Question

What rational number should be substracted from -9/25 to get 7/10​

Answer 1

★ How to do :-

Here, we are given with one of the rational number that should be subtracted from the other number. We are also given with the answer obtained while solving those two rational numbers. But, we are not given with the second number that the first number should be subtracted with. We are asked to find the same. Here, we use the concept of shifting the numbers from one hand side to the other which changes it's sign. We can find the value of other fraction. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{(-9)}{25} - x = \dfrac{7}{10}}$

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

${\tt \leadsto x = \dfrac{(-9)}{25} - \dfrac{7}{10}}$

LCM of 25 and 10 is 50.

${\tt \leadsto x = \dfrac{(-9) \times 2}{25 \times 2} - \dfrac{7 \times 5}{10 \times 5}}$

Multiply the numerator and denominator of both fractions on RHS.

${\tt \leadsto x = \dfrac{(-18)}{50} - \dfrac{35}{50}}$

Subtract the remaining fractions.

${\tt \leadsto x = \dfrac{(-18) - 35}{50} = \dfrac{(-53)}{50}}$

Write the obtained fraction as a mixes fraction.

${\tt \leadsto x = \dfrac{(-53)}{50} = - 1 \dfrac{3}{50}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: fraction \: is \: \: - 1 \dfrac{3}{50}}}}}$

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Verification :-

${\tt \leadsto \dfrac{(-9)}{25} - x = \dfrac{7}{10}}$

Substitute the value of x.

${\tt \leadsto \dfrac{(-9)}{25} - \dfrac{(-53)}{50} = \dfrac{7}{10}}$

LCM of 25 and 50 is 50.

${\tt \leadsto \dfrac{(-9) \times 2}{25 \times 2} - \dfrac{(-53)}{50} = \dfrac{7}{10}}$

Multiply the numerator and denominator of first fraction.

${\tt \leadsto \dfrac{(-18)}{50} - \dfrac{(-53)}{50} = \dfrac{7}{10}}$

Write the number on LHS with one sign which has two signs.

${\tt \leadsto \dfrac{(-18) + 53}{50} = \dfrac{7}{10}}$

Add the values in denominator on LHS.

${\tt \leadsto \dfrac{35}{50} = \dfrac{7}{10}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \dfrac{7}{10} = \dfrac{7}{10}}$

So,

${\sf \leadsto LHS = RHS}$

Answer 2

Answer:

Step-by-step explanation: