Math 20 - Lesson 56




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Transcript:
A PORTLAND COMMUNITY COLLEGE MATHEMATICS TELECOURSE. A COURSE IN ARITHMETIC REVIEW PRODUCED AT
PORTLAND COMMUNITY COLLEGE.
HERE ARE SOME ENGLISH MEASUREMENTS AND THEIR EQUIVALENTS THAT YOU MIGHT BE FAMILIAR WITH
AND A FEW PERHAPS YOU'RE NOT.
12 INCHES AND 1 FOOT ARE THE SAME THING. 3 FEET AND 1 YARD ARE THE SAME LENGTH. 5280
FEET IS 1 MILE. AND HERE ARE SOME EQUIVALENT MEASUREMENTS IN WEIGHTS, TIMES AND VOLUMES.
THESE EQUIVALENT MEASURES YOU'LL FIND IN COOKBOOKS, DICTIONARIES, SCIENCE BOOKS AND AT THE BACK
OF YOUR TEXTBOOK AS WELL AS IN THIS LESSON.
AS WE STUDY MEASUREMENT, LET'S DEFINE IT JUST A LITTLE BIT MORE CAREFULLY THAN WE DO IN
OUR DAILY LIVES. IT'S A NUMBER WRITTEN WITH A UNIT OF MEASURE. AN EXAMPLE. 56 FEET, 56
OUNCES, 56 MILES, AND 56 POUNDS. AND THIS LIST GOES ON AND ON. A VERY LONG LIST. COULD
FILL A BOOK. THE POINT IS MOST PEOPLE CONCENTRATE TOO MUCH ON THIS. IN DOING SO THEY'D BE TEMPTED
TO SAY THEY'RE ALL EQUAL BECAUSE THEY ALL HAVE THE NUMBER 56.
AND OF COURSE 56 FEET AND 56 POUNDS AREN'T EVEN THE SAME THING, AND 56 FEET FOR SURE
IS NOT EQUAL TO 56 MILES. SO THESE ARE NOT EQUAL. AND THE THING THAT MAKES THEM TO BE
UNEQUAL ARE THE DIFFERENT UNITS OF MEASURE.
SO WHEN YOU PUT THE TWO TOGETHER, WE HAVE AN ENTIRELY NEW NUMBER CALLED MEASUREMENT.
DO NOT THINK OF THIS AS JUST A NUMBER WITH A WORD TACKED ON TO IT. THINK OF THIS AS A
BRAND NEW KIND OF NUMBER CALLED MEASUREMENT. JUST AS IN ELEMENTARY SCHOOL YOU LEARNED THAT
THIS WAS A 3 AND THIS WAS A 2, AND YOU PUT THEM TOGETHER IN A CERTAIN MANNER, AND IT
CREATES A BRAND NEW NUMBER THAT'S NOT EQUAL TO EITHER ONE OF THOSE. SO JUST AS YOU'RE
NOT CONFUSED INTO THINKING THIS IS A 3 OR A 2, DON'T BECOME CONFUSED AND THINKING THIS
IS 56. IT'S 56 FEET, WHICH IS A DIFFERENT NUMBER FROM 56 OUNCES, ET CETERA. AND THESE
KINDS OF NUMBERS WE WILL REFER TO AS MEASUREMENTS. SEE, A MUCH MORE FORMAL DEFINITION THAN PERHAPS
YOU'RE USED TO.
LET'S DEFINE SOME OF THE THINGS YOU CAN DO BETWEEN NUMBERS AND MEASUREMENTS AND MEASUREMENTS
AND MEASUREMENTS. FIRST, YOU CAN MULTIPLY OR DIVIDE A NUMBER WITH A MEASUREMENT. EXAMPLE.
HERE IS A PURE NUMBER TIMES A MEASUREMENT. IF YOU'RE MULTIPLYING A NUMBER TIMES A MEASUREMENT,
YOU MULTIPLY THE NUMBER TIMES THE NUMBER PART OF THE MEASUREMENT AND, IN A SENSE, STICK
THE MEASUREMENT ON. IT'S A LITTLE BIT MORE TECHNICAL THAN THAT, BUT THAT'S GOOD ENOUGH
FOR THE TIME BEING.
