143
Year review: coordinates, fractions, sets and logic
Textbook: Part 4, lesson 143, pp. 99–100
GoalYear review: the coordinate grid and number ray, fraction of a number, sets and logic.
New words
coordinate · koordinatafraction · ulushdistance · masofaset · to‘plam
Explanation
In the coordinate grid a point is written with two numbers: (4; 2) means 4 squares right and 2 squares up from the origin. On a number ray the distance between two points is the larger coordinate minus the smaller. To find 1/n of a number we divide it by n; to find the rest we subtract that part from the whole. For sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
Worked examples
A rectangle has vertices (1; 1), (5; 1), (5; 4), (1; 4). Its length is 5 − 1 = 4 and its width 4 − 1 = 3 squares. Perimeter (4 + 3) × 2 = 14, area 4 × 3 = 12 squares.
1/5 of 450 is 450 : 5 = 90. 1/4 of 80 is 80 : 4 = 20, and the rest is 80 − 20 = 60. 12 + 9 − 5 = 16 – the number of elements in the union.
Class activity
“Battleship”: pairs hide a ship (a rectangle) on a squared grid and find each other’s ship by calling coordinates such as (3; 2).
Practice
1
An orchard has 80 trees and 1/4 of them are apple trees. How many trees are not apple trees?
60
2
On a number ray point A is at 5 and point B is at 12. What is the distance between them in units?
7
3
What is the perimeter in squares of the rectangle with vertices (1; 1), (5; 1), (5; 4), (1; 4)?
14
4
In a class 12 children go to the English club and 9 to the Russian club, and 5 go to both. How many children go to at least one club?
16
5
A = {2, 4, 6}, B = {4, 6, 8}. Is the statement “A ∩ B = {4, 6}” true or false?
True: 4 and 6 are in both sets.