TO THE READER: The author of this work to him will be recognized very if you to him present your opinion about this work that I offer to him, as well as its presentation and impression. I also thank for any other suggestion to him. My direction email is: [email protected]
FIRST EDITION 2009.
® Copyright. 2006. ® copyright Javier González Cázares Name of the publication house: Gaussian Registries Nº 03-2006-071115045600-01, SEP and Nº 03-2007-081615321700-01, SEP
Rights of Author Art. 184 ® Rights in proceeding no. 2693 17 of August of the 2009 ® * Translated of Spanish with the original title: “Matemáticas con Word y Excel”, of Javier Gonzalez Cázares
INTRODUCTION...............................................................................................................5 PREFACE TO THE EDITION IN ENGLISH…………………………………………….6 FIRST PART I. EDIT OF EQUATIONS--------------------------------------------------------------------------------------------------------------7 PRACTICE # 1. ¿ HOW YOU WOULD WRITE FORMULAS And EQUATIONS IN The LEAF WORD? 8 PRACTICE # 2. "TO EXPRESS A FRACTION IN WHOLE NUMBER And FRACTION 11 PRACTICE # 3. "ARITHMETICAL OPERATIONS WITH EXCEL" 12 PRACTICE # 4. "EQUATIONS OF FIRST DEGREE" (WITH A VARIABLE) 14 PRACTICE # 5. "SOLUTION OF EQUATIONS OF FIRST DEGREE". (METHOD BY FORMULA) 16 PRACTICE # 6. "BINARY SYSTEM" 18 PRACTICE # 7. "THE ARITHMETICAL PROGRESSION" 19 PRÁCT ICA # 8. "FACTORS OF DIVISION 21 PRACTICE # 9. "DRAWING WITH EXCEL" 22 PRACTICE # 10. "IT APPLIES YOUR KNOWLEDGE" 23 "PROBABILITY And STATISTIC" 23 PRACTICE # 11 PRACTICE # 12
SECOND PART II. GENERAL CONCEPTS. -----------------------------------------------------------------------------------------------------------28 PRACTICE 1 3: FRACTIONS REPRESENTED IN CIRCULAR GRAPHS 42 PRACTICE 14: FRACTIONS IN GRAPH DE BARS 43 PRACTICE 15: CIRCULAR GRAPH OF FRACTIONS 46 PRACTICE 16: FRACTIONS 48 PRACTICE 17: SUM And SUBTRACTION OF FRACTIONS 53 PRACTICE 18: SECOND PART: EXTREME OF FRACTIONS 55 PRACTICE 19: ARITHMETICAL MULTIPLICATION 57 PRACTICE 20: FORTUNE-TELLER OF NUMBERS 60 PRACTICE 21: TO DRAW FIGURES GEOMETRICS 63 PRACTICE 22: AREA OF FIGURES IN EXCEL 66 PRACTICE 23: AREA OF A TRIANGLE IN SPACE 68 PRACTICE 24: AREA OF A TRIANGLE IN THE SPACE (THREE STRAIGHT LINES IN THE SPACE) 71 PRACTICE 25:CHEMICAL BALANCE 73 PRACTICE 26: VERIFICATION OF EQUATIONS 75 PRACTICE 27: POLAR COORDINATES And RECTANGULAR COORDINATES 78 PRACTICES 28: INEQUALITIES WITH INECUATIONS 81 PRACTICE 29: SYSTEMS OF EQUATIONS BY RULE DE CRAMER. 85 PRACTICE 30: RULE DE KRAMER 2 (CONTINUATION) 88 PRACTICE 31: SYSTEMS OF LINEAR EQUATIONS (METHOD REGULATES DE CRAMER) 89 PRACTICE 32: LINEAR EQUATIONS BY GAUSSIAN ELIMINATION 93 PRACTICE 33: QUADRATIC EQUATION 97 PRACTICE 34: EQUATIONS WITH AN INCOGNITO 99 PRACTICE 35: EQUATIONS WITH AN INCOGNITO; SECOND PART (USING SCROLL BARS) 100 PRACTICE 36: EQUATIONS WITH AN INCOGNITO; THIRD PART (CONTINUATION) 102 PRACTICE 37: EQUATIONS WITH AN INCOGNITO; FOURTH PART (IT MAKES HIS CALCULATION And IT VERIFIES) 104 PRACTICE 38: EQUATIONS BY RANDOM METHOD 105 PRACTICE 39: STATISTIC 106 PRACTICE 40: GRAPH OF TWO FUNCTIONS 109 PRACTICE 41: CHARTS IN THREE DIMENSIONS 112 PRÀCTICA 42: "INTERACTIVE PARÁBOLA".EXAMPLES 115 PRACTICE 43: PARABOLA (MINIMUM And MAXIMUM) 118 PRACTICE 44: GRAPH OF TWO FUNCTIONS (INTERSECTION OF TWO CURVES) 122 PRACTICE 45: SLOPE OF A STRAIGHT LINE. 1RA. PART 124
4 PRACTICE 46: SLOPE OF A STRAIGHT LINE. 2DA. PART PRACTICE 47: SLOPE OF A STRAIGHT LINE. 3RD. PART PRACTICE 48: REMARKABLE PRODUCTS PRACTICE 49: CIRCLE(With rectangular and polar coordinates) PRACTICE 50: CIRCLE OUTSIDE ORIGIN PRACTICE 51: INTERSECTION BETWEEN A STRAIGHT LINE And A CIRCLE PRACTICE 52: TRIGONOMETRICAL FUNCTIONS: "COSINE" PRACTICE 53: SYSTEMS OF EQUATIONS TWO Xs TWO PRACTICE 54: FUNCTION SPECIFIES PRACTICE 55: EXPLICIT FUNCTION. CONTINUATION P RÁCTICA 56: EQUATION OF THE PARABOLA OUTSIDE ORIGIN PRACTICES 57: GENERAL EQUATION OF THE PARABOLA PRACTICE 58: CHART OF POLAR FUNCTIONS WITH ANIMATION PRACTICE 59: VECTOR (Using coordinated polar)
126 129 131 135 137 140 143 148 152 154 157 160 162 167
GLOSSARY ---------------------------------------------------------------------------------------------- 170
INTRODUCTION THIS WORK THAT APPEARS IN WRITTEN FORM, AT FIRST WAS A SERIES OF LOOSE AND DISORDERED EXERCISES. ALTHOUGH ORIGINALLY "NIÑOS HEROES" WERE DONE FOR THE STUDENTS OF THE TELESECUNDARIA, OF THE COMMUNITY OF BUENAVISTA, FRESNILLO, ZAC., MEXICO; IN ORDER TO EVALUATE A WORK OF INVESTIGATION BUT OF EQUAL WAY THEM THE STUDENT OR STUDENT OF SECONDARY GENERAL OR TECHNIQUE CAN USE. THEY GO OF THE SIMPLE THING, FROM LIKE WRITING FORMULAS IN THE WORD PROGRAM, NOT WITHOUT BEFORE PUTTING A PROBLEM SO THAT THEY MAKE IT IN HOME. IN EXCEL YOU WILL BE ABLE TO APPLY FORMULAS OR TO DEDUCE THEM FOR DIFFERENT CASES. CHILDBIRTH OF WHICH THE STUDENT MUST EXERCISE ITSELF FIRST IN THE HALL CLASS, THAT INCLUDES/UNDERSTANDS WELL HOW TO SOLVE MATHEMATICAL PROBLEMS AND SOON TO VERIFY ITS RESULTS IN THE HALL CALCULATION. ALL GOOD KNOWLEDGE MUST HAPPEN THROUGH AN APPROPRIATE PRACTICAL REFLECTION. THE IDEA IS THAT IT LEARNS TO EXERCISE AND TO COMMUNICATE BETWEEN HIS COMPANIONS AND TEACHERS HIS RESULTS, OF HOW TO USE THE LEAF EXCEL IN THE LABORATORY OF MATHEMATICS, IN SOME CASES THERE IS MAS OF TWO WAYS TO FOLLOW FOR A SAME SOLUTION, MOST OPTIMAL IS THE ONE THAN YOU CHOOSE. IT IS CERTAIN THAT THERE IS AN ENDLESS NUMBER OF WAYS TO ARRIVE, THE JOKE IS TO KNOW AS HE IS BEST, THE LESS MOST TEDIOUS ONE, MORE BETTER IN THE KNOWLEDGE AND APPLICATION TO THE GIVEN PROBLEM. THE EXPERIENCE IN THE HALL SAMPLE THAT A MOTIVATION IN MATHEMATICAL SHOWS ONE BETTER TOLERANCE TO LEARN AND SEARCH OTHER WAYS. THE DISCUSSION ON IF HE IS APPROPRIATE OR NOT THIS RESOURCE IS IN THE HALL CLASSES, WITH THE OWN ONES INVOLVED: LIKE