AND IF YOU'RE DIVIDING A MEASUREMENT BY A NUMBER, YOU DIVIDE THE NUMBER INTO THE MEASUREMENT
PART. 4 IN THIS CASE TIMES FEET. SO YOU CAN MEASURE, MULTIPLY OR DIVIDE A PURE NUMBER
WITH A MEASUREMENT. BUT YOU CANNOT ADD OR SUBTRACT A NUMBER AND A MEASUREMENT.
THIS KIND OF A PROBLEM, 48 FEET, A MEASUREMENT, AND 19, A NUMBER, THE SUM OF THOSE IS SIMPLY
A MEANINGLESS STATEMENT AS FAR AS THESE NEXT FEW LESSONS ARE CONCERNED. LIKE MEASUREMENTS
CAN BE ADDED OR SUBTRACTED DIRECTLY. FOR EXAMPLE, IF I ADD 5 OUNCES TO 7 OUNCES, SINCE THEY
ARE LIKE MEASUREMENTS, I SIMPLY ADD THEIR NUMBER VALUES AND APPEND THE MEASUREMENT.
SAME THING WITH SUBTRACTING. IF I'M SUBTRACTING LIKE MEASUREMENTS, I SIMPLY SUBTRACT THEIR
NUMBER PARTS AND APPEND THE MEASUREMENT.
BUT WHAT ABOUT IF YOU'RE SUBTRACTING NUMBERS THAT ARE MEASURING THE SAME KIND OF A THING,
IN THIS CASE WEIGHT AND WEIGHT, BUT THEY'RE NOT LIKE MEASUREMENTS, HERE WE HAVE POUNDS
AND OUNCES; HOW DO WE HANDLE THAT? WELL FIRST, LET'S LOOK AT ANOTHER MATTER, THAT IS HOW
DO WE CHANGE FROM ONE UNIT OF MEASURE INTO ANOTHER UNIT OF MEASURE.
NOW FIRST, TO EVEN BE ABLE TO DO IT, THEY MUST BOTH BE MEASURING THE SAME THING. THIS
IS LENGTH AND SO IS THIS. I CANNOT CHANGE YARDS TO POUNDS, THEY MUST BE MEASURING THE
SAME KIND OF A THING: LENGTHS, AREAS, VOLUMES, POUNDS, OR WEIGHT OR WHATEVER IT IS. OKAY.
NOW, THIS INSTRUCTION SAYS TO CHANGE ONE UNIT OF MEASURE INTO ANOTHER, REPLACE THE UNIT
OF MEASURE. SO I'M GOING TO REPLACE THIS UNIT OF MEASURE BY AN EQUIVALENT MEASURE AND DO
THE MULTIPLICATION THAT'S SORT OF IMPLIED HERE. SO OUR QUESTION IS: WHAT'S A YARD, A
UNIT, EQUAL TO IN FEET? AND IF YOU DIDN'T KNOW, YOU'D LOOK IT UP IN A TABLE OF CONVERSIONS.
IN THIS CASE ONE YARD, THERE'S MY UNIT, ONE UNIT, IS 3 FEET. SO I'LL REPLACE MY UNIT YARD
BY 3 FEET AND TREAT THIS AS A MULTIPLICATION. SO 4.5 TIMES 3 IS 13.5 FEET. SO 4 AND A HALF
YARDS AND 13 AND A HALF FEET ARE MEASURING THE SAME LENGTH. SO AGAIN, TO CHANGE A UNIT
OF MEASURE, REPLACE THE UNIT ITSELF BY WHATEVER IT'S EQUAL TO IN THE NEW UNIT AND THEN MULTIPLY.
NOW, SOMETIMES IN DOING THAT YOU GET INVOLVED WITH FRACTIONS. LET'S SAY WE WISH TO CHANGE
48 INCHES INTO FEET. FIRST THING YOU ASK IS: ARE THEY MEASURING THE SAME KIND OF AN ENTITY?
IN THIS CASE THEY'RE BOTH MEASURING LENGTH. IF THEY WEREN'T, YOU MIGHT HAVE A CONVERSION
THAT'S SIMPLY NOT POSSIBLE BECAUSE IT'S NOT LEGAL, LIKE CHANGING INCHES TO POUNDS. THAT'S
JUST NOT POSSIBLE.
