62
Dividing a segment into equal parts
Textbook: Part 2, lesson 62, pp. 72–74
GoalDividing a segment into equal parts, finding its midpoint and the length of a broken line.
New words
segment · kesmamidpoint · kesmaning o‘rtasibroken line · siniq chiziqlink (part of broken line) · bo‘g‘in
Explanation
To find the midpoint of a segment, measure its length, divide by 2, measure that distance from one end and mark the point. If the number of centimetres is odd, change to millimetres first: 9 cm = 90 mm, 90 : 2 = 45 mm. To divide into three equal parts, divide the length by 3. The length of a broken line is the sum of the lengths of all its links.
Worked examples
The midpoint of a 9 cm segment is 4 cm 5 mm from an end (90 mm : 2 = 45 mm).
1 dm 4 cm = 14 cm; the midpoint is at 14 : 2 = 7 cm. Dividing 12 cm into 3 parts gives parts of 4 cm.
Class activity
“Fold to check”: children measure a given segment with a ruler, find and mark its midpoint, then fold the strip to check.
Practice
1
An 18 cm segment is divided into 3 equal parts. How long is each part, in cm?
6
2
How far, in mm, is the midpoint of a 7 cm segment from its end?
35
3
The links of the broken line ABCD are AB = 3 cm 8 mm, BC = 5 cm 6 mm, CD = 4 cm 9 mm. What is its length in mm?
143
4
How many metres is 3 km 450 m?
3450
5
A 2 m rope is cut into 8 equal pieces. How long is each piece, in cm?
25