Math 20 - Lesson 53


Uploaded by PCCvideos on 15.09.2009

Transcript:
A PORTLAND COMMUNITY COLLEGE MATHEMATICS TELECOURSE. A COURSE IN ARITHMETIC REVIEW. PRODUCED AT
PORTLAND COMMUNITY COLLEGE.
YOU HAVE PROBABLY ASKED AT THIS POINT WHY PERCENTS? WHAT ARE THEY USED FOR? A BUSINESS
FRIEND OF MINE, WHEN I ASKED HIM WHAT HE WOULD TELL MY STUDENTS, SIMPLY SAID THAT THE PERCENT
IS SIMPLY THE TALLY UNIT IN ALL OF BUSINESS. AS IN ANY GAME, YOU HAVE A BASIC WAY OF KEEPING
SCORE, KEEPING TRACK OF WHERE YOU ARE. THAT'S WHAT THE PERCENT DOES TO BUSINESS AS WILL
SEE IN THE NEXT TWO UNITS APPLICATION PROBLEMS.
FOR INSTANCE SIMPLE SENTENCE STATEMENTS LIKE THESE FOLLOWING THREE: WHAT IS 12.5 PERCENT
OF 30 THOUSAND DOLLARS? OR 240 DOLLARS IS 18 PERCENT HOW MUCH? OR 360 DOLLARS IS WHAT
PERCENT OF 4 THOUSAND DOLLARS?
SUCH STATEMENTS AS THAT IS THE BEGINNING OF MOST BUSINESS SITUATIONS AND MOST BUSINESS
QUESTIONS. AND TO PROCEED WITH A BUSINESS, WE HAVE TO BE ABLE TO ANSWER THOSE SIMPLE
QUESTIONS. IN FACT, THE DESIRE TO BE ABLE TO SOLVE THESE TYPES OF PROBLEMS IS PERHAPS
ONE OF THE PRINCIPAL REASONS FOR MOST STUDENTS TO BE TAKING THIS PARTICULAR COURSE. WE SHALL
DEVELOP TWO SIMPLE TECHNIQUES FOR DOING THIS, THAT IS SOLVING THIS TYPE OF SIMPLE PROBLEM.
BUT FIRST LET'S DEVELOP A TECHNICAL VOCABULARY USED MORE IN BUSINESS THAN EVEN IN MATHEMATICS.
IF YOU HAVE A SIMPLE SENTENCE WHERE WE SAY SOMETHING CALLED A IS SOMETHING PERCENT. HERE
WE SYMBOLIZED IT BY R OF SOMETHING ELSE, HERE CALLED B, OR SOMETHING PERCENT OF SOMETHING
IS SOMETHING. NOW NATURALLY THEY DON'T USE THESE PARTICULAR LETTERS. THEY USE NUMBERS
OR WORDS. WELL IN BUSINESS, THE NUMBER ATTACHED TO THE PERCENT WE CALL THE RATE OF PERCENT.
NOTICE IN BOTH CASES R, THE RATE OF PERCENT, IS THE NUMBER FOLLOWED BY A PERCENT. SO IF
CAN YOU REMEMBER THAT THE NUMBER FOLLOWED BY THE PERCENT IS WHAT BUSINESS CALLS THE
RATE OF THE PERCENT, HENCE OUR CALLING IT R.
B, IN THESE TWO SENTENCES, IS CALLED THE BASE. NOTICE IN BOTH CASES B FOLLOWS THE WORD OF.
SO IN A SIMPLE STATEMENT LIKE THIS A SIMPLE SENTENCE THE NUMBER FOLLOWING THE OF WE WILL
REFER TO BY THE WORD BASE.
AND A WE'LL CALL THE AMOUNT THAT IS COMPARED TO B. HENCE, THE USE OF A. AND NOTICE IN THIS
CASE A IS BEFORE A IS HERE AND IS AFTER IS HERE, BUT IN EITHER CASE IT'S ATTACHED BEFORE
OR AFTER TO THE IS.
