Certainly! Let's find the other number step-by-step given that the sum of two rational numbers is [tex]\(\frac{-5}{8}\)[/tex] and one of the numbers is [tex]\(\frac{7}{16}\)[/tex].
1. Define the problem:
We are given:
[tex]\[
\text{Sum of two numbers} = \frac{-5}{8}
\][/tex]
And one of these numbers is:
[tex]\[
\text{One number} = \frac{7}{16}
\][/tex]
2. Set up the equation:
Let [tex]\(x\)[/tex] be the other number we need to find. The problem can be translated into the equation:
[tex]\[
\frac{7}{16} + x = \frac{-5}{8}
\][/tex]
3. Isolate [tex]\(x\)[/tex]:
To find [tex]\(x\)[/tex], we need to isolate it on one side of the equation. This can be done by subtracting [tex]\(\frac{7}{16}\)[/tex] from both sides:
[tex]\[
x = \frac{-5}{8} - \frac{7}{16}
\][/tex]
4. Find a common denominator:
To subtract these fractions, we need a common denominator. The least common denominator (LCD) of 8 and 16 is 16. Convert [tex]\(\frac{-5}{8}\)[/tex] to a fraction with the denominator 16:
[tex]\[
\frac{-5}{8} = \frac{-5 \times 2}{8 \times 2} = \frac{-10}{16}
\][/tex]
5. Perform the subtraction:
Now we can subtract the fractions with the common denominator:
[tex]\[
x = \frac{-10}{16} - \frac{7}{16}
\][/tex]
Combine the numerators over the common denominator:
[tex]\[
x = \frac{-10 - 7}{16} = \frac{-17}{16}
\][/tex]
6. Final Answer:
Therefore, the other number is:
[tex]\[
x = \frac{-17}{16}
\][/tex]
To match this with our problem, converting [tex]\(\frac{-17}{16}\)[/tex] into decimal form:
[tex]\[
\frac{-17}{16} = -1.0625
\][/tex]
So, the other number is [tex]\(-1.0625\)[/tex].
Therefore, the other number is [tex]\(\frac{-17}{16}\)[/tex] or in decimal form [tex]\(-1.0625\)[/tex].
