To find the location of a point on the number line that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(A = 31\)[/tex] to [tex]\(B = 6\)[/tex], follow these steps:
1. Calculate the difference between [tex]\(B\)[/tex] and [tex]\(A\)[/tex]:
[tex]\[
\text{Difference} = B - A
\][/tex]
Substituting the values, we have:
[tex]\[
\text{Difference} = 6 - 31 = -25
\][/tex]
2. Determine the distance to move from [tex]\(A\)[/tex] to the desired point:
We need to move [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex]. So, we calculate:
[tex]\[
\text{Distance} = \text{Difference} \times \frac{2}{5}
\][/tex]
Substitute the calculated difference:
[tex]\[
\text{Distance} = -25 \times \frac{2}{5} = -10
\][/tex]
3. Find the location of the point by adding this distance to [tex]\(A\)[/tex]:
[tex]\[
\text{Location} = A + \text{Distance}
\][/tex]
Substitute the values:
[tex]\[
\text{Location} = 31 + (-10) = 21
\][/tex]
Therefore, the location of the point that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(A = 31\)[/tex] to [tex]\(B = 6\)[/tex] is [tex]\(21\)[/tex].
