A fraction (from Latin: fractus, "broken") represents a part of a whole.

Transcription

1 Math 4. Class work. Fractions. A fraction (from Latin: fractus, "broken") represents a part of a whole. Look at the picture on the right: the whole chocolate bar is divided into equal pieces: (whole chocolate bar ) (equal parts) = (whole chocolate bar ) (equal parts) = (of whole chocolate bar) + + = = = 4 = (To divide chocolate bars between kids we can give each kid of each chocolate bar, altogether = = = ). 4 To divide 4 pizzas equally between friends we will give each friend of each pizza. Each friend will get 4 = 4 = 4 which is exactly whole pizza ( = = ) and.

2 Mark following fractions on the number line:,,, 7, 0 When we are talking about fraction we usually mean the part of a unit. Proper fractions are parts of a unit; improper fractions are sums of a natural number and a proper fraction. Sometimes we want to find a part of something which is not, but can be considered as a single object. For example, among my 0 pencils are yellow. How many yellow pencils do I have? What does it mean to find out of 0? The whole pile of all of all these pencils is a single object and we want to calculate how many pencils does a little pile of of 0 contain? is times, and of 0 is 0. So of 0 pencils will be twice more: 0 = 0 Exercises.. Rewrite these expression of division as fractions: Example: = 9 = = 6 =. Compare: 8 6

3 4 4. Calculate: + + = = = 4. a. What is bigger, the number c or of the number c? Why? b. What is bigger, the number b or of the number b? Why? c. What is bigger, of a number m or of a number m? Why?. a. 7 b. of all students in the class is 4. How many students are there in the class? of all students in a class is 0. How many students are there in a class? 6. In the school cafeteria there are tables. There are 0 seats at each table. At the lunch time 4 of all sits were occupied by students. How many students were in the cafeteria? 7. An apple worm was eating an apple. On the first day it ate half of the apple, on the second day it ate half of the rest, and on the third day it ate half of the rest again. On the fours day it ate all the leftovers. What part of the apple did it eat on the fourth day? 8. Peter spent hours doing his homework. of this time, he spent doing his math homework and 4 of the remaining time he spent on the history assignment. How many minutes did Peter spent on his history assignment and how many minutes did he spent doing his math homework?

4 9. Write the expression for the following problems: a. packages of cookies cost a dollars. How many dollars do of the same packages cost? b. bottles of juice cost b dollars. How many bottles can one buy with c dollars? 0. Come up with the word problem which can be solved using the following expression: ; (This expression is equivalent of shorter expressions:.. 6 ) Geometry. Points, lines, and plane. There are two possibilities of mutual location of the line and the point on the plane: a point lies on a line or a point doesn t lie on the straight line. If lines have common points these lines coincide. Two straight line can intersect (then they have one common point) or they can be parallel. Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

5 Each straight line divides a plane into two domains. In these domains any two points on one side of the line may be connected without crossing the line itself and any two points on the two different sides of the lane can t be connected without crossing the line. Enclosed area on a plane is the area limited by a closed curved line (or chain of line segments) any points of which can be connected without crossing the curved line (or series of line segments) and any point inside of the limit can t be connected with any point outside of the limit without crossing the curved line (or chain of line segments). Circle is the set of all points in a plane that are at a given distance from a given point, the center. Exercises. (Problems marked with * are more difficult.). How it can be that two straight lines do not intersect but they are not parallel?. Draw all possible position of a circle and a straight line on a plane. How many common points can the circle and the line have? (To draw circles use compass, to draw liens always use ruler!). One straight line divides a plane into parts. How many parts do straight lines divide a plane into? Three lines? Find all possible solutions. (*Four lines? Try to find all possible solutions.)

6 4. a. Michel drew three lines, no two of which are parallel, and marked points on each of the three lines. He marked points altogether. How can this be? b. Michel drew three lines, no two of which are parallel, and marked points on each of three lines. He marked 4 points altogether. How can this be?. Draw the picture as below in your homework and mark with color pencil a. Line AB b. Line segment AB c. Ray AB d. Ray BA (When drawing use rulers to draw parallel lines. Try to draw a nice picture) 6. Draw the line a and mark points A, B, C, D, K on the line a so that a. Point C belongs to the segment [AB]; b. Point D belongs to the ray AB and doesn t belongs to the segment [AB]; c. Point K belongs to the ray BA and doesn t belongs to the segment [AB];