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
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