NOW, OUR SUGGESTION WAS TO REPLACE THE INCH UNIT WITH AN EQUIVALENT UNIT IN FEET. SO CHECKING
OUR TABLES, WE SEE THAT 12 INCHES IS 1 FOOT. SO YOU HAVE TO AT THIS POINT SORT OF SEE THAT
THEREFORE 1 INCH IS 1/12 OF THAT OR 1/12 OF A FOOT.
NOW, SOMETIMES THIS ISN'T QUITE SO OBVIOUS TO SEE, SO IN A LATER LESSON, WE'LL GIVE YOU
A LITTLE BIT MORE SOPHISTICATED TECHNIQUE FOR DOING THIS. BUT IN THIS LESSON IT WILL
BE SIMPLE, AND WE FEEL YOU WILL SEE THIS RELATIONSHIP.
SO GOING BACK TO OUR GIVEN PROBLEM, OUR INCH UNIT IS GOING TO BE REPLACED BY ITS EQUIVALENT,
WHICH IS 1/12 OF A FOOT. NOW, DOING THE MULTIPLICATION, 48 TIMES 1/12 IS 4 FEET. AND WE'RE DONE. REPLACE
THE UNIT BY ITS EQUIVALENT IN THE OTHER UNIT, THEN MULTIPLY.
NOW, LET'S SAY SOMEONE HAD MEASURED A LONG LENGTH AND FOUND IT TO BE 5 YARDS, 2 FEET
AND 7 INCHES LONG. WE'D LIKE TO HAVE THE WHOLE THING IN INCHES. SO 5, REPLACE THE YARD BY
ITS EQUIVALENT, WHICH IS 3 OR 36 INCHES, SINCE WE WANT IT ALL IN INCHES. 2, REPLACE THIS
UNIT FOOT BY 12 INCHES. OF COURSE 7 IS ALREADY IN INCHES. SO 5 TIMES 36 IS 180 INCHES. AND
2 TIMES 12 INCHES IS 24 INCHES. AND 7 INCHES IS 7 INCHES. NOW THAT THEY'RE ALL IN THE SAME
UNIT, LIKE UNITS, WE CAN ADD THEIR NUMBER PART. WHICH GIVES ME 11, 1, 2. SO WE KNOW
THAT 5 YARDS, 2 FEET, 7 INCHES IS IN FACT 211 INCHES.
GOING BACK TO THIS PROBLEM, WE NOW HAVE A CLUE. I'M GOING TO BORROW 1 FROM THE 3 POUNDS
WHICH WOULD GIVE ME 2 POUNDS PLUS 1 POUND. SO I'M NOT PLAYING WITH THIS YET, JUST THIS.
BUT THE 2 POUNDS I'LL LEAVE ALONE AND CONVERT 1 POUND TO 16 OUNCES. NOW FROM THIS, THIS
IS 3 POUNDS, 2 POUNDS PLUS 1 POUND WHICH IS 16 OUNCES, I WILL SUBTRACT THE LIKE UNITS
OF MEASURE. 12 OUNCES FROM 16 OUNCES IS POSSIBLE.
AND OF COURSE, HERE I HAVE THE 2 POUNDS STILL. SO 3 POUNDS FROM 12 OUNCE, SUBTRACT 12 OUNCES
IS 2 POUNDS, 4 OUNCES.
LET'S DO ONE MORE A LITTLE BIT MORE SMOOTHLY, BUT LET'S WARM UP WITH AN ADDITION ONE FIRST.
IF YOU'RE ADDING COMPOSITE MEASURES, WHICH FREQUENTLY WE DO, THEN THE RULE THERE IS TO
SIMPLY LINE UP THE LIKE UNITS OF MEASURE PRETTY MUCH AS WE LINED UP LIKE PLACES IN DECIMALS.
AND THEN YOU ADD THE LIKE UNITS OF MEASURE JUST AS WE ADDED LIKE PLACES. SO YOU GET 7
INCHES HERE AND 9 FEET HERE. SO 5 FOOT, 2 INCHES PLUS 4 FEET, 5 INCHES IS 9 FEET, 7
INCHES.
NOW, IT'S THE SAME WITH SUBTRACTION. WHEN YOU HAVE COMPOSITE MEASURES, THEN LINE THEM
UP BY LIKE UNITS. THEN SUBTRACT ONLY THE LIKE UNITS. SO 5 OUNCES FROM 9 OUNCES IS 4 OUNCES.
