Question

find ten rational numbers between 3/5and3/4?​

Answer 1

Step-by-step explanation:

To find ten rational numbers between two numbers , we have to make them equivalent.

3/5 & 3/4

LCM=20

3/5 can be, 3/5× 4/4=12/20

3/4 can be , 3/4×5/5=15/20

Now the denominators are equal , so let us find ten numbers . Multiply it by the number which will make ten numbers .

2nd step ,

12/20×4/4=48/80

15/20×4/4=60/80

So , ten rational numbers between 48/80 & 60/80

are:

49/80 , 50/80 , 51/80 , 52/80 ,53/80 , 54/80 , 55/80 ,56/80 , 57/80 , 58/80 ,59/80

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Answer 2

Step-by-step explanation:

$\huge \underline \mathbb {SOLUTION:-}$

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(i) 26 and 91

Expressing 26 and 91 as product of its prime factors, we get,

26 = 2 × 13 × 1

91 = 7 × 13 × 1

Therefore, LCM (26, 91) = 2 × 7 × 13 × 1 = 182

And HCF (26, 91) = 13

Verification

Now, product of 26 and 91 = 26 × 91 = 2366

And Product of LCM and HCF = 182 × 13 = 2366

Hence, LCM × HCF = product of the 26 and 91.

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(ii) 510 and 92

Expressing 510 and 92 as product of its prime factors, we get,

510 = 2 × 3 × 17 × 5 × 1

92 = 2 × 2 × 23 × 1

Therefore, LCM(510, 92) = 2 × 2 × 3 × 5 × 17 × 23 = 23460

And HCF (510, 92) = 2

Verification

Now, product of 510 and 92 = 510 × 92 = 46920

And Product of LCM and HCF = 23460 × 2 = 46920

Hence, LCM × HCF = product of the 510 and 92.

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(iii) 336 and 54

Expressing 336 and 54 as product of its prime factors, we get,

336 = 2 × 2 × 2 × 2 × 7 × 3 × 1

54 = 2 × 3 × 3 × 3 × 1

Therefore, LCM(336, 54) = = 3024

And HCF(336, 54) = 2×3 = 6

Verification

Now, product of 336 and 54 = 336 × 54 = 18,144

And Product of LCM and HCF = 3024 × 6 = 18,144

Hence, LCM × HCF = product of the 336 and 54.

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