AND THE B AGAIN IS BEFORE OR AFTER THE WORD IS. NOW THESE THREE ITEMS, PARTICULARLY IF
YOU ARE TO GO INTO A BOOKKEEPING OR ACCOUNTING COURSE, IS BEST TO BE MEMORIZED. NOTE AND
REMEMBER AS SOON AS POSSIBLE THAT THE NUMBER FOLLOWED BY A PERCENT WE CALL THE RATE OF
PERCENT. ALSO REMEMBER THAT THE NUMBER WHICH FOLLOWS OF BUSINESS PEOPLE WILL CALL THE BASE
OF THE TRANSACTION. AND THE NUMBER WHICH IS JUST BEFORE OR AFTER THE WORD IS, IS REFERRED
TO AS THE AMOUNT. NOW REMEMBERING THE WORD BASE, RATE, AND AMOUNT IS MORE NECESSARY IF
WE'RE TALKING TO YOUR BUSINESS COLLEAGUES. IN MATH WE'LL DEVELOP SOME SIMPLER TECHNIQUES.
IT WILL HELP FOR THIS TECHNIQUE TO LEARN AND REMEMBER THESE TRANSLATIONS: THAT THE WORD
PERCENT WHETHER IT IS WRITTEN THIS WAY OR THIS WAY, THEY'RE BOTH WORDS, MEANS IN MATH
TIMES ONE HUNDRED WHETHER YOU CHOOSE TO WRITE IT AS A DECIMAL OR AS A FRACTION, WHICH EVER
YOU PREFER. THE WORD IS OR IN ANY FORM OF THE VERB TO BE, GENERALLY TRANSLATES TO EQUAL.
AND THE WORD OF, TRANSLATES TO TIMES. AND THE PHRASE WHAT, HOW MUCH, OR ANY PHRASE DESIGNATING
THE FACT THAT YOU DON'T KNOW SOMETHING IS REPLACED BY A VARIABLE, A LETTER TO STAND
FOR THE NUMBER YOU DON'T KNOW. AGAIN, PERCENT MEANS TIMES .01. IS MEANS EQUAL. OF MEANS
TIMES. WHAT HOW MUCH MEANS AN UNKNOWN. MEMORIZE THIS VERY QUICKLY. THIS IS WHERE OUR WORKING
TOOLS WILL COME FROM.
AN EXAMPLE: 240 IS ALREADY MATHEMATICS. BUT THE WORD IS, WHEN TRANSLATED TO MATHEMATICS
BECOMES EQUAL. 18 IS ALREADY MATHEMATICS. SO THAT BECOMES 18. PERCENT IS NOT MATHEMATICS.
IT BECOMES TIMES .01. OF BECOMES TIMES. AND HOW MUCH BECOMES MY UNKNOWN, AND WE CAN USE
WHATEVER LETTER WE WISH. HOWEVER, WE MIGHT AS WELL USE B SINCE IT FOLLOWS THE WORD OF
TO GET USED TO THE WORD BASE, WHICH IS ONE OF OUR BUSINESS WORDS. NOW WE HAVE A SIMPLE
EQUATION WHICH WE'VE BEEN LEARNING TO SOLVE THROUGHOUT THIS COURSE. NOTICE IN THIS CASE
IT SAYS 18 TIMES .01 WHICH IF I MULTIPLY IS .18 TIMES B. THIS SIDE WE WILL LEAVE ALONE.
NOW HAD YOU WANTED TO YOU COULD HAVE CHANGED THIS INTO THIS ALL IN ONE MOVE. BUT NOW YOU
RECOGNIZE THAT THIS IS AN EQUATION WHERE THE UNKNOWN HAS A MULTIPLIER, AND TO UNDO MULTIPLICATION,
WE SIMPLY DIVIDE. THAT UNDOES THAT LEAVING ME WITH MY UNKNOWN BASE B. AND ON THIS SIDE
WE SIMPLY DIVIDE THIS EITHER BY HAND OR BY A CALCULATOR, AND WE GET THIS DOLLAR VALUE
ROUNDED TO THE NEAREST PENNY.
SO WHAT WE DO IS TRANSLATE EACH MARK IN OUR SIMPLE SENTENCE TO ITS MATH EQUIVALENT THEREBY GETTING
A SIMPLE EQUATION WE HAVE BEEN SOLVING ALL ALONG. SO WE SIMPLY SOLVE FOR THE UNKNOWN
AND WE'RE DONE. THIS METHOD IN YOUR TEXT BOOK WILL BE REFERRED TO AS METHOD 1.
THERE IS SECOND METHOD WE'LL REFER TO AS METHOD 2, WHICH INVOLVES SIMPLY MEMORIZING A SMALL
FORMULA THAT THE AMOUNT OVER BASE IS EQUAL TO THE RATE OVER 100, AND THAT'S A PROPORTION.
