Question

add the rational numbers 1.27 bar on 7 in 0.13 bar on 3​

Answer 1

$Let \: x = 1.2\bar{7} \:and \: y = 0.1\bar{3} \:are$

$two \: rational\: numbers$

$i) x = 1.2\bar{7} \: --(1)$

/* Multiplying bothsides of equation (1) by 10, we get */

$\implies 10x = 12.\bar{7} \: \: --(2)$

/* Multiplying bothsides of equation (2) by 10, we get */

$\implies 100x = 127.\bar{7} \: \: --(3)$

/* Subtract equation (2) from equation (3) , we get */

$\implies 90x = 115$

$\implies x = \frac{115}{90} \: --(4)$

$Let \: x = 1.2\bar{7} \:and \: y = 0.1\bar{3} \:are$

$two \: rational\: numbers$

$ii) y = 1.1\bar{3} \: --(5)$

/* Multiplying bothsides of equation (5) by 10, we get */

$\implies 10y = 11.\bar{3} \: \: --(6)$

/* Multiplying bothsides of equation (6) by 10, we get */

$\implies 100y = 113.\bar{3} \: \: --(7)$

/* Subtract equation (6) from equation (7) , we get */

$\implies 90y = 102$

$\implies y = \frac{102}{90} \: --(8)$

$Sum \: of \: x \: and \:y$

$= x + y$

$= \frac{115}{90} + \frac{102}{90}$

$= \frac{115+102}{90}$

$= \frac{217}{90}$

$= 2.4\bar{1}$

Therefore.,

$Sum \:of \:1.2\bar{7} \:and \: 0.1\bar{3} =2.4\bar{1}$

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Answer 2

Step-by-step explanation:

soln.

Let x = 1.27 and y = 0.13 are two rational numbers.

1. x= 1.27 -------(i)

Now,

Multiplying both sides of equation (i) by 10, we get

=> 10x = 12.7 ---------(ii)

Again,

Multiplying both sides of equation (ii) by 10, we get

=> 100x = 12.7 --------(iii)

Now,

Subtract equation (ii) from equation (iii), we get -

=> 100x - 10x = 127.7 - 12.7

=> 90x = 115

=> x = 115/90 --------(iv)

Let x = 1.27 and y = 0.13 --------

2. y = 0.13 --------(v)

Now,

Multiplying both sides of equation (v) by 10 we get

=> 10y = 1.3 ---------(vi)

Again,

Multiplying both sides of equation (vi) by 10 we get

=> 100y = 13.3 ---------(vii)

Now,

Subtract equation (vi) from equation (vii), we get

=> 100y - 10y = 13.3 - 1.3

=> 90y = 12

=> y = 12/90

Now,

Sum of x and y

= x + y

= 115 + 12

90 90

= 115+12

90

= 127

90

=1.41

therefore, sum of 1.27 and 0.13 = 1.41

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So guys hope it helps u ...... and I didn't had that bar so, I used underline, so thank you guys ...