AUTHORITIES, TEACHERS, STUDENTS AND PARENTS OF FAMILY. IN ORDER TO UNDERSTAND THIS BOOKLET IT IS NECESSARY TO SEAT AND TO USE THE COMPUTER, IS TO SAY ACTUALLY. THE LAST ADVANCES IN THE TECHNOLOGY OF THE INFORMATION ALLOW THAT THE MATHEMATICAL ONE IS MORE EXPERIMENTAL. THE STUDENT ALWAYS COMPLAINT OF THE TEDIOUS THING THAT IS TO SOLVE OPERATIONS WITH VARIABLES. HE MATTERS, THAT THE STUDENT LEARNS AN ALGORITHM OR THAT IS ALL THE DAY SOLVING ONLY A PROBLEM? OR, NOT EVEN TO BE ABLE TO SOLVE IT? ONCE LEARNED THE METHOD, HE CAN HAPPEN TO EXPERIMENT AND LOOK FOR OTHER ALTERNATIVES, LIKE REPRESENTING NUMBERS WITH DRAWINGS, WHICH AMPLE THE FIELD OF REFLECTION OF APPLICATIONS AND KNOWLEDGE. THE USE OF OTHER METHODS ALTHOUGH DOES NOT KNOW THEM CAN CAUSE THAT IT HAS A AUTORREFLEXIÓN AND IT CAN PROPOSE OTHER ROUTES OF SOLUTION. IT IS NOT SCARED TO KNOW, IT EXPERIMENTS, IT LOOKS FOR, DOES, ALTHOUGH IT IS MISTAKEN. THESE WORDS THAT WILL FIND IN ALL THE TEXT, ARE A REFLECTION THAT THROUGHOUT THE YEARS I HAVE HAD, AND THAT I THANK FOR MY WIFE JOSEFINA, MY CHILDREN JAVIER ANTONIO AND M. JOSEFINA ADRIANA SU UNDERSTANDING, PATIENCE AND ENTHUSIASM. TO PROFESSORS JOSE.ANGEL GUERRERO LOERA AND LUIS MANUEL AGUAYO RENDON TO BELIEVE IN MY WORK, AND MY FRIEND AND COMPANION OF IN FIGHT FELIPE H. CORTEZ VÁZQUEZ.
J. G. C. JUNIO 2006
6 PREFACE TO THE EDITION IN ENGLISH
This edition has in addition corrections to the edition in Spanish, as they are of style but better even of concept, improve in some cases the result and proposing are added.
The idea to update this work to Office 2007, has been with the idea to spread the mathematical one between that they initiate in this field, to communicate the most complete image of the mathematical field, to offer a greater interaction and participation. But mainly to motivate to that the knowledge flow between creators and students.
Although the difficulty between the mathematicians of the emergent countries now called is distrust towards everything what is technology –that has an historical origin in the formation of colonial societies–, does not have to be reason for not letting pass the opportunity to provoke changes in the economy, sciences, industry and culture.
This work would have to be reviewed and although corrected errors them, as well as their foundations exist to be verified and to be evaluated by the interested ones.
Many mathematical problems exist still that must be solved, and with the traditional methods to do them “by hand” (“a mano”), time and loss of energy have been beside the point very expensive in. With a technology like this one, John Neper (1550-1617) had saved half of his life in constructing his famous tables of logarithms.
All the examples are resolute in the decimal system, reason why if it handles another system makes the changes necessary. J. G. C. OCTOBER 2009
7 FIRST PART I.
The MathType’s translation facilities can be used as component of a more comprehensive document conversion process1, is a very useful tool in Word, transfers formulas, equations, etc. In office 2007 we can accede to the publisher of equations in the card Insert, click Equation
For example: The following you formulate writting in Word:
In order to begin to write, it writes within this image
b2 2a 3x 2
3x 1 ( x 1)( x 1)
x 3 1)( x 2)
TOPPING, Paul; Using MathType to Create TEX and MathML Equations; Design Science, Inc., 4028 Broadway, Long, Beach, CA 90803; USA; e-MAIL [email protected]
; URL: www.mathtype.com
Note: MathType’s Word support is written in that product’s Visual Basic language. The source code is accessible and may be used as the basis for your own conversion scheme.
6d 2c 3d d 2 c 2d
For the first example, we opened and Editor of equations gives click in Immediately it appears.
In order to begin to write, it writes within this image
It begins to write the equation, as well as one appears:
In the end it is this way:
II. PRACTICE # 1 1. ¿ HOW YOU WOULD WRITE FORMULAS And EQUATIONS IN The LEAF WORD? Objective: You will use your abilities to write mathematical formulas and equations in the computer. Order of steps:
9 You open a New Word Document, you write the title "HOW TO MAKE EQUATIONS", soon to center. Like subtitle "the life of Diofant". In Insert + Table choose opened Insert Table click, Number of columns 2, Number of arrows 9, click in OK
With your mouse, in the first column you write "LANGUAGE VERNÁCULA", with the right cursor, you write "LANGUAGE Of ALGEBRA", the pictures that we will fill are those of the left side, those of the right you will fill you to them after the dictation. Second picture, first column (next to be brief so on to third picture and), writes: 1. Traveller! Here the rest of Diofanto were buried. And the numbers can show, OH, miracle, how it releases was his life, 2. Whose sixth part constituted its beautiful childhood 3. One twelfth part to its life had passed in addition, when with hair covered in its chin 4. And the seventh part of its existence passed in a sterile marriage 5. It spent a quinquennium more and it made the birth happy of his precious first-born, (Note: between rows 6 and 7, column 1, you choose To divide to Cells… give click. Again click) 6. that it gave his body, his beautiful existence, to the Earth, that lasted only half of the its father 7. And with deep pain it descended to the grave, having survived four years the decease of his son 8. (Note: you choose two columns in this last row, you go to Table + Dividir Cells… click, you select Negrita, click) Tell me how many years Diofanto had lived when the death arrived to him.
Once finalized all the dictation, you will put the appropriate variables and constants to each step that was indicated, when you have finished it compares your results with the teacher and solves in your house this incognito, that surely you will be surprised of the result.