ONE FRACTION SET EQUAL TO ONE FRACTION, AND WE JUST RECENTLY COMPLETED A WHOLE CHAPTER
ON HOW TO SOLVE PROPORTIONS. THIS PERHAPS WOULD BE EASIER TO REMEMBER IN THIS FORM.
SIMPLY REMEMBER IS OVER OF EQUALS PERCENT OVER 100. MOST MATH TEACHERS PREFER THIS FORM,
BUT MOST BUSINESS INSTRUCTORS PERHAPS HAVE NOT SEEN THIS FORM AND THEY PREFER THIS BECAUSE
TO THEM AMOUNTS, BASES, AND RATES ARE SIMPLY THE TOOLS OF THEIR TRADE.
LET'S SOLVE THAT VERY SAME PROBLEM BY THIS METHOD. WE SIMPLY ASK WHAT NUMBER IS ATTACHED
TO THE IS. AND WE CAN SEE THE 240 IS. NOT THE 18 EVEN THOUGH IT'S AGAINST IT BECAUSE
THE 18 CLEARLY IS ATTACHED TO THE PERCENT. SO THE IS IS REPLACED BY 240 IN OUR FORMULA.
THEN WE ASK WHAT NUMBER IS ATTACHED TO THE OF? WELL THAT'S HOW MUCH. SO I'LL CALL THAT
BY A LETTER, IN THIS CASE B, BECAUSE AGAIN BASE IS WHAT FOLLOWS THE OF, BUT ANY LETTER
WOULD HAVE DONE. EQUALS, PERCENT, IT'S CLEARLY THE 18 THAT'S ATTACHED TO THE PERCENT. AND
THEN THIS 100 IS SIMPLY A CONSTANT TO THIS TYPE OF SITUATION.
NOW REMEMBER IN SOLVING A PROPORTION WE TAKE THIS TOP TIMES THAT BOTTOM, SET IT EQUAL TO
CAUSE BOTTOM TIMES THAT TOP, THEN DIVIDE BOTH SIDES BY THE MULTIPLIER OF THE UNKNOWN, THEN
DO THE DIVISION, AND YOU'RE DONE.
IN TIME WITH A LITTLE BIT OF PRACTICE, YOU WILL PROBABLY END BY PREFERRING ONE METHOD
TO THE OTHER. IF ALL STUDENTS PREFER ED THIS METHOD OR THE LAST, IT WOULD BE THE ONLY ONE
TAUGHT, BUT ABOUT HALF WILL PREFER THIS IF THEY'RE GOOD AT PROPORTIONS, AND THE OTHER
HALF WILL PREFER THE METHOD WE JUST HAD IF THEY'RE GOOD AT SOLVING SIMPLE EQUATIONS.
IT'S A MATTER OF PREFERENCE, NOT A MATTER OF EASE.
LET'S SOLVE ANOTHER PROBLEM BY METHOD 1. METHOD 1 COULD ACTUALLY BE CALLED THE TRANSLATION
METHOD BECAUSE IT SIMPLY INVOLVES TAKING EACH WORD OR NUMBER AND TRANSLATING IT STEP BY
STEP TO MATHEMATICS. SEE? 360 IS MATHEMATICS. IS IS EQUAL. WHAT IS MY UNKNOWN. PERCENT MEANS
TIMES .01. OF MEANS TIMES. 4000 MEANS 4000. THEN, IN THIS EQUATIONS, ANY ARITHMETIC THAT
IS INDICATED THAT YOU CAN DO, DO IT. SO THIS SAYS TIMES, AND IT'S BETWEEN THESE TWO, SO
I'LL DO IT AND I'LL GET 40 TIMES THE X AND IF YOU HAVE AN EQUATION WHERE THE UNKNOWN
IS BEING MULTIPLIED BY A NUMBER, YOU UNDO THE MULTIPLICATION BY DIVISION, AND NOW YOU
HAVE YOUR ANSWER. X IS 360 DIVIDED BY 40, WHICH IS 9. SO AS IT TURNS OUT, 360 IS 9 PERCENT
OF 4 THOUSAND DOLLARS.
LET'S DO A PROBLEM NOW BY METHOD 2. AND METHOD 2 COULD EASILY BE CALLED THE IS OVER OF METHOD.
