Question

Find any 10 rational number between -7/9 and 1/9​

Answer 1

Answer:

Let x be the rational number the given two numbers then:

59<x<910

⟹x−59=910−x

⟹2x=59+910

⟹2x=5×109×10+9×910×9

⟹2x=13190

⟹x=131180

131180 is the require rational number

Answer 2

Answer -

• 10 rational numbers between -7/9 and 1/9 are -76/99, -75/99, -74/99, -73/99, -72/99, -71/99, -70/99, -69/99, -68/99 and -67/99.

Given -

• Two rational numbers -7/9 and 1/9.

To find -

• Any 10 rational numbers between -7/9 and 1/9.

Step-by-step explanation -

• Here, we are asked to find any ten rational numbers between -7/9 and 1/9.

We know that -

$\bf \dfrac{ - 7}{ \: \: \: 9} , \dfrac{ - 6}{ \: \: \: 9} , \dfrac{ - 5}{ \: \: \: 9} \: ... \: \dfrac{1}{9}$

We notice that there are only seven integers between -7/9 and 1/9. Thus, writing the given rational numbers with denominator 9 is not sufficient.

So, to insert 10 rational numbers, we will multiply both the numerator and denominator of each rational number by (10 + 1) that is, 11.

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Multiplying the numerator and denominator of the numbers with 11 -

$\tt \longmapsto \dfrac{ - 7}{ \: \: \: 9} = \dfrac{ - 7 \times 11}{ \: \: \: \: 9 \times 11} = \dfrac{ - 77}{ \: \: \: 99}$

$\tt \longmapsto \dfrac{1}{9} = \dfrac{1 \times 11}{9 \times 11} = \dfrac{11}{99}$

Now,

$\bf\dfrac{ - 77}{ \: \: \: 99} , \dfrac{ - 76}{ \: \: \: 99} , \dfrac{ - 75}{ \: \: \: 99} \: ... \: \dfrac{11}{99}$

Hence -

• Any ten rational numbers between -7/9 and 1/9 are -76/99, -75/99, -74/99, -73/99, -72/99, -71/99, -70/99, -69/99, -68/99 and -67/99.

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