10 II To HOW TO MAKE EQUATIONS This exercise to use the "MathType", you will make a dictation, takes care of errors of mathematical spelling and handwriting. Next the life of Diofant is related, in epitaphic of its tomb: THE DIOFANTO LIFE2 LANGUAGE VERNACULAR LANGUAGE Of ALGEBRA Traveller! Here the rest of Diofanto were buried. And the numbers can show, OH, miracle, how it releases was his life,
Whose sixth part constituted its beautiful childhood
One twelfth part to its life had passed in addition, when with hair covered in its chin
And the seventh part of its existence passed in a sterile marriage
It spent a quinquennium more and it made the birth happy of its precious firstborn, that it gave its body, its beautiful existence, to the Earth, that lasted only half of the its father And with deep pain it descended to the grave, having survived four years the decease of its son.
x 2 x
It tell me how many years Diofant had lived when the death arrived to him Obvious the result you will do it "by hand", since it beams of regular way or in your house, and your results you compare with your companions and teacher. Exercises: It finds the variables and constants:
PERELMAN, Y, "Algebra recreativa", Ed. Quinto Sol, Mexico, 1983, Pág. 46.
11 1. It is tried to surround a rectangular land and to divide it in three parts with two inner and parallel fences to one of his sides. Find the dimensions of the land if the length overall of the fences has to be of 800 ms and the area of the land is 19.200 ms 2. 2. A page with 3 plg more of length than of width, has 80 plg 2 of impression. Find the dimensions of the page. PRACTICE # 2 "TO EXPRESS A FRACTION IN WHOLE NUMBER AND FRACTION" 2. A FRACTION WRITES IN THE LEAF EXCEL, ITS SIMPLER FORM. It is easy in the Excel leaf only is to know how they are made by hand. Objective: That the student can express the division as were taught to him in primary and expresses fractions improper in whole and remainder. Order of steps: It opens a new leaf of Excel, writes the title "TO EXPRESS a FRACTION IN WHOLE NUMBER and FRACTION", soon in the C6 cell writes the numerator of the fraction, in the C7 cell writes the denominator of the fraction. Center and with Crtl + 1, Wild for the division ray. In B9 it writes "EXPRESS:" In B11 the formula writes =IF(C7=0,"indeterminada",INT(C6/C7)) In C11 it writes "WHOLE".
It selects cells from B11 to D11 (row) lowering a row (D12), choosesing personalize in Home + Merge and center. In the cell E11 the formula writes = MOD ( C6 , C7 ), it gives Crtl + 1, it down chooses line for the line of division.
In the cell E12 the formula writes = C7 it gives ENTER. NOTE: you can change to the numerator and denominator for different results.
EXERCISES: 1. It applies the divisibilidad criterion to find the multiples of any number. How to find if a number is splitter another number.
PRACTICE # 3 “ARITHMETICAL OPERATIONS WITH EXCEL” 3. IT CONDUCTS DIFFERENT ARITHMETICAL PENCIL OPERATIONS, SOON VERIFIES YOUR RESULTS IN THE SPREADSHEET EXCEL. Objective: You will learn how to conduct arithmetical operations with computer. Used expressions or symbols: You will use the following symbols in Excel, like ( + ), ( - ), ( * ), ( / ), ( ^ ), ( ABS), (COS), (SIN), (INT), (EXP), (FACT), (DEGREES), (PI), (POWER), (SQRT), (MOD). Examples: It conducts the following operation by hand: (4)*(-5)*(-2) How much it is to you? Well, now it introduces these operations in a new Excel leaf: First you must write in the cell B7 soon the equal sign so that it is solved like a formula, the operation (4)*(-5)*(-2)
In the end it gives ENTER. Your result is equal when introducing to Excel leaf?, if it is not thus it corrects. Example: now it makes 4*9 + 50/10, by hand; soon in Excel, it remembers that first you must introduce equal sign ( = ).
In the following exercises, first to solve by hand and later in Excel. EXAMPLES (8+5)*(2) 8+5*2 (8/2+5)*(1+8) 8^4 6*(8+9-(15/3)^2) ABS(-789) COS(60) SINE (60) WHOLE NUMBER (15.548888) EXP(1) FACT(8) DEGREES (1) PI()
14 POWER (4,3) RAIZ (144) REMAINDER 3 4 FACTORIAL 8 8*2-5^3*(1/8) 8^2*5+3/1-8 8+2^(5-3)*3*1/8 8^(2+5)-3^1/8 8^(2*5)/3+1-8 It remembers that first you must do it by hand and soon in Excel, it compares your results and it concludes. I recommend to you that the steps 3 to follow in an operation of Arithmetic can vary according to is the case, but first you must consider that first you conduct the operations that are within the parentheses, soon multiplications, divisions and powers, finally you carry out the sums or subtractions.
PRACTICE # 4 “EQUATIONS OF FIRST DEGREE” (WITH A VARIABLE) 4. IT APPLIES YOUR KNOWLEDGE OF CLEARS OF EQUATIONS TO FIND A "FORMULA” THAT SOLVES EQUATIONS OF FIRST DEGREE OF THE FORM:
ax=b An equation is a statement in which two amounts are equal, the equals sign is placed in the middle of these two. The equations have one, two or more letters, variable or incognito calls. By means of algorithms we can find the values of the variables, these they are replaced in the equations, they make equal as well to both members of the equation, it is to say satisfy to, or is a solution of. The total of the solutions is known him like set of solutions. It is as well as for the general formula of an equation to prioritize degree with a variable and a constant it will be:
Its solution, for when: It is: 3
--------------------- Formula (1)
For more examples: http://homepage.cem.itesm.mx
15 Of equal way when, an equation with a variable is had and two constants, the rank of a is the same one:
The general formula is:
Reason why clearing it is had.
-------------------- Formula (2)
In both cases, the value of a, will not be zero, by definition. Objective: Find you the algorithm general or particular Excel, for equations of first degree. Order of steps: It opens a new Excel document. The title writes "EQUATIONS OF FIRST DEGREE (WITH a VARIABLE)", soon in the interjection to, "the case for a constant", writes respectively in the cells B8 and B9 to and b, now the values of each one of them, those that you want. Immediately, "the value of the variable is:", in the B12 cell, x writes "=", C12 cell the corresponding formula. As the formulas are defined based on which the denominator is not zero, since he would give to a indetermination or an infinite number us, to solve them is necessary another course advanced more, but so far we put a restriction to our formula. = IF (C8=0," indeterminate ", C9/C8) Why "indeterminate? Consultation to your teacher. In summary it would be thus:
Once finished, you begin in the following cell writing: "b) the case for a variable and two constants". And you follow the same procedure that the previous one, only that now in the formula you will add the following thing: =IF (C21=0, “Indeterminate”, (C23-C22)/C21)
In summary: It verifies your values, changing the values of coefficients and constants, it by hand makes these calculations and in the computer. EXERCISES: 1. For next equations to deduce the general formulas:
ax ax ax
b c b c b
ax b ax b ax b
c c c
Once deduce the formulas; to aplicate now in the Excel program, soon head of cattle to solver for different values.