AND 2 POUNDS FROM 5 POUNDS IS 3 POUNDS. SO 5 POUNDS, 9 OUNCES, SUBTRACT 2 POUNDS, 5 OUNCES
IS 3 POUNDS, 4 OUNCES. REALLY NO MORE DIFFICULT THAN SUBTRACTING THE DECIMALS.
BUT IN DECIMALS SOMETIMES YOU HAD TO CARRY OR BORROW. SO IT IS WITH UNITS. TO WE HAVE
4 FEET, 10 INCHES PLUS 3 FEET, 8 INCHES. NOW, ADDING ONLY THE LIKE UNITS, WE GET 18 INCHES
AND 7 FEET. AND THERE'S NOTHING WRONG WITH THAT EXCEPT THAT WE REMEMBER THAT 12 INCHES
IS THE SAME THING AS 1 FOOT. SO IF I SUBTRACT 12 FROM HERE, I HAVE TO ADD ITS EQUIVALENT,
OR 1 FOOT, OVER HERE TO KEEP THE MEASUREMENT THE SAME OR BALANCED.
SO THIS GIVES ME 6 INCHES HERE AND 8 FEET HERE. OR IN SHORT, WE WILL THINK OF THIS 18
INCHES AS 12 INCHES PLUS 6 INCHES. I KEPT THE 6 INCHES AND THE 12 INCHES CARRIED OVER
HERE AS 1 FOOT.
AND FINALLY BACK TO OUR SUBTRACTION OF MIXED UNITS. 25 POUNDS AND 3 OUNCES, SUBTRACT 8
POUNDS AND 10 OUNCES. BUT IN THIS CASE, I CANNOT SUBTRACT 10 OUNCES FROM 3 OUNCES. SO
I'LL BORROW 1 OF MY POUNDS. BUT THAT 1 POUND IS 16 OUNCES. NOW, IF YOU DIDN'T KNOW THAT,
YOU WOULD CHECK IT WITH A TABLE. AND SEE, 16 OUNCES IS 1 POUND. SO I CAN REPLACE 1 POUND
BY ITS EQUIVALENT, WHICH IS 16 OUNCES. AND AGAIN, CHECK ALMOST ANY DICTIONARY OR COOKBOOK
OR PEECHEE FOLDERS OR TEXTBOOKS AND THEY HAVE THESE CONVERSIONS OF UNITS SOMEWHERE IN MOST
OF THEM.
BUT OUR 16 PLUS 3 OUNCES, THE 3 ORIGINALLY WITH THE 16 I BORROWED FROM THE 1 POUND, GIVES
ME 19 OUNCES. AND 10 OUNCES WILL SUBTRACT. AND OF COURSE 8 POUNDS FROM 24 POUNDS IS 16
POUNDS. AND I'M DONE. SO SOMETIMES YOU HAVE TO CARRY UNITS, AND SOMETIMES YOU HAVE TO
BORROW UNITS, BUT BE VERY CAREFUL THAT YOU BORROW AN EQUIVALENT AMOUNT OF UNITS.
LET'S GO BACK TO AN EARLIER PROBLEM AND PLAY WITH IT A LITTLE BIT. THIS LESSON ESSENTIALLY
CONSISTS OF THREE PARTS. ONE OF CONVERTING FROM ONE UNIT OF MEASURE OR MULTIPLE MEASURES
TO ANOTHER, AND WHAT WE'VE JUST DONE, ADDING AND SUBTRACTING WITHIN ANY ONE UNIT. RECALLING
THAT WE CAN ONLY ADD OR SUBTRACT LIKE UNITS TO LIKE UNITS. THAT'S WHY WE CAN'T ADD THESE
UNTIL THEY'RE ALL IN THE SAME UNIT. USUALLY WHEN WE HAVE MULTIPLE UNITS IN APPLICATION,
IT'S MOST USEFUL TO GO DOWN TO THE SMALLEST UNIT, IN THIS CASE, INCH.
BUT TECHNICALLY, IF YOU UNDERSTAND THE PROCEDURE, I DON'T HAVE TO ALWAYS GO TO THE SMALLEST
UNIT. I CAN GO TO ANY OTHER UNIT, INCLUDING FEET AND YARDS HERE, OR EVEN OTHERS THAT I
DON'T HAVE, PERHAPS MILES. SO JUST TO UNDERSTAND THAT, LET'S CONVERT THIS SERIES OF MEASURES,
WHICH IMPLIES AN ADDITION HERE EVEN THOUGH WE USUALLY DON'T WRITE THEM.
