7 page: 6.24 1. Write each fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions: Solution: 2. Mark 2/6, 4/6, 8/6 and 6/6 on the number line and put appropriate signs between fractions given below: (i) 5/6 …….. 2/6 (ii) 3/6 ……. 0/6 (iii) 1/6 …… 6/6 (iv) 8/6 …… 5/6 Solution: (i) We know that 5/6 > 2/6 as 5 > 2 and the denominator is same. (ii) We know that 3/6 > 0/6 as 3 > 0 and the denominator is same. (iii) We know that 1/6 < 6/6 as 6 > 1 and the denominator is same. (iv) We know that 8/6 > 5/6 as 8 > 5 and the denominator is same. 3. Compare the following fractions and put an appropriate sign: (i) 3/6 …… 5/6 (ii) 4/5 …… 0/5 (iii) 3/20 …… 4/20 (iv) 1/7 ……. 1/4 Solution: (i) We know that 3/6 < 5/6 as 3 < 5 and the denominator is same. (ii) We know that 4/5 > 0/5 as 4 > 0 and the denominator is same. (iii) We know that 3/20 < 4/20 as 3 < 4 and the denominator is same. (iv) We know that 1/7 < 1/4 as 7 > 4 and if the numerator is same then the fraction having smaller denominator is larger. 4. Compare the following fractions using the symbol > or <: (i) 6/7 and 6/11 (ii) 3/7 and 5/7 (iii) 2/3 and 8/12 (iv) 1/5 and 4/15 (v) 8/3 and 8/13 (vi) 4/9 and 15/8 Solution: (i) We know that 6/7 > 6/11 as the fraction having smaller denominator is larger. (ii) We know that 3/7 < 5/7 as 3 < 5 and the denominator is same. (iii) We know that 8/12 = (2 × 2 × 2)/ (2 × 2 × 3) = 2/3 Hence, 2/3 = 8/12 (iv) We know that 1/5 = (1/ 5) × (3/3) = 3/15 which is lesser than 4/15 Hence, 1/5 < 4/15 (v) We know that 8/3 > 8/13 as the fraction having smaller value of denominator is larger. (vi) We know that 4/9 = (4/9) × (8/8) = 32/72 15/8 = (15/8) × (9/9) = 135/72 So we get 32/72 < 135/72 Hence, 4/9 < 15/8. 5. The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form: (i) 2/12 (ii) 3/15 (iii) 8/50 (iv) 16/100 (v) 10/60 (vi) 15/75 (vii) 12/60 (viii) 16/96 (ix) 12/75 (x) 12/72 Page 4 Exercise 6.7 page: 6.24 1. Write each fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions: Solution: 2. Mark 2/6, 4/6, 8/6 and 6/6 on the number line and put appropriate signs between fractions given below: (i) 5/6 …….. 2/6 (ii) 3/6 ……. 0/6 (iii) 1/6 …… 6/6 (iv) 8/6 …… 5/6 Solution: (i) We know that 5/6 > 2/6 as 5 > 2 and the denominator is same. (ii) We know that 3/6 > 0/6 as 3 > 0 and the denominator is same. (iii) We know that 1/6 < 6/6 as 6 > 1 and the denominator is same. (iv) We know that 8/6 > 5/6 as 8 > 5 and the denominator is same. 3. Compare the following fractions and put an appropriate sign: (i) 3/6 …… 5/6 (ii) 4/5 …… 0/5 (iii) 3/20 …… 4/20 (iv) 1/7 ……. 1/4 Solution: (i) We know that 3/6 < 5/6 as 3 < 5 and the denominator is same. (ii) We know that 4/5 > 0/5 as 4 > 0 and the denominator is same. (iii) We know that 3/20 < 4/20 as 3 < 4 and the denominator is same. (iv) We know that 1/7 < 1/4 as 7 > 4 and if the numerator is same then the fraction having smaller denominator is larger. 