Question

What should be added to the double of the rational number -7/3 so that 3/7 is obtained.​

Answer 1

Answer: 107/21 or 5.09

Step-by-step explanation:

Step:-1. Let the number should be added be 'a'...

Step:-2. Form the equation from given data..

➡ a + (2 x -7/3) = 3/7

Step:-3 Solve the equation..

➡ a + (-14/3) = 3/7

Step:-4. Transposing (-14/3) to R.H.S.

➡ a = 3/7 + 14/3

Step:-5. Solve the equation...

➡ a = (9+ 98)/21

{LCM = 21}

Step:-6. Solve the equation...

➡ a = 107/21

Step:-7. Solve the equation...

➡a = 5.09

Answer 2

$\huge\mathfrak\blue{Answer:}$

Rational Numbers:

• Rational Number are the numbers which can be written in the form of p/q where p and q are integers and q is not equal to zero
• For ex : 2/3 , 3/5 , 5/7 etc

Given:

• We have been given two rational numbers -7/3 and 3/7

To Find:

• We have to find a number which should be added to double of -7/3 so that 3/7 is obtained

Solution:

Let the required number = x

Given two rational numbers - 7/3 and 3/7

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$\underline{\large\mathfrak\red{According \: to \: the \: Question:}}$

Number that should be added to the double of -7/3 so as to obtain 3/7

$\implies \sf{ x + 2 \left ( \dfrac{-7}{3} \right ) = \dfrac{3}{7}}$

$\implies \sf{ x - \dfrac{14}{3} = \dfrac{3}{7}}$

$\implies \sf{ x = \dfrac{3}{7} + \dfrac{14}{3} }$

Taking LCM on Right Hand Side we get

$\implies \sf{ x = \dfrac{3 \times 3 + 14 \times 7}{21} }$

$\implies \sf{ x = \dfrac{9 + 98}{21} }$

$\implies \boxed{\sf{ x = \dfrac{107}{21}}}$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{Required \: Number = \dfrac{107}{21} }}$

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$\large\purple{\underline{\underline{\sf{Extra \: Information:}}}}$

• All whole numbers are rational numbers
• All integers are rational numbers
• All decimal numbers are rational numbers
• All fractional numbers are rational numbers