LET'S ACTUALLY TRANSLATE THEM ALL INTO YARDS. AND OUR TECHNIQUE WAS THIS, IF YOU'RE GOING
TO CHANGE FOR INSTANCE, IN THIS CASE, INCHES TO YARDS, YOU REPLACE INCH BY ITS EQUIVALENT
IN YARDS. SO WE ASK: 1 INCH IS HOW MANY YARDS? WELL, FOR THAT YOU NEED A TABLE OF VALUES.
AND IF YOU DON'T HAVE ONE READILY AVAILABLE, KNOW THAT TABLES OF CONVERSION VALUES ARE
USUALLY FOUND AT THE BACK OF TEXTBOOKS, IN SHOP MANUALS OR SCIENCE BOOKS, AT THE BACK
OF DICTIONARIES, PARTICULARLY COLLEGIATE DICTIONARIES, ALMOST ALWAYS HAS IT ON STUDENT NOTEBOOKS,
PARTICULARLY THE PEECHEE FOLDER NOTEBOOKS, IN COOKBOOKS AND SO ON.
IN JUST ABOUT ANY KIND OF A TECHNICAL BOOK IN SHORT. AND THAT JUST GIVES YOU AN IDEA
OF HOW IMPORTANT THIS IS IF ALMOST ANY BOOK OR FOLDER YOU PICK UP WILL HAVE CONVERSION
OF UNITS SOMEWHERE ON IT. BUT HAVING FOUND IT, THEN YOU CAN USE IT FOR YOUR CONVERSION
OF UNITS.
IN THIS CHAPTER, WE WILL USE UNITS THAT MOST PEOPLE KNOW JUST FROM THEIR COMMON, EVERYDAY
LIVING. SO MOST PEOPLE KNOW THAT THERE ARE 36 INCHES IN 1 YARD. BUT IN THIS PARTICULAR
CASE, WE DON'T WANT 36 INCHES, WE WANT 1 INCH. SO A CONVENIENT WAY OF LOOKING AT THIS IS
THIS: TREAT THIS AS AN EQUATION. AND RECALL FROM ALL OF OUR PREVIOUS LESSONS, I CAN DIVIDE
BOTH SIDES OF THE EQUATION BY ANYTHING I WISH. AND 37, 36 INTO 36 IS 1, OF COURSE, INCHES.
THEN I HAVE TO DIVIDE THE OTHER SIDE BY 36, SO I HAVE HERE 1/36, AND OF COURSE, YARD.
SO 1 INCH IS 1/36 OF A YARD.
NOW, IT'S THE SAME THING WITH FEET. I WILL REPLACE FEET BY WHAT I WANT IS YARDS. AND
EITHER YOU WILL KNOW THAT 1 FOOT IS 1/3 OF A YARD, AND IF YOU DIDN'T, ON YOUR TABLE YOU
WOULD FIND THAT 1 YARD IS 3 FEET, AND IN EFFECT NOW DIVIDE BOTH SIDES BY 3. AND THIS GIVES
ME 1 FOOT ON THIS SIDE AND 1/3 OF A YARD. SO THAT 1 FOOT IS 1/3 OF A YARD.
AND OF COURSE, YARD HERE IS WHAT I WANT. SO NOW I HAVE 5 YARDS PLUS 2/3 OF A YARD PLUS
7/36 OF A YARD. NOW THAT THEY ARE ALL THE SAME UNITS, YARDS, I HAVE PERMISSION TO ADD
WHAT WE WILL LATER IN ALGEBRA CALL THE COEFFICIENTS, WE CALL HERE THE NUMBER PART OF THE MEASUREMENT.
SO 5 PLUS 2/3 PLUS 7/36, AND OF COURSE WE'RE RIGHT BACK INTO REVIEWING FRACTIONS, AREN'T
WE? GETTING COMMON DENOMINATORS HERE, I HAVE 24/36 PLUS 7/36 IS 31/36 AND THE 5 YARDS.