PRACTICE # 5 “SOLUTION OF EQUATIONS OF FIRST DEGREE” (METHOD BY FORMULA) 5. IT APPLIES YOUR KNOWLEDGE OF CLEARS OF EQUATIONS TO FIND A "FORMULA”, WHICH SOLVES EQUATIONS OF FIRST DEGREE OF THE FORM:
ax b cx d OBJECTIVE: That you determine the value of a variable from a formula that you deduce in your hall or your house, to be able to solve equations of first degree in general forms. Be the general formula, for an equation: The solution will be:
ax d a
b b c
17 This formula is applied when: a
Ordered steps: Now, it opens a new document Excel. The problem to solve is: The theory writes as it comes in the Excel presentation, soon in the cells B50, B51, B52 Y
B53, the letters of each constant or coefficient successively. From C50 to C53, the values of each constant or coefficient
For example: The value which you introduce in the computer, by a = 8, it is in the cell C50, to add 8 beams ENTER and it is added automatically, to do successively with the other constants.
Once finished, in the E52 cell we put x =, to say soon that the value of X is…, in the F52 cell, we put what follows: =IF (C50-C52 =0," infinitely, without real solution ", (C53-C51)/ (C50-C52))
It verifies your results, in the notebook. It voluntarily changes the values for different problems. EXERCISES: 1. On the basis of the proposed algorithm it solves for one of the following cases, it bases your deductions on Word the Publishing leaf of equations, and soon to apply to Excel, for each case, it varies his values to verify your results:
ax b cx d ax b cx d
ax b cx d
PRACTICE # 6 “BINARY SYSTEM” 6. IT TURNS A NUMBER DECIMAL TO THE BINARY SYSTEM THE SPREADSHEET. Objective: You will use the binary algorithm to change to the decimal system. Order of steps: You open a New Excel Document, you write the title "BINARY SYSTEM OF NUMERATION", point to aside and write "EXPRESSES the BINARY NUMBER To NUMBER DECIMAL", aside you write "INTRODUCES ANY BINARY NUMBER IN the ROW OF the TABLE:”. We are going to form a table from B8 until J11, you tighten Crtl + 1, choose Format Cell +Border + Outline + Inside + OK, soon for each row choose a Color of different Filling. In the row POSITION, you add in C8 number 8, D8 the 7 and so on until J8. In the row POWER, you add in C9 the formula = (2) ^7, in, D9 the formula = (2) ^6, and so on until J9.
In the row BINARY NUMBER, put on the binary number that you look for. Well-taken care of Ten that you begin to put it of right to left.
19 In the row POSITIONAL VALUE, in the C11 cell, put the formula = C10*C9, in cell D11, put on the formula = D10*D9, and so on until the J11 cell.
From the A14 cell, you write "THEREFORE the BINARY NUMBER TURNED To NUMBER DECIMAL IS:”. SUM In the B15 cell, you write the formula = SUM(C11:J11). It is of this form:
It verifies that the values of the formulas well are reviewed. Exercises: there are east exercise but in the quinary system this exercise in the system octal
PRACTICE # 7 "THE ARITHMETICAL PROGRESSION” 7. IT INCREASES 0.5 TO THE VALUE OF 1, TO KNOW ITS BEHAVIOR, TO USE THE CONCEPT OF ARITHMETICAL PROGRESSION Objective: To apply linear or progressive a succession of numbers. You open a new Excel document, Beams just like this in the figure.
Selects Home + fill + Series.
The Series, is Rows + Step value 0.5 + Stop value 5 next OK.
It is thus:
Exercises: 1. It makes in progressive order of 2.0. 2. It makes in order regressive (or decreasing) of the order of – 6. 3. another one in order of - 12. 4. The following problem, is said that it solved the great mathematician Gaussian, of boy when his teacher of School let to his students add all the consecutive numbers from the one to the one hundred. a)Resuélvalo by hand, for it I propose to him writes down all the numbers to add them, soon finds the relation among them. b) To contrast its result with the following formulas: n = to + [ (N - 1) x r ] S = (to + n) x N/2
21 to = first term of the progression n = last term of the progression r = reason N = number of terms S = sum of the terms of a to n. Which is the succession of the following formula? It calculates this by means of significants, is to say very great to know the conjecture correct.
PRACTICE # 8 “DIVISION FACTORS” 8. IT FINDS THE FACTORS OF DIVISION OF ANY NUMBER USING THE SPREADSHEET EXCEL. Objective: You will remember it forms in how finding the splitter of any number and the use of the splitters to solve examples. Order of steps: It opens a new Excel document, pon the title with size 20, font Times, capital letters, "FACTORS OF DIVISION”. Next you will put the formulas, for example, in the C4 cell, pon any number, next in the cell D4, the number to which "you will guess" if it is division factor, in the E4 cell, you add the formula = IF(MOD(C4,D4)=0, "is SPLITTER, CONGRATULATIONS!", "YOU WERE MISTAKEN, TRIES Again"), in the H4 cell when is not the division you put = IF(C4=1, "YOU FINISHED, CONGRATULATIONS", "IT CONTINUES"). Once finished, you must put the formula from which you obtain the quotient, from the C5 cell, this way: = C4 / D4. For the other cells since you will find more splitters, copy.
EXERCISES: this same exercise but with two factors; same but with three or more factors
22 PRACTICE # 9 “DRAWING WITH EXCEL” 9. YOUR IMAGINATION TO DRAW FIGURES IN THE LEAF EXCEL Objective: You will draw in the Excel leaf, having used your imagination. Order of steps: It opens a new Excel leaf, soon selects all the document. With the mouse it selects the number of rows that you wish, next, Home + Format + Rows height, selects 6.
Now, with the mouse it selects the number of columns that you wish, In the superior corner of the leaf of I calculate gives to click and select all the cells, to continuation next in the card Home + format + Column width. Select 3. Click, OK:
Soon there are drawings as if each picture was vectors or pixels of a figure, for it use the filling color, selects Fill Color
that you wish and. The others run of your account. As you see in the example that is next:
EXERCISES: it elaborates your own drawings.
PRACTICE # 10 "IT APPLIES YOUR KNOWLEDGE"
24 10. IN THE SPREADSHEET FIRST IN A COLUMN, THERE ARE A TABULATION FROM -1,5 TO +2, SOON CALCULATES FOR EACH DATA WITH THE FUNCTION 1 , IT FORMS ONE SECOND COLUMN, WHEN YOU FINISH, CHARTS THESE y x DATA. Objective: You will apply your knowledge to find the behavior of a series of data, in a graph. Order of steps: When expressing values, magnitudes or other data by means of tables, we can intuit its behavior, but when they are many data is very difficult, reason why we will use a technique of Excel to be able to relate the numbers to figures is to say graphical Cartesians. It opens a new Excel document, soon put the title "WONDERFUL FUNCTIONS", soon "to graphic the function” and you put the formula:
It begins with the first column, you put X, later for down you put number – 1,5, ENTER, in that cell Home + Fill + Series, click. Select column with Step value of o.3 and Stop value 2. In the following column next to X, you put and, later ENTER, in that cell you add the formula = 1/A6, ENTER, select to that formula it copies, soon it selects downwards all the cells and it give ENTER to copy the formula and it alongside applies it according to the data.
As time the column alongside collects all the previous data like ordered data, in D6, you put = A6, in the F6 cell you put = B6, ENTER, copy and you select them for all the found values. You select the two columns, it gives click in Assistant for graphs, and you follow the steps that already you know, and in the end you have left of the following form:
1. 2. 3. 4.
