To determine the other rational number when the sum of two rational numbers is given as [tex]\(\frac{-3}{8}\)[/tex] and one of those numbers is [tex]\(\frac{3}{16}\)[/tex], follow these steps:
1. Let the two rational numbers be [tex]\(a\)[/tex] and [tex]\(b\)[/tex]. We are given that their sum is:
[tex]\[
a + b = \frac{-3}{8}
\][/tex]
2. Suppose one of the rational numbers, [tex]\(a\)[/tex], is given as [tex]\(\frac{3}{16}\)[/tex]. Then our equation becomes:
[tex]\[
\frac{3}{16} + b = \frac{-3}{8}
\][/tex]
3. To isolate [tex]\(b\)[/tex], we need to subtract [tex]\(\frac{3}{16}\)[/tex] from both sides of the equation:
[tex]\[
b = \frac{-3}{8} - \frac{3}{16}
\][/tex]
4. Next, find a common denominator to perform the subtraction. The least common multiple of 8 and 16 is 16. Rewrite [tex]\(\frac{-3}{8}\)[/tex] with a denominator of 16:
[tex]\[
\frac{-3}{8} = \frac{-6}{16}
\][/tex]
5. Now substitute [tex]\(\frac{-6}{16}\)[/tex] in place of [tex]\(\frac{-3}{8}\)[/tex]:
[tex]\[
b = \frac{-6}{16} - \frac{3}{16}
\][/tex]
6. Perform the subtraction:
[tex]\[
b = \frac{-6 - 3}{16} = \frac{-9}{16}
\][/tex]
Hence, the other rational number is:
[tex]\[
b = \frac{-9}{16}
\][/tex]
So, the solution is:
[tex]\[
\frac{3}{16} + \frac{-9}{16} = \frac{-3}{8}
\][/tex]
