Rational Numbers (Exercise 4.3) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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Exercise 4.3        page no: 4.12 
 
1. Determine whether the following rational numbers are in the lowest form or not: 
(i) (65/84) 
(ii) (-15/32) 
(iii) (24/128) 
(iv) (-56/-32) 
 
Solution: 
(i) Given (65/84) 
Here we can observe that 65 and 84 have no common factor their HCF is 1. 
Thus, (65/84) is in its lowest form. 
 
(ii) Given (-15/32) 
Here we can observe that -15 and 32 have no common factor i.e., their HCF is 1. 
Thus, (-15/32) is in its lowest form. 
 
(iii) Given (24/128) 
Here we can observe that HCF of 24 and 128 is not 1. 
Thus, given rational number is not in its simplest form. 
 
(iv) Given (-56/-32) 
Here we can observe that HCF of 56 and 32 is 8 and also not equal to 1. 
Therefore the given rational number is not in its simplest form. 
 
2. Express each of the following rational numbers to the lowest form: 
(i) (4/22) 
(ii) (-36/180) 
(iii) (132/-428) 
(iv) (-32/-56) 
 
Solution: 
(i) Given (4/22) 
We know that HCF of 4 and 22 is 2 
By dividing the given number by its HCF we get 
(4 ÷ 2/22 ÷ 2) = (2/11) 
Therefore (2/11) is the simplest form of the given number 
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Exercise 4.3        page no: 4.12 
 
1. Determine whether the following rational numbers are in the lowest form or not: 
(i) (65/84) 
(ii) (-15/32) 
(iii) (24/128) 
(iv) (-56/-32) 
 
Solution: 
(i) Given (65/84) 
Here we can observe that 65 and 84 have no common factor their HCF is 1. 
Thus, (65/84) is in its lowest form. 
 
(ii) Given (-15/32) 
Here we can observe that -15 and 32 have no common factor i.e., their HCF is 1. 
Thus, (-15/32) is in its lowest form. 
 
(iii) Given (24/128) 
Here we can observe that HCF of 24 and 128 is not 1. 
Thus, given rational number is not in its simplest form. 
 
(iv) Given (-56/-32) 
Here we can observe that HCF of 56 and 32 is 8 and also not equal to 1. 
Therefore the given rational number is not in its simplest form. 
 
2. Express each of the following rational numbers to the lowest form: 
(i) (4/22) 
(ii) (-36/180) 
(iii) (132/-428) 
(iv) (-32/-56) 
 
Solution: 
(i) Given (4/22) 
We know that HCF of 4 and 22 is 2 
By dividing the given number by its HCF we get 
(4 ÷ 2/22 ÷ 2) = (2/11) 
Therefore (2/11) is the simplest form of the given number 
 
 
 
 
 
 
 
(ii) Given (-36/180) 
We know that HCF of 36 and 180 is 36 
By dividing the given number by its HCF we get 
(-36 ÷ 36/180 ÷ 36) = (-1/5) 
Therefore (-1/5) is the simplest form of the given number 
 
(iii) Given (132/-428) 
We know that HCF of 132 and 428 is 4 
By dividing the given number by its HCF we get 
(132 ÷ 4/-428 ÷ 4) = (33/-107) 
Therefore (33/-107) is the simplest form of the given number 
 
(iv) Given (-32/-56) 
We know that HCF of 32 and 56 is 8 
By dividing the given number by its HCF we get 
(-32 ÷ 8/-56 ÷ 8) = (4/7) 
Therefore (4/7) is the simplest form of the given number 
 
3. Fill in the blanks: 
(i) (-5/7) = (…/35) = (…/49) 
(ii) (-4/-9) = (…/18) = (12/…) 
(iii) (6/-13) = (-12/…) = (24/…) 
(iv) (-6/…) = (3/11) = (…/-55) 
 
Solution: 
(i) (-5/7) = (-25/35) = (-35/49) 
 
