Question

What is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is subdivided into equal sections.

1. A line segment from 0 to you 75, divided in 3 equal sections. A bracket enclosed the first section, labeled with a question mark.
2. A line segment, from 0 to 75, divided into 5 equal sections. A bracket includes the first 3 sections, labeled with a question mark.
3. A line segment, from 0 to 50, divided into 5 sections. A bracket includes all sections, except the first and last, labeled question mark.

Answer 1

1. The length of the marked portion of the first line segment is
`\( (75)/(3) = 25 \)` units.

2. The length of the marked portion of the second line segment is
`\( (3)/(5) * 75 = 45 \)` units.

3. The length of the marked portion of the third line segment is
`\( (50)/(5) - (0)/(5) - (50)/(5) = 40 \) units.`

Step-by-step explanation:

For the first line segment, dividing the total length of 75 units into 3 equal sections results in each section being
`\( (75)/(3) = 25 \)` units long. The bracket encloses the first section, so the length of the marked portion is 25 units.

In the second line segment, dividing the total length of 75 units into 5 equal sections gives each section a length of
`\( (75)/(5) = 15 \)` units. The bracket includes the first 3 sections, so the length of the marked portion is
`\( 3 * 15 = 45 \) units.`

For the third line segment, dividing the total length of 50 units into 5 equal sections results in each section being
`\( (50)/(5) = 10 \)` units long. The bracket excludes the first and last sections, so the length of the marked portion is
`\( 5 * 10 - 0 - 10 = 40 \)` units.

In summary, the calculations are based on the principles of dividing the total length into equal sections, and the length of the marked portion is determined by the specified sections enclosed by the brackets.