To find the location of the point on the number line that is [tex]\(\frac{2}{9}\)[/tex] of the way from [tex]\(A = 5\)[/tex] to [tex]\(B = 23\)[/tex], follow these steps:
1. Calculate the distance between [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[ \text{Distance} = B - A = 23 - 5 = 18 \][/tex]
2. Determine the fraction of the distance:
[tex]\[ \text{Fraction of the distance} = \frac{2}{9} \times \text{Distance} = \frac{2}{9} \times 18 \][/tex]
3. Simplify this calculation:
[tex]\[ \frac{2}{9} \times 18 = 2 \times 2 = 4 \][/tex]
4. Add this fraction of the distance to point [tex]\(A\)[/tex]:
[tex]\[ \text{Point} = A + \text{Fraction of the distance} = 5 + 4 = 9 \][/tex]
Therefore, the location of the point that is [tex]\(\frac{2}{9}\)[/tex] of the way from [tex]\(A = 5\)[/tex] to [tex]\(B = 23\)[/tex] is [tex]\(9\)[/tex].
To summarize:
- The distance between [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is [tex]\(18\)[/tex].
- The point that is [tex]\(\frac{2}{9}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex] is located at [tex]\(9\)[/tex] on the number line.