It answers the following questions: It explains the behavior of the graph. What happens in point x = 0? Can be modified the behavior of the graph? It explains as it is the division of a constant number between zero
EXERCISES: THERE ARE A GRAPH OF THE FOLLOWING DATA X Y -3 -21.25 -2.5 -10 -2 -1.25 -1.5 5 -1 8.75 -0.5 10 0 8.75 0.5 5 1 -1.25 1.5 -10 2 -21.25 2.5 -35 IT EXPLAINS ITS BEHAVIOR. a) how it is its graph? b) it explains when the curve has an increase or diminution c) this graph is followed in other matters and applications very. in which matters? in which applications of the real life?
26 d) The table shows the brake horsepower in H.P., at several speeds, of certain Pelton turbine, as it has been verified by means of a series of tests. Construct a graph that shows to the relation between brake horsepower in H.P. and the number of RPM. Power in H.P. 0.625 0.668 0.673 0.658 0.640 0.590 0.530 0.475 0.390
RPM 1120 1360 1500 1750 1980 2100 2340 2500 2700
PRACTICE # 11 "PROBABILITY AND STATISTIC" I 11. STATISTIC: IN THE FOLLOWING TABLE THE TEMPERATURES OF THE YEAR OCCUR, CALCULATES THE TEMPERATURE AVERAGE. MONTH
JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER
10 14 20 22 24 25 26 24 20 18 15 12
Objective: apply to the formulas of statistic and probability to solve simple examples. Solution: It opens a new spreadsheet Excel, soon you add these data like table, and put on click in B18 you put the formula: = AVERAGE (B5:B16)
PRACTICE 12 "PROBABILITY AND STATISTIC" II 12. PROBABILITY: HOW MANY EXCHANGES CAN TAKE CONTROL OF THE 9 LETTERS OF WORD FRESNILLO? Solution: a letter F, a R, one E, a S, a N, an I, two Ls and one O: The formula to calculate the number of exchanges with n objects,
n! n1 !n2 !n3 !...
You open a new Excel document, you write down your results, with the previous formula: In the spreadsheet it is thus: =FACT(C3)/(FACT(C4)*FACT(C5)*FACT(C6)*FACT(C7)*FACT(C8)*FACT(C9)*FA CT(C10)*FACT(C11)) See as it is in the leaf:
28 EXERCISES: 1. Of how many ways four pairs can seat around a table if men and women have to alternate themselves? 2. In the statistic problem it finds the fashion, the maximum value by formula, minimum value by formula; in addition it makes a graph de barras vertical.
SECOND PART GENERAL CONCEPTS Excel in the School is a didactic tool with a great potential, although we only use the basic options. It is a computer that allows us: to conduct heavy and complex operations between rows or columns, to order or to look for data and to present/display in graphical form the obtained results, with mathematical formulas of a way fast and easy. Algorithms, models, visualizations, and mathematical uses in execution can be put naturally and with effectiveness through interactive constructions of the leaf of balance and creative graphical exhibitions. This paper demonstrates the techniques that allow educators to design exhibitions animated graphics in their constructions of the balance leaf to produce demonstrations in the hall class to heighten the mathematical understanding, whereas also it presents/displays to students with the new and attractive visual mechanisms in his tasks and mathematical projects. This educative experience makes the development of skills and abilities efficient that allow obtaining better results in the handling of the algebraic language. The use of computer science like attractive means reflects to deepen algebraic concepts using the creativity, the knowledge and the mathematical reasoning. It handles images designed by the user from algebraic expressions when those that the creation of formulas allow their execution. When this happens, algebraic language, algebraic expressions, graphics of functions and its results extend the level of conceptualization and understanding. The abilities necessary to include/understand this text are: To use letters to represent numbers, to evaluate algebraic expressions, to identify algebraic expressions, to construct algebraic expressions, to represent categories of numbers by means of algebraic expressions, to use procedures to identify the parts of a term, to classify algebraic expressions according to the number of terms. The author has interest in developing in the student or teacher: the creative, analogical and critical thought, its interest and capacity to know the reality, to use the knowledge and to select, to process, to organize and to synthesize information, the personal initiative, the creativity, the work in equipment, to create attitudes of rigor, patience and fulfillment of the tasks, to use the software of intention like creative means in the conceptualization and understanding of algebraic expressions.
What must use is its notebook, pencil, computer of the scholastic laboratory, elementary book of mathematics and an average one to keep its tasks.
TYPES OR TEST EXERCISES The Developer card helps us to insert Pictures of Controls and ActiveX, for it looks for Insert Controls and it selects some type of Form Controls or ActiveX click in them.
He is usual that the controls are formed mainly through Visual Basic (VBA). The Properties dialog box for the scrollbar:
When inserting the control, we click with the right button of the Mouse on this control, this so that it appears to us the picture of dialogue of properties of this control. This picture of dialogue as well has in the superior end a picture combining or combobox, which will allow us to form the properties of some other control which we must in the present book with no need to be selecting this one previously. There are two options for the visualization of the properties. First in alphabetical form and second by categories.
The Mode Design, it can modify whichever times is necessary the different controls from our book. The way design is activated when the attached icon is stood out, to activate only makes it lack click on him. In order to leave the way design, it will be enough with returning has to click in this same icon. It is possible to clarify that when we are in the way design the different controls will not be operative, reason why will be necessary to leave this way to be able to use these controls. MAIN PROPERTIES OF THE CONTROL PANEL LinkedCell This property that will use more, is tie with the control at issue. In some cases it will serve so that the control shows the content of this cell, although in most of the cases the one will be the control that conditions the content of this cell. In order to form the control, it will only be necessary to introduce the value rather or the position of the cell that is desired to tie. We recommended doing it in absolute terms, by ej. "A1 ". This is, the cell produced by the concurrence of the column "To” and Row "1 ". Value This property denotes the Value that will have the control. According to it is the interaction that has the control, the value of this one will change. For example in the case of a button of alternating, the property value takes the values "TRUE" (true) or "FALSE" (false) according to it treats. In the case of a control knob of number, the property value will take the value of the respective sequence.
Name This property denotes him name of the control, by Excel defect assigns to a name made up of the type of control but a corelative one to him, for example "CommandButton1". This will serve later to identify this control and to form it for example through macros or VBA.
Min, Max, SmallChange Corresponding they indicate the minimum value of the control, the maximum and the value in which this one will be changing (increase or decrement, according to is the case) whenever click becomes on anyone of the arrows of this control. The value of SmallChange property can be any whole number, although the interval of values recommended is from -32767 to +32767. The predetermined value is 1. In the Excel leaf, sometimes it must modify the presentation of graphs, cells, or another thing. Here recommendations.
31 Source: In this card we can specify options about the source in which are going away to visualize the selected data, or the style, the source itself, the size, the emphasized type of, color and several effects more. Also we can see like in all other cards it shows of which we are doing. Almost all the commands who are in this card, them we can find in the bar of tools Format.
Border: it defines the type of line and the color of all the edges (internal and external) that the selected rank has. Fill: it defines the bottom of the cell or selected rank (generally a color).
32 Protection: it has options with respect to the protection of the selected rank or cell. The graphs now are more dynamic, since directly it inserts them: go to Insert + Charts and you select the Chart that wishes. BAR OF FORMULAS Bar located in the superior part of the window that shows to the constant value or formula used in the active cell. In order to write or to modify values or formulas, it selects to a cell or a graph, writes the data and, next, it presses TO ENTER. Also it can make double click in a cell to modify the data in her directly.
