Question

What should be added to twice the rational number -7/11 to get 5/7
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Answer 1

Answer:

-7/22 is the answer friend

Step-by-step explanation:

• -7/11/2
• -7/11×1/2
• -7/22

Answer 2

★ How to do :-

Here, we are given that two times a number becomes the first number of the statement. We are also given with the answer that will be obtained when we add the twiced rational number and an other number. But, we are not given with the second number that the twiced number should be added with. We can find the answer of this question by a concept called as the transposition method. In this method, we shift the fractions from one hand side to the other. By this method, the sign of the appropriate number or fraction changes. We can also check that wether our answer is correct or not. We can do this by verification method which will be done at last. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \bigg( \dfrac{(-7)}{11} + \dfrac{(-7)}{11} \bigg) + y = \dfrac{5}{7}}$

First let's add the numbers in bracket.

Write both numerators with a common denominator.

${\sf \leadsto \bigg( \dfrac{(-7) + (-7)}{11} \bigg) + y = \dfrac{5}{7}}$

Write the second number with one sign.

${\sf \leadsto \bigg( \dfrac{(-7) - 7}{11} \bigg) + y = \dfrac{5}{7}}$

Subtract the numbers.

${\sf \leadsto \dfrac{(-14)}{11} + y = \dfrac{5}{7}}$

Shift the fraction on LHS to RHS, changing it's sign.

${\sf \leadsto y = \dfrac{5}{7} - \dfrac{(-14)}{11}}$

LCM of 7 and 11 is 77.

${\sf \leadsto y = \dfrac{5 \times 11}{7 \times 11} - \dfrac{(-14) \times 7}{11 \times 7}}$

Multiply the numerators and denominators of both fractions.

${\sf \leadsto y = \dfrac{55}{77} - \dfrac{(-98)}{7}}$

Write both numerators with a common denominator.

${\sf \leadsto y = \dfrac{55 - (-98)}{77}}$

Write the second number with one sign.

${\sf \leadsto y = \dfrac{55 + 98}{77}}$

Add the numbers to get the answer.

${\sf \leadsto y = \dfrac{153}{77} = 1 \dfrac{76}{77}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: 1 \dfrac{76}{77}.}}}}$

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Verification :-

${\sf \leadsto \dfrac{(-14)}{11} + y = \dfrac{5}{7}}$

Substitute the value of y.

${\sf \leadsto \dfrac{(-14)}{11} + 1 \dfrac{76}{77} = \dfrac{5}{7}}$

Write the second number on LHS as improper fraction.

${\sf \leadsto \dfrac{(-14)}{11} + \dfrac{153}{77} = \dfrac{5}{7}}$

LCM of 11 and 77 is 77.

${\sf \leadsto \dfrac{(-14) \times 7}{11 \times 7} + \dfrac{153}{77} = \dfrac{5}{7}}$

Multiply the numerators and denominators of first fraction.

${\sf \leadsto \dfrac{(-98)}{77} + \dfrac{153}{77} = \dfrac{5}{7}}$

Write both numerators with a common denominator.

${\sf \leadsto \dfrac{(-98) + 153}{77} = \dfrac{5}{7}}$

Add the numbers.

${\sf \leadsto \dfrac{55}{77} = \dfrac{5}{7}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{5}{7} = \dfrac{5}{7}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!