99
Comparing numbers on the number ray
Textbook: Part 3, lesson 99, pp. 95–97
GoalComparing numbers with the number ray: the point with the smaller coordinate lies to the left; map scale.
New words
further left · chaproqdacomparison · taqqoslashmap scale · masshtaborder · tartib
Explanation
The coordinate of a point is its distance from zero. So the point with the smaller coordinate lies further left and the point with the larger coordinate further right. This is another way to compare numbers. If coordinates are given as expressions we first calculate them. On a map it works similarly: 1 cm on the map stands for a fixed distance, e.g. if 1 cm = 20 km, then 6 cm = 6 × 20 = 120 km.
Worked examples
A(2 705) and B(2 750): 2 705 < 2 750, so A lies to the left of B.
Roughly: Tashkent – 0, Samarkand – 300, Bukhara – 570 (km). From Samarkand to Bukhara it is 570 − 300 = 270 km.
Class activity
“Who is on the left?”: the teacher says two numbers and children show the ray with their arms and find which is further left. Harder level: expressions instead of numbers (for example 60 : 2 and 7 × 4).
Practice
1
Which point lies further left: A(2 750) or B(2 705)?
B
2
On a map 1 cm = 30 km. Two towns are 7 cm apart on the map. What is the real distance in kilometres?
210
3
On a ray Tashkent is 0, Samarkand 300, Bukhara 570 (km). How many kilometres is it from Samarkand to Bukhara?
270
4
In what order, left to right, are C(94), A(409), B(490) on the ray?
C, A, B
5
Which point lies further left: A(120 : 4) or B(5 × 7)?
A