Like predetermined value, Excel calculates a formula of left to right, beginning by the equal sign (=). The arguments can be logical numbers, text, values like TRUE or FALSE, matrix, values of error like # N/A or references of cell. The argument that is designated will have to generate a valid value for the same one. The arguments also can be constant, formulas or other functions. The syntax of a function begins by the name of the function, followed of an opening parenthesis, the separated arguments of the function by commas and a parenthesis of closing. In order to introduce a formula that contains a function, it clicks in the cell in which it wishes to introduce the formula. Once it completes the formula, presses TO ENTER.
ABSOLUTE, RELATIVE AND MIXED REFERENCES Excel always uses relative references for the directions of cells introduced in the formulas. This means that the used references will change of agreed way after copying the formula from a cell to another one. Very frequently this one is the wished behavior. In certain cases it is necessary to avoid that the references to cells change when the formula to a new position is copied. For it it is necessary to use absolute references. It is possible to use absolute references for relative rows and for columns, or vice versa. The relative references become absolute introducing the character dollar ($) before the letter of the column or the number of row, that is wanted to maintain invariable. If it is desired that it changes neither the index of rows nor of columns, it is necessary to both put the character dollar ($) in front of each one of indices. An absolute reference can be inserted of two different forms: 1. According to the formula is introduced, keys in character $ in front of the row index, back if it is column that is wanted to maintain constant. 2. Placing the point of insertion in the bar of references so that it is within the reference to the cell, pressing the F4 key goes cyclical through relative, absolute references and by both
33 mixed cases. In the cases in which only one of the two dimensions is tried that, row or column, he remains constant is used a mixed reference, that is to say, a reference that contains absolute and relative references simultaneously. For example, the reference $A5 avoids that it changes the column, whereas the row adapts whenever the formula is copied. With A$5 it happens the opposite: the column changes, whereas row 5 always remains constant. REFERENCES AND NAMES The references to cells are used to talk about to the content of a cell or group of cells. The use of references allows using values of different cells or groups from cells of a spreadsheet to make certain calculations. References to cells of another spreadsheet can be introduced also, introducing the name of that leaf before the reference to the cells, and separating them by the admiration sign (), for example: (Sheet1! B5:C6). It is important to know that in the references to cells or groups of cells, Excel does not distinguish between capital and very small letters. NAMES OF CELLS AND SETS OF CELLS Sometimes it turns out annoying to have to repeatedly use references such as B2:B4 or B2:D3; C5:D6 in a spreadsheet, or to select such ranks time and time again. Excel solves east problem allowing to define names and to assign them to a cell or to a selection. These names of cells or ranks can be used in the formulas, be created composed names, and even be assigned a more significant name to the constants of more frequent use. The use of names in the spreadsheets diminishes the possibility of introducing errors and allows remembering with greater facility the references to cells. At the time of creating names, it agrees to consider certain rules: 1 the names must always begin by a letter or the emphasized character (_); after this first character, any set of letters, numbers can be used and special characters. 2 spaces in target cannot be used. Like alternative to the spaces in target, a character of emphasized or a point can be used. 3 Although names can have up to 256 characters, agrees that they are shorter. Since the formulas are limited 256 characters, the long names leave less. NAMES OF CELLS And RANKS Or GROUPS OF CELLS. The form simplest to define names is by means of the commando to Formulas + Define Name + New Name. For it, the following steps can be followed: 1. To select the cell, the rank or the multiple rank to which it wishes to assign the name. 2. To choose the card Formulas + Define Name, with which the shown one in the figure is opened to a dialogue picture as.
3. To key in the name that wishes - in this case concept - in the picture Book Names of Work. 4. To click in Adding or OK. Another possibility - simpler it is to select to the cell or ranks of cells to which it is desired to give a name, and soon click on the picture of names of the reference bar. The reference to the active cell is replaced by the name keying. When pressing OK the selected cells they are registered with the name keying. If what is desired it is to change a name to cells it must come from the following way: 1. To select the cell, rank or multiple rank to which it wishes to change the name. 2. To activate the picture of names in the reference bar. 3. To change the name and to press To OK. In order to erase a name the button can be used To eliminate of the dialogue picture GRAFICS If the values of a graph are made up of great numbers, change automatically, can be reduced or increase the text of the axis and make it more legible. For example, if the values oscillate between 1.000.000 and 50.000.000, it can show numbers 1 50 with in the axis with a label that it indicates that the units are millions. Make the following thing: Create a graph. Select with the right button of the mouse the axis of values that this constituted by numbers of great magnitude. Select to the option Format of axis. Choose the unit of more appropriate visualization to the data and give Close.
FORMULAS AUDITING Sometimes it is mistaken in the formula, when it passes this, in Card + Trace Precedents or Trace Dependents…
This action determines if the elimination of a certain cell can have detrimental effects on the leaf. Thus, if it is wanted to eliminate a cell, but security is not had on if the spreadsheet it is affected by the elimination, can be resorted to the bar Audit finding the cells that depend on her (To track Employees) as well as the cells on which it depends (To track Precedents). Next are arrows that indicate the selected thing. The arrows remain in screen until the leaf keeps or until clica on the button To take off All the Arrows.
In order to include new a series of data in a graph the new rank of data is copied and it sticks on the graph. PROTECTION OF A LEAF The cells by defect come blocked. If we wished to unblock some of them we must do the following thing: First Home late Format, Cell, eyelash to protect, to clear the square of verification that this putting by defect in Unlocked. If we marked Hidden not it will see the content of the cell in the bar of formulas. This becomes when it is not desired that somebody sees the formula of a cell. Later the leaf is due to protect with: Tools, To protect, To protect leaf. Actions can be allowed him more or less the user. If we did not allow to select the blocked and unblocked cells him it will not be able to be positioned with the cursor on them. If we solely let select the unblocked ones to him we will find with something similar to a form.
Some abbreviations of keyboard Ctrl + C Ctrl + V Ctrl + X Ctrl + Z
Copy Paste Cut Undo
37 To protect cells With Format, Cell, Protects, to clear the square of Blocked verification in obtains that in these cells it is possible to be written after executing Tools, Protecting, To protect leaf. To hide formulates it in a cell With Format, Cell, to protect, Hidden the cells are marked whose formulas or contained sight in the line of edition are desired to hide. Later it is had to protect the leaf, with Tools, to protect, to protect leaf. INTERPOLATION and EXTRAPOLATION. The interpolation and the extrapolation are two concepts of modeled mathematical, are very important to do predictions in the s natural, social, economic science s, etc.; specially, the students will begin to explore models linear or not linear. An introduction can be done using an interactive leaf of balance. "To interpolate or to extrapolate" the spreadsheet allows to discover the graphical difference re two or more terms with only one understanding of the equation of a line. In a leaf it selects with the mouse, the line to graphic, soon with the right button chooses To Add Trendline…
To select TrendLine to its pleasure
Choose, click Display Equation on Chart.
As it is seen, the equation of the straight line appears which gives a behavior us. IN ORDER TO PRESENT/DISPLAY A GRAPH IT CAN MAKE THE FOLLOWING THING: Previously it makes its graph normally, is recommended that it chooses Dispersion, for the graphs. When it already is, in the Lines of Division, click Layout + Gridlines, choose something: Primary Horizontal Gridlines or Primary Vertical Gridlines
Soon in the graph, right click in some of the two lines and chooses Format of Lines of Division, discontinuous Plots, Customized, Lines, click in the color that you prefer, To click. For the color of the layout area, it give click in this area and Format of layout area, choose Wild No, Area None, next OK.