YOU SIMPLY SETUP THE BARE BONES OF PROPORTION. NOTICE THAT WE ALWAYS HAVE 100 HERE. NOW YOU
SIMPLY ASK WHAT NUMBER IS ATTACHED TO THE IS? THAT'S THE 360. WHAT NUMBER IS ATTACHED
TO THE OF? THAT'S THE HOW MUCH, MY UNKNOWN. WHAT NUMBER'S ATTACHED TO THE PERCENT? THAT'S
THE 18. NOW YOU SIMPLY SOLVE THE PROPORTION. TOP TIMES BOTTOM, SET EQUAL TO BOTTOM TIMES
TOP, DIVIDE BOTH SIDES BY THE MULTIPLIER OF THE UNKNOWN, DO THE WORK, AND YOU'RE DONE.
AND WE HAVE 2 THOUSAND DOLLARS. VERY SIMPLE, BOTH TECHNIQUES. IN ONE CASE YOU MEMORIZE
A LITTLE PROPORTION. IN THE OTHER CASE YOU MEMORIZE SORT OF A SMALL THREE OR FOUR PART
DICTIONARY OF ENGLISH TO MATHEMATICS.
LET'S DO ANOTHER ONE BY METHOD 1 NOW. THAT IS THE TRANSLATION METHOD. WORD BY WORD NOW.
THE WORD WHAT IS MY UNKNOWN. THE WORD IS IS EQUAL. NOW IN THIS CASE, LET'S TRANSLATE THIS
ALL AT ONCE. TO GET A AWAY FROM A PERCENT WE MOVE THE DECIMAL POINT TWO PLACES AWAY.
WE HAVE .125. THE WORD OF IS TIMES. 3 THOUSAND 30 THOUSAND OF COURSE IS MATHEMATICS. NOW
IN THIS CASE WE'RE LUCKY. WE'RE DONE REALLY EXCEPT FOR ARITHMETIC. IT SAYS MY UNKNOWN
IS THAT TIMES THAT. SO DOING THAT MULTIPLICATION WE GET $3,750. SEE HOW VALUABLE THOSE EXERCISES
OF SOLVING EQUATIONS HAVE BEEN ALL ALONG IN THIS BOOK?
NOW LET'S DO YET ONE MORE PROBLEM BY METHOD 2. OR THE IS OVER OF METHOD. WHAT NUMBER'S
ATTACHED TO THE IS? ITS THE UNKNOWN. WHAT NUMBER'S ATTACH TO THE OF? 30 THOUSAND. WHAT
NUMBER'S ATTACHED TO THE PERCENT? 12.5. AND OF COURSE THE CONSTANT ONE HUNDRED. NOW TOP
TIMES BOTTOM IS 100 TIMES X EQUALS BOTTOM TIMES TOP, WHICH WE COULD DO BY HAND OR WITH
CALCULATOR, AND WE WOULD GET 375 THOUSAND. DIVIDE BOTH SIDES BY THE MULTIPLIER OF THE
UNKNOWN, WHICH IS A POWER OF 10 HERE, AND THAT'S ONE OF OUR SHORTCUTS. SO MY ANSWER
IS $3,750, WHICH IS 12.5 PERCENT OF 30 THOUSAND. VERY CUTE BUT VERY EASY AND EFFECTIVE METHODS.
MOST PROBLEMS IN FACT THAT OCCUR IN SCIENCE OR BUSINESS USUALLY INVOLVE FAIRLY MESSY NUMBERS.
AND THERE'S WHERE CALCULATOR USE IS VERY, VERY CONVENIENT. AND IF YOU HAVE BEEN FOLLOWING
THE PROPORTIONS REVIEW PARTS OF THE LAST THREE LESSONS, THEN WE HAVE A PECULIAR SHORTCUT
FOR THIS, PARTICULARLY IF WE USE THE IS OVER OF APPROACH. METHOD 1 WORKS JUST AS WELL,
BUT IN THIS PARTICULAR APPROACH, IF WE SIMPLY SET UP OUR WORKING PROPORTION AND REPLACE
THESE BLANKS, THESE WORDS, AND THIS IS A WORD, WITH THE APPROPRIATE NUMBER OR VARIABLE, WE
GET LET'S SEE: 558.37 IS ATTACHED TO THE IS, SO IT REPLACES THE IS. WHAT IS ATTACHED TO
THE PERCENT. ISN'T IT? IT SAYS WHAT PERCENT. SO THAT'S MY UNKNOWN. LET'S CALL IT P FOR
PERCENT. AND OF COURSE OF IS ATTACHED TO THE 73.98. NOW WITH OUR SHORTCUT WE'VE BEEN PLAYING
WITH IN THE LAST FEW LESSONS, WE CAN WORK THIS OUT IN ONE SMOOTH MOVE ON THE CALCULATOR.