4. Compare the following fractions using the symbol > or <: (i) 6/7 and 6/11 (ii) 3/7 and 5/7 (iii) 2/3 and 8/12 (iv) 1/5 and 4/15 (v) 8/3 and 8/13 (vi) 4/9 and 15/8 Solution: (i) We know that 6/7 > 6/11 as the fraction having smaller denominator is larger. (ii) We know that 3/7 < 5/7 as 3 < 5 and the denominator is same. (iii) We know that 8/12 = (2 × 2 × 2)/ (2 × 2 × 3) = 2/3 Hence, 2/3 = 8/12 (iv) We know that 1/5 = (1/ 5) × (3/3) = 3/15 which is lesser than 4/15 Hence, 1/5 < 4/15 (v) We know that 8/3 > 8/13 as the fraction having smaller value of denominator is larger. (vi) We know that 4/9 = (4/9) × (8/8) = 32/72 15/8 = (15/8) × (9/9) = 135/72 So we get 32/72 < 135/72 Hence, 4/9 < 15/8. 5. The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form: (i) 2/12 (ii) 3/15 (iii) 8/50 (iv) 16/100 (v) 10/60 (vi) 15/75 (vii) 12/60 (viii) 16/96 (ix) 12/75 (x) 12/72 (xi) 3/18 (xii) 4/25 Solution: (i) 2/12 We know that HCF of 2 and 12 = 2 By dividing numerator and denominator by HCF of 2 and 12 2/12 ÷ 2/2 = 1/6 (ii) 3/15 We know that HCF of 3 and 15 = 3 By dividing numerator and denominator by HCF of 3 and 15 3/15 ÷ 3/3 = 1/5 (iii) 8/50 We know that HCF of 8 and 50 = 2 By dividing numerator and denominator by HCF of 8 and 50 8/50 ÷ 2/2 = 4/25 (iv) 16/100 We know that HCF of 16 and 100 = 4 By dividing numerator and denominator by HCF of 16 and 100 16/100 ÷ 4/4 = 4/25 (v) 10/60 We know that HCF of 10 and 60 = 10 By dividing numerator and denominator by HCF of 10 and 60 10/60 ÷ 10/10 = 1/6 (vi) 15/75 We know that HCF of 15 and 75 = 15 By dividing numerator and denominator by HCF of 15 and 75 15/75 ÷ 15/15 = 1/5 (vii) 12/60 We know that HCF of 2 and 12 = 12 By dividing numerator and denominator by HCF of 2 and 12 12/60 ÷ 12/12 = 1/5 (viii) 16/96 We know that HCF of 16 and 96 = 16 By dividing numerator and denominator by HCF of 16 and 96 16/96 ÷ 16/16 = 1/6 (ix) 12/75 We know that HCF of 12 and 75 = 3 By dividing numerator and denominator by HCF of 12 and 75 12/75 ÷ 3/3 = 4/25 (x) 12/72 Page 5 Exercise 6.7 page: 6.24 1. Write each fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions: Solution: 2. Mark 2/6, 4/6, 8/6 and 6/6 on the number line and put appropriate signs between fractions given below: (i) 5/6 …….. 2/6 (ii) 3/6 ……. 0/6 (iii) 1/6 …… 6/6 (iv) 8/6 …… 5/6 Solution: (i) We know that 5/6 > 2/6 as 5 > 2 and the denominator is same. (ii) We know that 3/6 > 0/6 as 3 > 0 and the denominator is same. (iii) We know that 1/6 < 6/6 as 6 > 1 and the denominator is same. (iv) We know that 8/6 > 5/6 as 8 > 5 and the denominator is same. 3. Compare the following fractions and put an appropriate sign: (i) 3/6 …… 5/6 (ii) 4/5 …… 0/5 (iii) 3/20 …… 4/20 (iv) 1/7 ……. 1/4 Solution: (i) We know that 3/6 < 5/6 as 3 < 5 and the denominator is same. (ii) We know that 4/5 > 0/5 as 4 > 0 and the denominator is same. (iii) We know that 3/20 < 4/20 as 3 < 4 and the denominator is same. (iv) We know that 1/7 < 1/4 as 7 > 4 and if the numerator is same then the fraction having smaller denominator is larger. 4. Compare the following fractions using the symbol > or <: (i) 6/7 and 6/11 (ii) 3/7 and 5/7 (iii) 2/3 and 8/12 (iv) 1/5 and 4/15 (v) 8/3 and 8/13 (vi) 4/9 and 15/8 Solution: (i) We know that 6/7 > 6/11 as the fraction having smaller denominator is larger. (ii) We know that 3/7 < 5/7 as 3 < 5 and the denominator is same. (iii) We know that 8/12 = (2 × 2 × 2)/ (2 × 2 × 3) = 2/3 Hence, 2/3 = 8/12 (iv) We know that 1/5 = (1/ 5) × (3/3) = 3/15 which is lesser than 4/15 Hence, 1/5 < 4/15 (v) We know that 8/3 > 8/13 as the fraction having smaller value of denominator is larger. (vi) We know that 4/9 = (4/9) × (8/8) = 32/72 15/8 = (15/8) × (9/9) = 135/72 So we get 32/72 < 135/72 Hence, 4/9 < 15/8. 