Until now, to copy formulas from a cell to other(s), one takes control of Ctrl. + C, but are another way to do it. When to is escri its formula underneath approaches the cursor the right of the picture. See that the cursor becomes an X, of click in the left button of the mouse and maintaining it, to drag to where wishes, single to loosen.
40 SOME USED FORMULAS ABS (value): It gives back absolute value of the argument number. Examples: The function Abs(-5) gives like result 5. The function ABS(10) gives like result 10. function Abs(-2) gives like result 2. RAND( ): This function gives back at random included/understood value between 0 and 1. This function does not have arguments. Whenever it is generated a random value different from will be previously calculated. CONCATENATE(): It unites several text elements in one single one. Their syntax is TO CONCATENATE (text1; text2; …); Text1, text2… they are of 1 to 30 text elements that will be united in a unique text element. The text elements can be text chains, numbers or references to unique cells. COS(number): This function calculates the cosine of the argument number. The angle comes expressed in radianes. INT (value): It gives back the whole part of the number, without concerning the magnitude of the part decimal. That is to say, it gives back to the number eliminating the part decimal. For example: INT(3.1) it gives like result 3. DEGREES (value): It turns the expressed argument radianes to degrees. For example, DEGREES (PI()) gives like result 180 degrees. DEGREES (PI()/2) it gives like result 90 degrees. MDETERM (matrix): It gives back the one determinant matrix. The argument matrix can be a rank of cells or a constant. This function gives back an only value. It is generated error code # VALUE! if at least one cell of the matrix contains a nonnumerical value or if the cell is empty. The matrix must have the same number of rows and columns; If it is not fulfilled this restriction, the function gives back error code # VALUE! MINVERSE (matrix): The result generated by this function is the inverse matrix of the argument that is of first type. In the example, it is explained how to calculate the inverse matrix. MMULT (matrix1, matrix2): The result of the function is matrix product of matrix1 and matrix2. The number of columns of matriz1 must be the same number of rows that matrix2. The matrix result has the same number of rows that matrix1 and the same number of columns that matrix2. Remember that as one is a function that gives back a matrix, procedure is similar to the explained one for function MINVERSA. RADIANS (): This function takes the argument angle that is expressed in degrees and gives back its equivalent one expressed in radians. For example: RADIANS (90) it gives like result 1,571, is to say PI/2. RADIANS (180) it gives like result 3,142, is to say PI
41 ROUND (number, num_digits): It gives back to the argument number, with the amount of decimal specified in the argument núm_decimals, making the approaches of I clear respective. For example, ROUND (1.4545, 2) gives like result 1.45. MOD (number, divisor): The function divides to the argument number between num_divisor and gives back to the remainder or rest of this division. If the division is exact, the remainder gives like result zero. Example, MOD (20, 5) gives like result 0, MOD (9, 4) gives like result 1, MOD (12,8) gives like result 4. SIN (number): This function gives back to the sine of the angle specified in the argument number. The angle goes expressed in radians. For example, in figure no. 21 it is possible to be observed that in each one of the cells of column B, the sine for the corresponding value of each one of the cells of the column To A calculates the right is including the graph of the function sine. IF (): it allows us to make a logical question, which can have two possible results True or False and of acting of one or another form according to the obtained answer. Structure: Logical IF (Logical_test; Value_if_true; Value_if_false). Checks whether a condition is met, and returns one value if True, and another value if False. What we write within the second and third argument they will be the actions that will be made in case that the answer to the logical question is true that is false. Both first arguments are only the obligatory ones for this function. In order to make the logical question we will be able to use the following operators of comparison:
= in order to ask if two values are equal, > to know if a value is greater than another one, < to ask for minor, > = with this we will be able to know if he is greater or equal, < = we asked for equal minor or, < > if they are different s Example: It imagines that in the A1 cell we wrote the age of a person and in the A2 cell we want that appears "the Greater" text in the case that the age is equal or superior to 18, whereas in it will to us appears "Smaller " in case the age is smaller of 18. The function that we would have to write would be = ";"Minor "IF(A1>=18;" Greater”). It observes that in the first argument we asked for greater or just as 18, if the answer to the question is True will be made the second argument: "Greater", however if the answer is false, we made the third argument: "Smaller". OR: This function also usually is used jointly with the function IF(). With her also we will be able to make several questions within If and the part that is in the reserved argument for when the question she is true, will be only made in the case that anyone of the answers to the questions within that is the true one. Structure: OR(Question 1; it asks 2; it asks 3;…)
42 Example: We will use the same previous example but we will let pass if the person is greater of 16 years or measures more than 150. This way whereupon one of the two is fulfilled will appear the text "Can happen". The only case that will appear "cannot happen", will be when the two questions are not fulfilled. = IF (OR (A1>16; B1>150);" It can happen";"Not can happen"). AND: This function usually is used jointly with the function IF(). It allows us to make instead of a question several. And the argument located in the true part will be only made of If in the moment that all the answers are true. Structure: AND (Question 1; it asks 2; it asks 3 ;…). Example: In the A1 cell, we will introduce the age and in the A2 the stature of the person measured in centimeters. In the A3 cell it will appear the text "Can happen" if the age is greater of 16 years and measures more than 150. In the case that some of the two conditions is not fulfilled, it will appear the text "cannot happen". = IF(Y(A1>16;B1>150);" It can happen ";"Not can happen") It observes that all the AND() function is written within the first argument of the function IF().
FRACTIONS REPRESENTED IN CIRCULAR GRAPHS And OF BARS Several types of graphs in the Excel leaf exist, for our case we will use those of Circular type and Bars, that is most appropriate.
PRACTICE 13 FRACTIONS REPRESENTED IN CIRCULAR GRAPHS 13. It explains as they are the steps to graphical a fraction in the leaf Excel. In order to begin, we will make that it varies the value of the denominator causing who each value in each cell is unitary, for it draws a bar of displacement of the bar of Forms, ties its value with the cell origin Order of the steps: It opens a new Spreadsheet Excel. The fraction writes that you want to represent, now writes number 1 (one), in the E6 cell, the F6 cell is = IF($4>=2,1,0), in G6 is: = IF($4>=3,1,0), in the H6 cell is = IF($4>=4, 1, 0), in I6 is = IF($4>=5, 1, 0), and so on until the X6 cell = IF($4>=20,1,0). Grafics these results: In the Insert card it looks for Charts and it chooses Pie click in 2-D Pie selects first:
Change the graph to represent it and modify its results. Put bars of sliding to the denominator.
It is important that you understand because the denominator is not equal to zero.
PRACTICE 14 FRACTIONS IN GRAPH DE BARS 14. CHART A FRACTION IN THE GRAPH DE BARS, VARIES THE DENOMINATOR OF THE FRACTION, FOR IT DRAWS A BAR OF DISPLACEMENT OF THE BAR OF FORMS, TIES THEIR VALUE WITH THE CELL ORIGIN. Objective: to include/understand the fraction from bars, using the Excel Leaf. Order of the steps:
44 It opens a new Excel leaf, and put the fraction that you want to represent. As we present/display to a fraction until tenth second part of a whole number, we will write twelve formulas to represent it. For example in the cell, D7 the formula is: = 1/B$3, in the E7 cell is: = IF ($B$3>1, D7), in the F7 cell is: = IF ($B$3>2, E7), in G7 is: = IF ($B$3>2, f 7), in H7 is: = IF ($B$3>2, G 7), in I7 is: = IF($B$3>2, H 7), in J7 is: = IF($B$3>2, H7), in K7 is: = IF($B$3>2, H7), in L7 is: = IF ($B$3>2, K7), in M7 is: = IF($B$3>2, L7), in N7 is: = IF ($B$3>2, M7), in O7 is: = IF ($B$3>2, N7). Select and graphs: Select the cells to chart:
In Insert 2-D chooses Bar soon Bar + Stacked Bar to give click
It appears the graph that follows:
Unlike which we did in Excel 2003, we will do the following thing: it selects the chart, soon in Switch Row/Column click, surprise!