WE FIND THE TWO DIAGONALS: THE ONE WITHOUT THE VARIABLE, AND THE ONE WITH. THE ONE WITHOUT
THE VARIABLES WE MULTIPLY, BUT WE CAN MULTIPLY THIS MENTALLY. CAN'T WE? 58.37 TIMES 100 IS
SIMPLY 5837. THEN WE DIVIDE BY THE NUMBER ON THE DIAGONAL WITH THE VARIABLE, SO DIVIDE
BY 73.98, AND WE'RE DONE, AND THAT IS MY PERCENT.
AT THIS POINT WE'D HAVE TO ASK WHOEVER WE WERE DOING THIS FOR WHERE THEY WANT US TO
ROUND OFF, AND THAT WILL GENERALLY BE THE CASE. SO REMEMBER THIS NUMBER IS GOING TO
BE THE PERCENT. SO LET'S SAY THAT THEY HAD ASKED US TO ROUND THIS TO THE NEAREST 10TH
OF A PERCENT. WELL SINCE THIS ALREADY IS IN PERCENTS, I CAN SEE IT'S GOING TO BE 78.89
AND THE 9 ROUNDS THAT 8 UP TO 9. SO WE SAY MY PERCENT IS 78.9. USUAL WE STICK THE PERCENT
SIGN BACK ON JUST TO LET THEM KNOW THAT IT IS A PERCENT WE WERE TALKING ABOUT AND TO
EMPHASIZE THE FACT IN OUR MINDS THAT THIS NUMBER AND THIS NUMBER ARE TRULY QUITE DIFFERENT.
OKAY SO WITH YOUR CALCULATOR AND WITH THIS IS OVER OF METHOD, YOU CAN SOLVE MOST OF THE
SIMPLE STORY PROBLEMS BY INSPECTION ALONE. PLEASE NOTE THAT IT'S THIS RELATIONSHIP AND
THESE WORDS THAT MAKES THIS PATTERN WORK, NOT THE NUMBERS THEMSELVES. HERE I'M USING
EXACTLY THE SAME TWO NUMBERS AS THE PROBLEM WE JUST WORKED BUT REVERSED, BUT REVERSING
THE NUMBERS CHANGES THE ENTIRE PROBLEM. IN FACT BEFORE WE SET UP OUR FORMULA TO SOLVE
THE PROBLEM, LET'S GET A FEEL FOR THE FACT THAT THIS IS TRUE. NOW NOTE WE KNOW THAT 100
PERCENT OF SOMETHING IS ITSELF. SO THIS IS CERTAINLY MORE THAN ITSELF, THIS NUMBER HERE.
SO IT'S GOT TO BE MORE THAN ONE HUNDRED PERCENT, WHERE AS THIS IS CERTAINLY LESS THAN THAT,
SO IT HAS TO BE LESS THAN ONE HUNDRED PERCENT, WHICH IT WAS. IT WAS 78 PERCENT.