SO WE CAN SAY THAT 5, 5 YARDS, 2 FEET, AND 7 INCHES IS 5 AND 31/36 OF A YARD OR ALMOST
6 YARDS.
THE POINT WE'RE TRYING TO MAKE IS THAT ALTHOUGH USUALLY WE'LL GO TO THE SMALLEST UNIT BECAUSE
WE CAN AVOID FRACTIONS BY DOING IT, WE COULD CHANGE THIS TO YARDS IF I WANTED TO OR FEET
IF I WANTED. THE CHOICE IS YOURS, OR WHATEVER YOU'RE GOING TO USE THIS FOR WILL DETERMINE
THAT CHOICE QUITE FREQUENTLY.
USUALLY IF OUR NUMBER PART OF OUR MEASUREMENT BEGINS TO BECOME TOO LARGE, WE WILL SEEK TO
CONVERT THIS TO THE NEXT LARGER UNIT OF MEASURE. SO AFTER WE GET A YARD LENGTH, THE NEXT LARGER
FOR MOST PEOPLE IS THE MILE. SO WE WOULD ASK: HOW DO WE GO ABOUT CONVERTING YARDS HERE TO
MILES? WELL, AGAIN OUR TECHNIQUE IS TO LEAVE THE NUMBER PART TEMPORARILY ALONE, BUT WE'RE
GOING TO CONVERT 1 YARD TO MILES. SO WE NEED A CONVERSION EQUIVALENT BETWEEN YARDS AND
MILES.
SO AGAIN, LOOKING IN ONE OF THOSE SOURCES, THIS TELLS ME THAT 1 MILE IS 1760 YARDS, BUT
WE WANT 1 YARD TO BE MILES. SO WE THINK THAT I WANT THIS TO BE 1, SO IF I DIVIDE BOTH SIDES
BY 1760, I GET THAT 1 YARD IS 1/1760 OF A MILE. SO I CAN REPLACE 1 YARD BY WHAT IT'S
EQUAL TO, AND THAT'S THIS.
BUT NOW, WE CAN SEE IF I MULTIPLY THIS TIMES THIS, IN EFFECT I'M GOING TO DIVIDE, 6512
DIVIDED BY 1760. AND IF I DO THAT, 6512 DIVIDED BY 1760, I GET 3.7. SO WE KNOW THIS MANY YARDS
IS 3.7 MILES. SO IF WE HAVE TOO MANY OF A UNIT, AGAIN, WATCH YOUR LITERATURE. YOU'LL
FIND INVARIABLY YOU'LL GO TO A LONGER OR LARGER UNIT OF MEASURE TO KEEP ITS NUMBER PART AS
SMALL AS POSSIBLE.
BUT IT DOES HAPPEN FREQUENTLY THAT WHEN YOU'RE TRYING TO FIND OUT HOW MANY YARDS ARE IN A
MILE, THE CONVERSION TABLE THAT YOU'RE USING JUST MIGHT NOT HAVE SUCH A RELATIONSHIP. SO
YOU HAVE TO MAKE DO WITH WHAT IT DOES GIVE YOU. SO IT DOES GIVE YOU VERY FREQUENTLY THAT
1 MILE IS 5280 FEET, AND IT'LL ALSO WILL TELL YOU OR YOU WILL ALREADY KNOW THAT 1 YARD IS
3 FEET.
SO WE DON'T WANT MILES AND FEET. WE WANT MILES, AND OVER HERE IF YOU WOULD, WE WANT THIS IN
YARDS. SO WE CAN REPLACE A FOOT BY HOW MANY YARDS. SO IF 1 YARD IS 3 FEET, 1 FOOT IS 1/3
OF A YARD. NOW DIVIDING THIS BY 1, MULTIPLYING BY 1/3 OR DIVIDING BY 3, WE GET WHAT WE HAD
FORMERLY, 1760 YARDS IS 1 MILE. SO FREQUENTLY IN ORDER TO GET A CONVERSION UNIT FROM A CHART,
YOU WON'T FIND IT DIRECTLY IN THE CHART, BUT YOU CAN USE WHAT THE CHART DOES GIVE YOU AND
WHAT WE'VE BEEN DOING TO CONVERT WITHIN THE CONVERSION TABLE ITSELF TO GET THAT RELATIONSHIP
WHICH WE NEED AT THAT MOMENT. SO DO BE PREPARED TO WORK WITHIN THE CONVERSION TABLE ITSELF.
