To solve the problem of determining what number should be subtracted from [tex]\(-1\)[/tex] to yield [tex]\(\frac{5}{3}\)[/tex], we can follow these steps:
1. Let's denote the unknown number we need to find as [tex]\( x \)[/tex].
2. According to the problem, subtracting [tex]\( x \)[/tex] from [tex]\(-1\)[/tex] should give us [tex]\(\frac{5}{3}\)[/tex]. This can be written as the equation:
[tex]\[
-1 - x = \frac{5}{3}
\][/tex]
3. To isolate [tex]\( x \)[/tex], first add 1 to both sides of the equation:
[tex]\[
-1 - x + 1 = \frac{5}{3} + 1
\][/tex]
Simplifying, we get:
[tex]\[
-x = \frac{5}{3} + 1
\][/tex]
4. We need to express 1 in terms of a fraction with the same denominator as [tex]\(\frac{5}{3}\)[/tex] to perform the addition. Recall that [tex]\(1 = \frac{3}{3}\)[/tex], so:
[tex]\[
-x = \frac{5}{3} + \frac{3}{3}
\][/tex]
5. Adding the fractions on the right-hand side:
[tex]\[
-x = \frac{5 + 3}{3} = \frac{8}{3}
\][/tex]
6. Therefore, we have:
[tex]\[
-x = \frac{8}{3}
\][/tex]
7. To solve for [tex]\( x \)[/tex], we multiply both sides by [tex]\(-1\)[/tex]:
[tex]\[
x = -\frac{8}{3}
\][/tex]
8. Converting [tex]\(-\frac{8}{3}\)[/tex] to a decimal, we find:
[tex]\[
x = -2.6666666666666667
\][/tex]
So, the number that should be subtracted from [tex]\(-1\)[/tex] to get [tex]\(\frac{5}{3}\)[/tex] is [tex]\(-2.6666666666666667\)[/tex].