SO HERE AGAIN USING THE IS OF TECHNIQUE WE START READING THE SENTENCE AND FIND THAT THE
73.98 IS ATTACHED TO THE IS: THEREFORE, IT REPLACES THE IS IN THE FORMULA. WHAT IS ATTACHED
TO THE PERCENT, SO IT REPLACES THE PERCENT IN THE FORMULA. AND WHAT IS JUST ANOTHER WAY
OF SAYING VARIABLE IN ALGEBRA. AND OF IS ATTACHED TO THE 58.37. SO IN THE FORMULA IT REPLACES
THE OF. AND IN THIS PARTICULAR FORMULA, THIS ALWAYS STAYS AS 100. NOW HERE AGAIN LET'S
SAY THAT IN THIS PROBLEM WE ALSO WANT TO ROUND TO THE NEAREST TENTH OF A PERCENT, AND AGAIN
LET'S USE OUR CALCULATOR SHORTCUT ON THIS. RECOGNIZING THAT OUR ANSWER WILL ALREADY BE
IN THE PERCENT THAT I WANT. HERE'S THE DIAGONAL THAT DOESN'T HAVE THE LETTER, SO I MULTIPLY
THOSE, WHICH I CAN DO MENTALLY. I DON'T NEED A CALCULATOR FOR THAT. SO 7, 3, 9, 8 NOW DIVIDED
BY THE NUMBER ON THE DIAGONAL WITH THE VARIABLE, SO DIVIDE BY 58.37 IS. AND I GET 126. THEN
I HAVE 74 AND THE 4 IS LESS THAN 5 SO I ROUND DOWN, THAT IS LEAVE THE 7 ALONE. SO 73.98
IS 126.7 PERCENT OF 58.37. AND SO THIS MUST BE SOMEWHAT MORE THAN A HUNDRED PERCENT, AND
THIS IS SOMEWHAT MORE THAN A HUNDRED. AND AGAIN THIS WORD IS REPLACED BY THE SYMBOL
FOR PERCENT.
YOU SEE WE DIDN'T HAVE TO MOVE THE DECIMAL POINT TO CONVERT TO IT A PERCENT BECAUSE IN
FACT THIS DIVIDE BY ONE HUNDRED THAT WE HAVE BUILT INTO THE FORMULA DOES A CONVERSION TO
A PERCENT FOR US. AND THAT'S A NICE THING ABOUT THIS IS OVER OF METHOD IS WHEN YOU'RE
DONE YOU'RE ABSOLUTELY DONE. IF IT WAS A PERCENT, SIMPLY STICK THE PERCENT ON BECAUSE THAT'S
EXACTLY WHAT YOU HAVE.
NICE. I HOPE YOU FIND IT BUT PLEASE ALSO NOTE THIS, THAT THESE TWO SENTENCES USED EXACTLY
THE SAME TWO NUMBERS BUT GOT TWO ENTIRELY DIFFERENT ANSWERS. AND THE POINT WE TRIED
TO MAKE IS THAT THE NUMBERS THEMSELVES DOES NOT CONSTITUTE THE PROBLEM. THE PROBLEM IS
THEIR RELATIONSHIP IN THE SENTENCE. THAT IS HOW ARE THOSE TWO NUMBERS RELATED? AND THE
SAME TWO NUMBERS ARE RELATED SIMPLY TWO DIFFERENT WAYS.
WITHIN MORE TRADITIONAL, CONSUMER OR BUSINESS MATH THIS TYPE OF PROBLEM FOR SOME REASON
BRINGS THE AVERAGE BEGINNING STUDENT TO A COMPLETE HALT. HOWEVER, WITH EITHER OF OUR
TWO METHODS IN THIS LESSON, THIS PROBLEM IS NO HARDER THAN EITHER OF OTHER TWO WE WORKED
ON.
YOU SEE IT HAS STILL THE SAME SENTENCE STRUCTURE AS THE OTHER. THERE IS AN IS, PERCENT, OF
SOMETHING. SO WE SIMPLY REPLACE OUR MODEL OR OUR FORMULA BY ITS APPROPRIATE NUMBER.
SO WE START READING. WE SEE THAT 428 IS ATTACHED TO THE IS. SO IT REPLACES THE IS. THE 10.5
IS ATTACHED TO THE PERCENT. SO IT REPLACES THE PERCENT. THE OF IS ATTACHED TO HOW MUCH.
WHICH IN BUSINESS CIRCLES, THEY WOULD CALL THE NUMBER THAT'S ATTACHED TO THE OF, THE
BASE. SO WE USE A B, BUT ANY LETTER WOULD HAVE DONE. AND 100 STAYS 100. THEN BY USE
BE OUR CALCULATOR SHORTCUT APPROACH, AGAIN WE MULTIPLY THE TWO ON THE DIAGONAL WITHOUT
THE VARIABLE AND WE CAN DO THAT MENTALLY. 42800. THEN DIVIDE BY THE NUMBER ON THE DIAGONAL
WITH THE LETTER, WHICH IS 10.5 EQUALS, AND THEN FIND OUT HOW ACCURATELY THIS IS TO BE
ROUNDED, AND LET'S SAY TO THE NEAREST HUNDREDTH, SO WE SEE IT'S 4076.19 TO THE NEAREST HUNDREDTH.
