To find the other number given that the sum of two rational numbers is -8 and one of the numbers is [tex]\(\frac{-15}{7}\)[/tex], follow these steps:
1. Understand the Given Information:
- We are given that the sum of two numbers is -8.
- One of the numbers is [tex]\(\frac{-15}{7}\)[/tex].
2. Set Up the Equation:
- Let [tex]\( x \)[/tex] be the other number we need to find.
- According to the problem, the sum of these two numbers should be equal to -8.
- This can be written as:
[tex]\[
x + \frac{-15}{7} = -8
\][/tex]
3. Isolate [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex], we need to isolate it on one side of the equation.
- Subtract [tex]\(\frac{-15}{7}\)[/tex] from both sides of the equation:
[tex]\[
x = -8 - \frac{-15}{7}
\][/tex]
4. Simplify the Right-Hand Side:
- Simplify the expression on the right-hand side:
[tex]\[
x = -8 + \frac{15}{7}
\][/tex]
- Since -8 can be written as [tex]\(\frac{-56}{7}\)[/tex] (because [tex]\(-8 \times 7 = -56\)[/tex]):
[tex]\[
x = \frac{-56}{7} + \frac{15}{7}
\][/tex]
- Now combine the fractions:
[tex]\[
x = \frac{-56 + 15}{7} = \frac{-41}{7}
\][/tex]
5. Conclusion:
- Therefore, the other number is:
[tex]\[
x = \frac{-41}{7}
\][/tex]
So, the other number is [tex]\(\frac{-41}{7}\)[/tex].
Thus, we have found that given the sum of two numbers is -8, and one of the numbers is [tex]\(\frac{-15}{7}\)[/tex], the other number is [tex]\(\frac{-41}{7}\)[/tex].
