The real number system

The Real Number System,[object Object]

N : 1,2,3,….,[object Object],Z : …,-2,-1,0,1,2,..,[object Object],Q :,[object Object],Irational:,[object Object]

Real Numbers,[object Object],Rational Numbers,[object Object], ¼ ⅓,[object Object],0.6 ,[object Object],- ⅔ √0.25,[object Object],Irrational,[object Object],Numbers,[object Object],π,[object Object],0.101001,[object Object],√2,[object Object],Integers,[object Object],- 4 -3,[object Object],-8,[object Object],Whole Numbers,[object Object],0,[object Object],Natural,[object Object],Numbers,[object Object],2 ,[object Object],5,[object Object]

Concept Summary,[object Object]

Operation of Integers,[object Object]

Four Fundamental Operations,[object Object]

1.1,[object Object],Integers and Their Symbols,[object Object],A,[object Object],+5,[object Object],0,[object Object],-5,[object Object],+5,[object Object],-5,[object Object],0,[object Object],Positive and Negative Numbers,[object Object],The numbers 5 and -5 can be drawn on a vertical or a horizontal line as follows. ,[object Object], thermometer,[object Object],Horizontal number line,[object Object],You may write:,[object Object],[object Object]

the temperature of 5 degrees below zero as -5 ºC. Verticalnumber line,[object Object]

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6,[object Object],Positive integers,[object Object],Negative integers ,[object Object],0 is neither positive nor negative ,[object Object],A set of integers; ..., 3, 2, 1, 0, 1, 2, 3, ... , can be symbolized as Z. ,[object Object],[object Object],Natural numbers ( bilanganAsli ) : 1, 2, 3, 4, …Whole numbers ( bilanganCacah ) : 0, 1, 2, 3, 4, …Integers ( bilanganBulat ) : …, -2, -1, 0, 1, 2, …,[object Object]

a. Determine all integers between 5 and 4.,[object Object],Example 1,[object Object],Solution:,[object Object], 4, 3, 2, 1, 0, 1, 2, 3,[object Object],b. Write all even integers between 6 and 11.,[object Object],Solution:,[object Object], The even integers between 6 and 11 are 4, 2, 0, 2, 4, 6, 8, and 10,[object Object],c. Write all odd integers between 7 and 8.,[object Object],Solution:,[object Object], The odd integers between 7 and 8 are -5, -3, -1, 1 , 3 , 5, and 7,[object Object]

B,[object Object],-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6,[object Object],Comparing and Ordering Integers,[object Object],-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6,[object Object],increase,[object Object], decrease,[object Object],What if we use a vertical number line?,[object Object],Change the sign  to <, >, or = on 4 7,[object Object], Solution:,[object Object],Example 2,[object Object],The number 4 is located on the right side of 7. Therefore, 4 > 7.,[object Object]

Problem 1,[object Object],Arrange the following numbers from the least to the greatest.,[object Object],a. 5, 3, 6, 6, 2, 4, 1,[object Object],b. 9, 5, 6, 12, 17, 8, 14 ,[object Object],Problem 1,[object Object],Solution :,[object Object],a. -6, -3, -1, 2, 4, 5, 6,[object Object],b. -14, -12, -5, 6, 8, 9, 17 ,[object Object]

The real number system

The real number system

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The real number system