Question

1. If a fraction a/b is a lowest terms, then HCF of a and bis

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Answer 1

Step-by-step explanation:

Every rational number can be put in the lowest form using the following steps:

Step I:  Let us obtain the rational number abab.

Step II: Find the HCF of a and b.

Step III: If k = 1, then abab is in lowest form.

Step IV: If k ≠ 1, then a÷kb÷ka÷kb÷k is the lowest form of a/b.

The following examples will illustrate the above procedure to convert a rational number into lowest form.

1. Determine whether the following rational numbers are in the lowest form or not.

(i) 13811381      

Solution:

We observe that 13 and 81 have no common factor, i.e., their HCF is 1.

Therefore, 13811381 is the lowest form of a rational number.      

(ii) 7296072960

Solution:

We have, 24 = 2 × 2 × 2 × 3 × 3 and 320 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5

Thus, HCF of 72 and 960 is 2 × 2 × 2 × 3 = 24.

Therefore, 7296072960 is not in the lowest form.

 

2. Express each of the following rational numbers to the lowest form.

(i) 18301830  

Solution:

We have,

18 = 2 × 3 × 3 and 30 = 2 × 3 × 5

Therefore, HCF of 18 and 30 is 2 × 3 = 6.

So, 18301830 is not in lowest form.

Now, dividing numerator and denominator of 18301830 by 6, we get

18301830 = 18÷630÷618÷630÷6 = 3535

Therefore, 3535 is the lowest form of a rational number 18301830.

 

(ii) −6072−6072     

Solution:

We have

60 = 2 × 2 × 3 × 5 and 72 = 2 × 2 × 2 × 3 × 3

Therefore, HCF of 60 and 72 is 2 × 2 × 3 = 12

So, −6072−6072 is not in lowest form.

Dividing numerator and denominator of −6072−6072 by 12, we get

−6072−6072 = 

Answer 2

Answer:

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Step-by-step explanation:

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