AND ALSO RECALL, AS A PART OF THIS LESSON, IF YOU'RE ADDING OR SUBTRACTING MEASUREMENTS,
THAT YOU CAN ONLY ADD LIKE MEASUREMENT TO LIKE MEASUREMENT. SO WHEN YOU HAVE MIXED MEASUREMENTS,
YOU USUALLY LINE THEM UP VERTICALLY TO GET THE LIKE MEASUREMENT WITH THE LIKE MEASUREMENT.
THEN ADD THOSE LIKE PARTS. SO IN THIS CASE, I WOULD GET 15 INCHES AND HERE 19 FEET.
BUT JUST LIKE TAKING AN IMPROPER FRACTION DOWN TO A PROPER FRACTION, IF THIS IS MORE
THAN ONE OF THESE AND IT IS BECAUSE 15 INCHES IS REALLY 12 INCHES PLUS 3 INCHES, AND 12
INCHES IS 1 FOOT. SO I'D TAKE 12 INCHES AWAY FROM THIS UNIT, LEAVING ME WITH 3 INCHES.
AND I WOULD ADD THAT 12 INCHES OVER HERE. SO IF YOU GET MORE THAN ONE OF THESE, YOU
TAKE IT OFF AND ADD IT OVER TO ONE OF THESE AND INCREASE THIS. SO THAT THIS SHOULD ALWAYS
BE LESS THAN ONE OF THESE TO BE CONSIDERED PROPER.
AND OF COURSE, THE SAME THING REGARDING SUBTRACTION. ONLY SUBTRACT INCHES FROM INCH AND FEET TO
FEET. I CAN SUBTRACT 18 FROM 42, BUT I SURE CAN'T SUBTRACT 9 FROM 3. SO THAT MEANS I MUST
BORROW ONE OF THESE FEET. BUT REMEMBER, 1 FOOT COMES OVER AS 12 INCHES, WHICH MAKES,
ADDED TO THIS NOW, GIVES ME 15 INCHES. NOW, I CAN SUBTRACT 9 FROM 15, GETTING OF COURSE
6 INCHES, AND SUBTRACTING HERE, GETTING 23 FEET.
SO BE SURE THAT WHEN YOU BORROW, YOU BORROW ONE OF THESE BECOMES THE APPROPRIATE AMOUNT
OVER HERE. SO 1 FOOT IS 12 INCHES, WHEREAS IF I WERE WORKING WITH WEIGHTS, IT BECOMES
AN ENTIRELY DIFFERENT MATTER. SO SEE, IT'S NOT JUST THESE NUMBER PARTS THAT DECIDES THE
ISSUE, IT IS THE MEASUREMENT ITSELF.
IN THIS CASE, I STILL CAN'T SUBTRACT 9 FROM 3, BUT NOW IF I BORROW 1 POUND, 1 POUND IS
16 OUNCES. WHEREAS 1 FOOT WAS 12 INCHES. SO THE 16 OUNCES THAT I BORROWED FROM THIS 1
POUND, ADDED TO 3 OUNCES, BECOMES NOW 19 OUNCES. NOW SUBTRACTING 9 FROM 19, I GET 10 OUNCES.
AND OF COURSE HERE I STILL GET THE 23, BUT NOW POUNDS INSTEAD OF FEET. SO SEE, YOU DON'T
CONCENTRATE ON JUST THE NUMBER PART. THE MEASUREMENT IS THE ONE THAT DETERMINES EVERYTHING THAT
YOU'RE GOING TO DO. SO PAY PARTICULARLY ATTENTION TO THESE AND THEIR EQUIVALENTS.
IF ONE HAS BEEN SHOPPING, WORKING IN A KITCHEN, OR WORKING AROUND THE HOUSE WHERE YOU DO MINOR
CARPENTRY, YOU'VE DONE MANY, MANY PROBLEMS LIKE THIS ALREADY. SO NOW WE'RE JUST TRYING
TO GENERALIZE IT SO YOU CAN APPLY THE SAME PRINCIPLE IN THOSE AREAS WHERE YOU PERHAPS
HAVEN'T WORKED. THIS SHOULD BE AN EASY LESSON FOR YOU. AT LEAST I HOPE SO. THIS IS YOUR
HOST, BOB FINNELL.