Sure, let’s solve this step-by-step.
1. Understanding the Problem:
We need to find the other rational number when the sum of two rational numbers is [tex]\(\frac{-4}{3}\)[/tex] and one of those numbers is -5.
2. Set Up the Equation:
Let's denote the other number as [tex]\( x \)[/tex].
We are given that:
[tex]\[
x + (-5) = \frac{-4}{3}
\][/tex]
This can also be written as:
[tex]\[
x - 5 = \frac{-4}{3}
\][/tex]
3. Isolate [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation. We do this by adding 5 to both sides of the equation:
[tex]\[
x - 5 + 5 = \frac{-4}{3} + 5
\][/tex]
Simplifying, we get:
[tex]\[
x = \frac{-4}{3} + 5
\][/tex]
4. Common Denominator:
To add [tex]\(\frac{-4}{3}\)[/tex] and 5, we first convert 5 to a fraction with a denominator of 3:
[tex]\[
5 = \frac{15}{3}
\][/tex]
5. Add the Fractions:
Now, add the two fractions:
[tex]\[
x = \frac{-4}{3} + \frac{15}{3}
\][/tex]
Combine the numerators over the common denominator:
[tex]\[
x = \frac{-4 + 15}{3}
\][/tex]
Simplify the numerator:
[tex]\[
x = \frac{11}{3}
\][/tex]
6. Final Answer:
So, the other rational number is:
[tex]\[
x = \frac{11}{3}
\][/tex]
In decimal form, [tex]\(\frac{11}{3}\)[/tex] is approximately:
[tex]\[
3.6666666666666665
\][/tex]
Therefore, the other rational number is [tex]\(\frac{11}{3}\)[/tex], or approximately 3.67.