SO $428 IS 10.5 PERCENT OF $4076.19. SEE, THIS TYPE OF PROBLEM OCCURS FAIRLY FREQUENTLY
WHEN YOU KNOW HOW MUCH INTEREST YOU PAID FOR TAX PURPOSES BECAUSE YOU JUST RECEIVED YOUR
BILL. AND USUALLY YOU KNOW WHAT THE INTEREST RATE IS BECAUSE YOU HAVE BEEN DEALING WITH
THAT FOR YEAR AFTER YEAR OR MONTH AFTER MONTH. BUT THE BASE IS CHANGING FROM MONTH TO MONTH
OR YEAR TO YEAR, SO FREQUENTLY YOU FORGOT WHAT THIS WAS, BUT IF YOU KNOW THESE TWO THIS
FORMULA ALLOWS TO YOU GET AT THE SOLUTION, AND YOU SEE THIS WAS NO HARDER THAN ANY OF
THE OTHER PROBLEMS WE GAVE YOU. WAS IT?
AND THE MATHEMATICAL TOOL THAT MADE IT SIMPLE FOR US WAS UNDERSTANDING WHAT A PROPORTION
WAS AND BEING ABLE TO SOLVE THAT PROPORTION VERY QUICKLY AND SMOOTHLY. BUT YOU MIGHT BE
ONE OF THOSE INDIVIDUALS THAT'S MORE INCLINED TO THE DICTIONARY OR TRANSLATION METHOD. IF
THAT WERE THE CASE, YOU'D SIMPLY GO DOWN THE SENTENCE AND START TRANSLATING WORD BY WORD.
SO 480 IS, 428 RATHER IS MATH. THE IS TRANSLATES TO EQUAL. AND THIS PART HERE WE CAN TRANSLATE
ALL AT ONCE IF WE WISH. TO GET AWAY FROM PERCENT WE MOVE IT TWO PLACES AWAY WHICH GIVES ME
.105, OR ELSE WE COULD HAVE TAKEN 10.5, REPLACED THE PERCENT TIMES .01, MULTIPLY THE TWO, AND
WE WOULD GET THIS. OF TRANSLATES TO TIMES AND HOW MUCH IS SOME VARIABLE. CALL IT N FOR
NUMBER. CALL IT B FOR BASE. CALL IT X FOR UNKNOWN. THE CHOICE IS YOURS. AND YOU CAN
SEE FROM MY ALGEBRA REVIEW PORTIONS THAT TO UNDO MULTIPLICATION, YOU DIVIDE BY WHATEVER
YOU WERE MULTIPLYING, BY OF COURSE. BUT YOU DIVIDE BOTH SIDES BY THE SAME AMOUNT. THIS
UNDOES THIS, ISOLATING THE VARIABLE. NOW ON YOUR CALCULATOR YOU JUST FOLLOW THROUGH WITH
THIS AND OF COURSE YOU'LL GET EXACTLY THE SAME ANSWER.
THERE, JUST FROM WATCHING THIS SINGLE LESSON ARE YOU BEGINNING TO FEEL A PREFERENCE? DO
YOU PREFER THE TRANSLATION METHOD OR ARE YOU ONE OF THE STUDENTS WHO ARE BEGINNING TO PREFER
THE IS OVER OF FORMULA, WHICH OF COURSE HAS AN ALTERNATE FORM: THE AMOUNT, BASE, RATE
FORMULA. IN TIME YOU WILL FIND YOURSELF MOVING TOWARDS ONE OR THE OTHER, BUT SO THAT YOU
CAN COMMUNICATE WITH OTHER PEOPLE WITHIN YOUR FIELD, YOU SHOULD BE REASONABLY COMFORTABLE
IN BOTH METHODS. AND AS TIME PASSES YOU'LL FIND SEVERAL OTHERS. SO IT'S NOT A MATTER
OF FORGETTING ONE AND JUST REMEMBERING THE OTHER. YOU SHOULD REMEMBER BOTH SO THAT YOU
CAN COMMUNICATE WITH OTHER PEOPLE. BUT THEN OF COURSE PREFER ONE, IF YOU WISH, FOR PERSONAL
WORK. THIS IS YOUR MATH HOST, BOB FINNELL. WE'LL SEE YOU AT THE NEXT LESSON WHERE WE'LL
DO SOME MORE PROBLEMS SOMEWHAT LIKE THIS ONE. GOOD LUCK.
Page: of 17