Math, asked by sudhamuthiah1983, 6 hours ago

The sum of two rational numbers is -7. If one of the numbers is –15/9, the other number is _____ (a) -21/10 (b) -57/16 (c) 7/9 (d) -118/19 ​

Answers

Answered by tgkm1004
1

Answer:

The correct option is option (d) –118/19.

Given :–

The sum of two rational numbers = –7.

One number = \sf \dfrac{-15}{19}

19

−15

To Find :–

The other number.

Solution :–

Let,

The other number be x.

According to the question,

One number + Other number = Sum of two rational numbers

We have,

One number = \sf \dfrac{-15}{19}

19

−15

Sum of two rational numbers = –7.

So,

\hookrightarrow\dfrac{ - 15}{19} + x = - 7↪

19

−15

+x=−7

\hookrightarrow x = - 7 - \dfrac{ - 15}{19}↪x=−7−

19

−15

\hookrightarrow x = \dfrac{ - 7}{1} - \dfrac{ - 15}{19}↪x=

1

−7

19

−15

\hookrightarrow x = \dfrac{ - 133 -( - 15)}{19}↪x=

19

−133−(−15)

\hookrightarrow x = \dfrac{ - 133 + 15}{19}↪x=

19

−133+15

\hookrightarrow x = \dfrac{ - 118}{19}↪x=

19

−118

Hence,

The other number is \sf \dfrac{-188}{19}

19

−188

The correct option is (d) –188/19.

Verification :–

One number + Other number = Sum of two rational numbers

We have,

One number = \sf \dfrac{-15}{19}

19

−15

Other number = \sf \dfrac{-118}{19}

19

−118

Sum of two numbers = –7

Now,

\hookrightarrow \dfrac{ - 15}{19} + \dfrac{ - 118}{19} = - 7↪

19

−15

+

19

−118

=−7

\hookrightarrow\dfrac{ - 15 + ( - 118)}{19} = - 7↪

19

−15+(−118)

=−7

\hookrightarrow\dfrac{ - 15 - 118}{19} = - 7↪

19

−15−118

=−7

\hookrightarrow\cancel \dfrac{ - 133}{19} = - 7↪

19

−133

=−7

\hookrightarrow - 7 = - 7↪−7=−7

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