5. The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form: (i) 2/12 (ii) 3/15 (iii) 8/50 (iv) 16/100 (v) 10/60 (vi) 15/75 (vii) 12/60 (viii) 16/96 (ix) 12/75 (x) 12/72 (xi) 3/18 (xii) 4/25 Solution: (i) 2/12 We know that HCF of 2 and 12 = 2 By dividing numerator and denominator by HCF of 2 and 12 2/12 ÷ 2/2 = 1/6 (ii) 3/15 We know that HCF of 3 and 15 = 3 By dividing numerator and denominator by HCF of 3 and 15 3/15 ÷ 3/3 = 1/5 (iii) 8/50 We know that HCF of 8 and 50 = 2 By dividing numerator and denominator by HCF of 8 and 50 8/50 ÷ 2/2 = 4/25 (iv) 16/100 We know that HCF of 16 and 100 = 4 By dividing numerator and denominator by HCF of 16 and 100 16/100 ÷ 4/4 = 4/25 (v) 10/60 We know that HCF of 10 and 60 = 10 By dividing numerator and denominator by HCF of 10 and 60 10/60 ÷ 10/10 = 1/6 (vi) 15/75 We know that HCF of 15 and 75 = 15 By dividing numerator and denominator by HCF of 15 and 75 15/75 ÷ 15/15 = 1/5 (vii) 12/60 We know that HCF of 2 and 12 = 12 By dividing numerator and denominator by HCF of 2 and 12 12/60 ÷ 12/12 = 1/5 (viii) 16/96 We know that HCF of 16 and 96 = 16 By dividing numerator and denominator by HCF of 16 and 96 16/96 ÷ 16/16 = 1/6 (ix) 12/75 We know that HCF of 12 and 75 = 3 By dividing numerator and denominator by HCF of 12 and 75 12/75 ÷ 3/3 = 4/25 (x) 12/72 We know that HCF of 12 and 72 = 12 By dividing numerator and denominator by HCF of 12 and 72 12/72 ÷ 12/12 = 1/6 (xi) 3/18 We know that HCF of 3 and 18 = 3 By dividing numerator and denominator by HCF of 3 and 18 3/18 ÷ 3/3 = 1/6 (xii) 4/25 We know that HCF of 4 and 25 = 1 By dividing numerator and denominator by HCF of 4 and 25 4/25 ÷ 1/1 = 4/25 Three groups of equal fractions: 2/12, 10/60, 16/96, 12/72, 3/18, 3/15, 15/75, 12/60, 8/50, 16/100, 12/75, 4/25 6. Isha read 25 pages of a book containing 100 pages. Nagma read ½ of the same book. Who read less? Solution: No. of pages in the book = 100 We know that Fraction of book Isha read = (25/100) ÷ (25/25) = 1/4 by dividing both numerator and denominator by HCF of 25 and 100 So the fraction of book Nagma read = 1/2 By comparing 1/4 and 1/2 we get the LCM of 4 and 2 = 4 Now convert the fraction into equivalent fraction having denominator as 4 1/4 × 1/1 and 1/2 × 2/2 1/4 < ½ Hence, Isha read less. 7. Arrange the following fractions in the ascending order: (i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9 (ii) 7/8, 7/25, 7/11, 7/18, 7/10 (iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41 (iv) 3/5, 1/5, 4/5, 2/5 (v) 2/5, 3/4, 1/2, 3/5 (vi) 3/8, 3/12. 3/6, 3/4 (vii) 4/6, 3/8, 6/12, 5/16 Solution: (i) 2/9, 7/9, 3/9, 4/9, 1/9, 6/9, 5/9 can be written in ascending order as 1/9, 2/9, 3/9, 4/9, 5/9, 6/9, 7/9 (ii) 7/8, 7/25, 7/11, 7/18, 7/10 can be written in ascending order as 7/25, 7/18, 7/11, 7/10, 7/8 (iii) 37/47, 37/50, 37/100, 37/1000, 37/85, 37/41 can be written in ascending order as 37/1000, 37/100, 37/85, 37/50, 37/47, 37/41Read More

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