Exercise 4.3
1. Determine whether the following rational numbers are in the lowest form or not:
(i) 65/84
Solution:
We observe that 65 and 84 have no common factor their HCF is 1.
Thus, 65/84 is in its lowest form.
(ii) (-15)/32
Solution:
We observe that -15 and 32 have no common factor i.e., their HCF is 1.
Thus, -15/32 is in its lowest form.
(iii) 24/128
Solution:
HCF of 24 and 128 is not 1.
Thus, given rational number is not in its simplest form.
(iv) (-56)/(-32)
Solution:
HCF of 56 and 32 is 8.
Thus, given rational number is not in its simplest form.
2. Express each of the following 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 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 is 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 (-32/0\-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