Explanation: 
Given (-5/7) = (…/35) = (…/49) 
Here (-5/7) × (5/5) = (-25/35) 
And also (-5/7) × (7/7) = (-35/49) 
 
(ii) (-4/-9) = (8/18) = (12/27) 
 
Explanation: 
Given (-4/-9) = (…/18) = (12/…) 
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Exercise 4.3        page no: 4.12 
 
1. Determine whether the following rational numbers are in the lowest form or not: 
(i) (65/84) 
(ii) (-15/32) 
(iii) (24/128) 
(iv) (-56/-32) 
 
Solution: 
(i) Given (65/84) 
Here we can observe that 65 and 84 have no common factor their HCF is 1. 
Thus, (65/84) is in its lowest form. 
 
(ii) Given (-15/32) 
Here we can observe that -15 and 32 have no common factor i.e., their HCF is 1. 
Thus, (-15/32) is in its lowest form. 
 
(iii) Given (24/128) 
Here we can observe that HCF of 24 and 128 is not 1. 
Thus, given rational number is not in its simplest form. 
 
(iv) Given (-56/-32) 
Here we can observe that HCF of 56 and 32 is 8 and also not equal to 1. 
Therefore the given rational number is not in its simplest form. 
 
2. Express each of the following rational numbers to the lowest form: 
(i) (4/22) 
(ii) (-36/180) 
(iii) (132/-428) 
(iv) (-32/-56) 
 
Solution: 
(i) Given (4/22) 
We know that HCF of 4 and 22 is 2 
By dividing the given number by its HCF we get 
(4 ÷ 2/22 ÷ 2) = (2/11) 
Therefore (2/11) is the simplest form of the given number 
 
 
 
 
 
 
 
(ii) Given (-36/180) 
We know that HCF of 36 and 180 is 36 
By dividing the given number by its HCF we get 
(-36 ÷ 36/180 ÷ 36) = (-1/5) 
Therefore (-1/5) is the simplest form of the given number 
 
(iii) Given (132/-428) 
We know that HCF of 132 and 428 is 4 
By dividing the given number by its HCF we get 
(132 ÷ 4/-428 ÷ 4) = (33/-107) 
Therefore (33/-107) is the simplest form of the given number 
 
(iv) Given (-32/-56) 
We know that HCF of 32 and 56 is 8 
By dividing the given number by its HCF we get 
(-32 ÷ 8/-56 ÷ 8) = (4/7) 
Therefore (4/7) is the simplest form of the given number 
 
3. Fill in the blanks: 
(i) (-5/7) = (…/35) = (…/49) 
(ii) (-4/-9) = (…/18) = (12/…) 
(iii) (6/-13) = (-12/…) = (24/…) 
(iv) (-6/…) = (3/11) = (…/-55) 
 
Solution: 
(i) (-5/7) = (-25/35) = (-35/49) 
 
Explanation: 
Given (-5/7) = (…/35) = (…/49) 
Here (-5/7) × (5/5) = (-25/35) 
And also (-5/7) × (7/7) = (-35/49) 
 
(ii) (-4/-9) = (8/18) = (12/27) 
 
Explanation: 
Given (-4/-9) = (…/18) = (12/…) 
 
 
 
 
 
 
On multiplying by -2 we get 
(-4/-9) × (-2/-2) = (8/18) 
Also on multiplying by -3 
(-4/-9) × (-3/-3) = (12/27) 
 
(iii) (6/-13) = (-12/26) = (24/-52) 
 
Explanation: 
Given (6/-13) = (-12/…) = (24/…) 
On multiplying by -2 
(6/-13) × (-2/-2) = (-12/26) 
Also multiplying by 4 
And also (6/-13) × (4/4) = (24/-52) 
 
(iv) (-6/-22) = (3/11) = (-15/-55) 
 
Explanation: 
Given (-6/…) = (3/11) = (…/-55) 
0n multiplying by -2  
(3/11) × (-2/-2) = (-6/-22) 
And also on multiplying by -5 
(3/11) × (-5/-5) = (-15/-55)