Clear the axes, and lines:
Change the values of the axes to be able to visualize them better:
Modify the values to see its representations, experiences its results.
PRACTICE 15 CIRCULAR GRAPH OF FRACTIONS 15. GRAFIQUE A FRACTION BUT VARIES The NUMERATOR And The DENOMINATOR OF The FRACTION, FOR IT DRAWS TWO BARS OF DISPLACEMENT OF The BAR OF FORMS, TIES HIS VALUE WITH The CELL ORIGIN. Objective: that it represents fractions with a circular graph: Order of the steps: Open a new Excel Leaf: In B7 and B8 it puts numbers and to express like fraction. Soon to tie with bars of displacement, the picture of forms:
Like note, the F7 cell ties the same with the cell B7. Make for the F8 cell; the values minimum are 1, and the maximum is 10. In F7 the formula = B7, in the F8 cell the formula to be able to evaluate an average or fraction is: = B8-b7. It selects these values:
In order to graph, in Insert: choose Pie + 2-D Pie:
Click in Finalizing. It changes the values as you wish, and experiences your results. Up to here the related thing to the graphs of fractions, can do hers inventing others; for example as they would be if we united two fractions. Exercise: this example can represent fractions smaller one, what happens when the fractions are greater to a whole number? Make the changes appropriate to be able to represent them suitably
PRACTICE 16 FRACTIONS 16. MAKE THE METHODOLOGY FOR CHART A FRACTION BY MEANS OF BARRAS, BUT IT VARIES THE NUMERATOR LIKE DENOMINATOR, USES TWO BARRAS OF DISPLACEMENT. Open a new Excel document In the Excel leaf it puts the fraction that is going to graph:
In the cell D9 put on the formula = B3, in the E9 cell the formula = B4-B3 to graphic the fraction:
49 In D11 = IF ($D$8=10;$X$7;$W$7),
The third number (2 by 1) is if in the T8 cell the formula is written =$O$4*$I$4 , in U8 it writes =IF($T$8>=10;MID($T$8;1;1);0) ; in V8 =IF($T$8>=10;MID($T$8;2;1);$O$4*$I$4) , in W8 the formula =Z7 +T8 , in X8 to put =IF($W$8>=10;MID($W$8;2;1);0) , in Y8 it writes down =W8 , and finally in Z8 is =IF($Y$8>=10;MID($Y$8;1;1);0) .
When tying these results with the cell I6 and H6, =IF($W$8>=10;$X$8;$W$8) and in addition =Z8 respectively.
In order to carry out the other multiplications of the tens and hundreds it makes the same procedure above written.
In the end it ties to the numbers with bars of displacement, 100 minimum values of and maximum of 999. EXERCISES. 1. how it would do so that one of the factors can change from values of 10 to 999? make the change in the spreadsheet. 2. What factors give like result an ascending value? 3. design a spreadsheet to make the multiplication interactive, as next one is:
PRACTICE 20 FORTUNE-TELLER OF NUMBERS 20. HE GUESSES THE NUMBER THAT I THINK USING SIMPLE ALGEBRAIC EQUATIONS. Objective: that you shape in equations the words of a given problem. Order of steps: Open a new Excel leaf, and put on like title "the fortune-teller of Numbers", soon in the A10 cell writes: “IT THINKS ABOUT a NUMBER”, in A11 writes “SUM”, in A12 the
61 “RESULT BY”, in A13 “SUBTRACTION”, A14 “SUBTRACTION the THOUGHT NUMBER”, in A15 “MULTIPLIES BY”, in A16 “SUBTRACTION”. It sees the figure following so that you DES an idea of how it would be.
Now it adds numbers as one is in the cells, C11 even C16.
The problem considers thus: It is an equation of first degree with a variable:
If we cleared, we have:
In order to raise the equation in Excel, they are only mechanical steps as you observe, reason why the constant coefficients of the variables and terms change according to the case, for example:
In the G11 cell, put the formula = C11; in D12 cell, = C12; in G12 cell, = C12*G11, in G13, = G12 – C13; in D14, = D13 – 1, in G14 put =G13; in D15, = C15*D14; in G15, = G14*C15; in D16 is =D15, but in G16, = G15-C16. In any place this writes, for example in the cell H20, “in the end it will say to you as it is the result and your you will say to him as it was the number”:
But this cell put a name: goes Formulas in Define Name. It defines the name, in this case, Number: next To OK:
Or, you can write in the bar of you formulate its name, simply written in Name Box, and to continuation ENTER: In A22 writte “then the thought number is equal to”. In the K22 cell, put the formula: = (number-G16)/D16 With your friends or companions it makes east exercise changing of situations stops “to guess of which numbers you thought”.
63 PRACTICE 21 TO DRAW FIGURES GEOMETRICS 21. IT DRAWS A SQUARE And A TRIANGLE IN The CARTESIAN PLANE EXCEL, USING The COORDINATES LIKE VERTICES OF The FIGURES Objective: To create geometric figures in the Cartesian plane, using the coordinates of its vertices. So that the points are united uses the Graphical "Dispersion with points…" Order of the steps: It draws a square: As a square has four points, tabulate those four points in the Cartesian plane but we repeated the first point for "closing" the figure.
We selected the points, en Insert choose Scatter + Scatter with Straight and Markers (click):
We have left therefore the figure:
We fit to colors of the area of layout and the appropriate scale for this example: Double click in Gridlines, next Layout + Primary Horizontal Gridlines + More Primary Horizontal…:
Select Format Major Gridlines in Line Style, choose Dash type, to continuation Close:
Continue until you have l to figure that wishes
For a triangle, we put the coordinates this way:
In order to be able to make the triangle interactive we used elementary trigonometry, to draw up or to calculate each point. All these points will be based on the point To, cells B5:C5. Each angle will have to be transformed to Radians, since the formulas therefore handle it. An equilateral triangle has the three equal angles of 60 degrees. The first point has like coordinates (1, 1), the second point calculates by cell B6 (= 2+E6; 1). Therefore in the cells B5, B8, C5, C6 and C8 put on 1
The third point with cell B7= (B6-1)/2+1 in x-axis,
The axis and, is obtained with; C7=ABS((B6-B5)*SIN(F5))+1
In order to close the triangle, point four is (1,1). Make now interactive adding Scroll Bar, linked Cell
EXERCISES: Create figures in the Excel Leaf, like pentagons rectangles, etc.
PRACTICE 22 AREA OF FIGURES IN EXCEL 22. IT CALCULATES IN The LEAF EXCEL, The AREA OF A SQUARE And A TRIANGLE, VARIES ITS VALUES USING A SCROLL BAR. Objective: That you calculate areas of different figures applying Excel.
67 EXERCISE 1 Order of the steps: Open a new Excel leaf, and calculate the area of a figure. Now it puts the coordinates of the square or rectangle.
Select these data and in assistant for graphs, it selects to present dispersion and the figure next:
Now the applied formula to calculate the area of the figure, in the G26 cell, the formula is = IF ((D6-D5)*(C5-C8)","