52
What division means in geometry
Textbook: Part 2, lesson 52, pp. 40–42
GoalUnderstand the geometric meaning of division with a remainder using a number ray and segments.
New words
segment · kesmanumber ray · sonli nurstep · qadamfitting in · sig‘ish
Explanation
a : b = c (remainder r) means that a segment of length b fits into a segment of length a exactly c times, and a piece of length r is left. For 23 : 5 on a number ray we take steps of 5 from 0: 5, 10, 15, 20 – that is 4 steps, and 3 more is needed to reach 23. So 23 : 5 = 4 (remainder 3), that is 23 = 5 × 4 + 3.
Worked examples
A 17 m path cut into 5 m pieces gives 3 pieces and 2 m is left (17 = 5 × 3 + 2).
On a number ray with steps of 4 we reach 0, 4, 8, 12, 16, 20; 23 : 4 = 5 (remainder 3).
Class activity
“Taking steps”: a number ray from 0 to 30 is drawn on the floor. Children take steps of 7 and find how many steps are needed and how much is left.
Practice
1
A 38 cm ribbon is cut into 6 cm pieces. How many whole pieces are there and how many cm are left?
6 pieces, 2 cm left (38 = 6 × 6 + 2)
2
On a number ray we take steps of 7 from 0 trying to reach 30. How many full steps do we take and how much is left?
4 steps (we reach 28), 2 is left
3
Along a 250 m path one flower is planted every 30 m. How many flowers are planted and how many metres are left after the last one? (No flower at the start.)
8 flowers (up to 240 m), 10 m is left
4
A number divided by 7 gives an incomplete quotient 12 and remainder 5. What is the number?
89