Chapter 1 The Characteristics of calculate Operation and its’ uses in problem solving

Chapter 1

The Characteristics of calculate Operation and its’ uses in problem solving

Matematika SMP Kelas 1 Page 2

(1. INTEGER)

1. Definition of Integer Integer is number that consist of BILANGAN CACAH (0, 1, 2, ….) and its’ negative(-1, -2, -3, ….: -0 is same with 0 and not be included separately anymore.

2. The uses of Integer

e.g:

The divers and the captain of the submarine should know the levels of sea deepness. For example, 10 m under sea surface is written -10 m.

3. The position of Integer in number line.

negative integer zero positive integer

A. Integer

4. Declaring relationship between two integers.

- If p located in the right side of q therefore p > q;

- If p located in the left side of q therefore p < q.


B. Calculate operation on Integer

1. Summation on Integer

a. Summation with aid tools

If the number is positive, the arrow will appoint to right, in

contrast if the number is negative, the arrow will appoint to left.

b. Summation without aid tools

1) The both numbers have same sign.

2) The both numbers have contrary sign.

2. The characteristics of Integer’s summation

a. closed character

b. commutative character

c. Having identical elements

d. associative character

e. Having the inverse

3. Subtraction on integer

a. Subtraction declared summation with contrary number

b. Subtraction with aid tools

4. Multiplication on Integer

If n is any positive integer, therefore

sebanyak n suku


The characteristics of multiplication on integer

a. closed characteristics

b. cumulative characteristics

c. associative characteristics

d. distributive multiplication on summation

e. distributive multiplication on subtraction

f. having identical elements

1. Rounded to nearest decimal number

2. Rounded to nearest hundred number

1. Definition of power of number

is a repeated multiplication by same numbers.


C. Assessing the result of multiplication and division of integer

D. Power of Integer

2. Characteristic of powered number

a. Multiplication character on powered number

b. Division character on powered number

c. power character on powered number

d. Power character on a multiplication or division


e.g:

In a physic’s experiment, a student was measuring the temperature of a chunk of ice. The temperature of he ice firstly was -5 c. after heating, the ice was changed to water with temperature 3 c. how much the increment of the temperature until it became water?

Solution :

The first temperature was -5 C. after heating, the ice became water with 3 C temperature. It means, the temperature of the ice had an increment, that is the difference between last temperature and first temperature . Take example by the increment of the ice was= t, so the condition could be written as t= 3-(-5) = 8. so, the temperature of the ice increased to 8 C until it became water.


E. The uses of calculate operation on integer for solving problem

(2. FRACTION)


A. Fraction number

A. Fraction number

1. Definition of fraction number

fraction number is number that can be declared that p,q as integer and q is 0. p is called numerator and q is called denominator.

2. Fraction with same value

is fractions that have same value.

In gaining fraction with same value, we can multiply or divide the numerator and the denominator with same number.

If we know a fraction with p,q 0 so = or =, which positive constant b is not zero.


3. Simplifying fraction

A fraction q 0 can be simplified by dividing the numerator and denominator with the biggest common factor(FPB).

In simplifying any fraction , q 0 , obtain = : , which a is the biggest common factor of p and q.

4. Declaring the relationship between two fractions.

In declaring the relationship between two fractions, we should compare the numerator if the denominator of both fractions are same.

5. Determining the position of fraction on number line

on number line fraction locate between two integers. For instance, if the line above, the distance between two integers that are neighboring divide by two, therefore the number line becomes:


6. Determining fraction that the value is between two fractions

In deciding fraction that the value is between two fractions, do the following steps:

a. similarize the denominator of both fractions. Then, determine the value of the fraction that located between the both fractions.

b. Change again the denominator if intended fraction has not be gained for next.

B. Calculate operation of fraction

1. Sum and subtraction of fraction.

a. Sum and subtraction of fraction with integer

b. Sum and subtraction of fraction with fraction

c. The characteristics on Sum and Subtraction of fraction

1. closed characteristics: a+b = c;

2. commutative characteristic: a+b=b+a;


3. closed characteristic: a+b = c

4. number (0) is identical element on summation

5. a+0=0+a=a

6. the inverse of a is –a and inverse of –a is a, so that a+(-a)= (-a) + a =0.

2. Multiplication of fraction

a. Multiplication of fraction by fraction.

b. The Characteristics of multiplication on fraction

1. closed characteristic: a b = c

2. commutative characteristic: a b = b a

3. associative characteristic: (a b) c = a (b c)

4. distributive multiplication characteristic on summation: a (b+c) = (a b) + (a c)

5. Distributive multiplication characteristic on subtraction: a (b-c)=(a b)-(a c)


6) a 1 = 1 a = a; number 1 is identical element on multiplication.

c. The inverse on multiplication

3. Division on fraction

4. Power of fraction

a. number of fraction powered by positive Integer

Occuring:

m factor

b. Characteristic of powered fraction number

occuring


5. Mixed Calculate operation on fraction

The characteristic of calculate operation:

a. Sum operation (+) is as strong as subtraction (+)

b. Multiplication operation 0 as strong as division(:).

c. multiplication operation 0 is stronger than Sum(+) and subtraction(-) operation


6. Calculate operation on decimal fraction

a. Sum and subtraction of decimal fraction

b. multiplication of decimal fraction

c. division of decimal fraction

C. Solving daily problem that has relation with fraction

For example:

Mr. Togar is an employer in a company. Every month he gets Rp 840.000 salary. 1/3 of his salary he uses for his household, 1/5 for tax, ¼ for his children education , the others for saving.

a. How much money saved by Mr. Togar?

b. How much money for each need?


„Thanks“

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Chapter 1 The Characteristics of calculate Operation and its’ uses in problem solving