- WELCOME TO A LESSON ON AMERICAN UNITS AND CONVERSIONS.
THE GOAL OF THE VIDEO
IS TO CONVERT FROM ONE AMERICAN UNIT OF MEASURE TO ANOTHER.
THE UNITED STATES CUSTOMARY SYSTEM,
ALSO CALLED THE AMERICAN SYSTEM,
IS THE MOST COMMONLY USED SYSTEM OF MEASUREMENT
IN THE UNITED STATES.
HOWEVER, THE UNITED STATES IS THE ONLY INDUSTRIALIZED NATION
THAT DOES NOT MAINLY USE THE METRIC SYSTEM
IN ITS COMMERCIAL AND STANDARDS ACTIVITIES,
ALTHOUGH THE METRIC SYSTEM IS UNIVERSALLY USED IN SCIENCE
AND INCREASINGLY IN MEDICAL, GOVERNMENT,
AND OTHER SECTORS OF INDUSTRY.
SO HERE'S A TABLE OF CONVERSIONS FOR LENGTH, CAPACITY, WEIGHT,
AND TIME.
YOU MAY WANT TO PAUSE THE VIDEO TO REVIEW THIS,
BUT I WILL ASSUME YOU'VE BEEN EXPOSED TO THIS ALREADY.
THERE ARE TWO METHODS FOR CONVERTING
AMONG MEASUREMENT UNITS.
THE FIRST METHOD IS MULTIPLYING AND DIVIDING,
WHERE WE MULTIPLY WHEN CONVERTING FROM A LARGE UNIT
TO A SMALLER UNIT.
AND WE DIVIDE WHEN CONVERTING FROM A SMALLER UNIT
TO A LARGER UNIT.
HOWEVER, THE METHOD I'M GOING TO USE IN THIS VIDEO
WILL BE THE METHOD OF USING UNIT FRACTIONS
WHERE WE MULTIPLY BY UNIT FRACTIONS
AND EACH UNIT FRACTION THAT WE MULTIPLY BY
MUST BE EQUAL TO ONE.
THE NUMERATOR WILL CONTAIN THE MEASUREMENT UNIT
WE WANT IN OUR ANSWER,
WHILE THE DENOMINATOR WILL CONTAIN THE MEASUREMENT
WE WANT TO CHANGE.
LET'S GO AHEAD AND TAKE A LOOK AT HOW THIS WILL WORK.
IF WE WANT TO CONVERT 45 INCHES TO FEET,
THE FIRST STEP IS TO WRITE 45 INCHES IN FRACTION FORM.
SO THAT WOULD BE 45 INCHES/1.
NEXT, WE'RE GOING TO MULTIPLY IT BY A UNIT FRACTION.
SO WE'RE GOING TO LOOK AT THE TABLE BELOW
AND SEE IF WE CAN FIND A RELATIONSHIP
BETWEEN INCHES AND FEET.
AND NOTICE THAT WE HAVE 1 FOOT EQUALS 12 INCHES.
SO TO SET UP OUR UNIT FRACTION,
WE'RE FIRST GOING TO PLACE OUR UNITS IN THE CORRECT POSITION,
MEANING WE WANT FEET IN OUR ANSWER
SO WE'LL PUT FEET IN THE NUMERATOR.
AND WE WANT INCHES TO CHANGE,
SO WE'LL WRITE INCHES IN THE DENOMINATOR.
SO NOTICE HOW THE UNIT OF INCHES WILL SIMPLIFY OUT.
NEXT, THE CONVERSION IS 1 FOOT IS EQUAL TO 12 INCHES.
SO WE'LL HAVE 1 FOOT IN THE NUMERATOR
AND 12 INCHES IN THE DENOMINATOR.
NOW WE CAN SEE THAT INCHES WILL SIMPLIFY OUT.
SO NOW WE MULTIPLY THE NUMERATORS TOGETHER,
45 x 1 FOOT WOULD BE 45 FEET.
AND OUR DENOMINATOR WOULD BE 1 x 12 OR 12.
SO TO DO THIS FINAL CONVERSION,
REMEMBER A FRACTION BAR IS JUST A DIVISION SYMBOL.
SO WE'LL TAKE 45 AND DIVIDE BY 12.
45 DIVIDED BY 12 GIVES US 3.75 FEET.
NUMBER TWO, WE HAVE 6 MILES.
WE WANT TO CONVERT THIS INTO YARDS,
SO THE FIRST STEP IS PUT 6 MILES/1
AND WE'RE GOING TO MULTIPLY BY A UNIT FRACTION.
AND SOMETIMES IT WILL TAKE MORE THEN ONE.
SO NOW WE'LL GO TO THE TABLE
AND SEE IF WE CAN FIND AN EQUATION
THAT RELATES MILES TO YARDS.
IF WE STICK TO JUST THIS TABLE, THE ONLY CONVERSION THAT WE SEE
IS THAT ONE MILE IS EQUAL TO 5,280 FEET.
BUT THERE IS ANOTHER EQUATION HERE THAT RELATES FEET TO YARDS.
SO THAT TELLS US THAT WE'RE GOING TO HAVE
TWO UNIT FRACTIONS.
THE FIRST ONE WE'RE GOING TO CONVERT MILES INTO FEET.
WE WANT MILES TO SIMPLIFY OUT,
SO WE'LL PUT MILES IN THE DENOMINATOR
AND WE'LL HAVE FEET IN THE NUMERATOR.
AND THE CONVERSION IS 1 MILE IS 5,280 FEET.
NOTICE, NOW MILES WOULD SIMPLIFY OUT,
BUT NOW WE'RE LEFT WITH FEET AND WE STILL WANT YARDS.
SO WHAT THAT MEANS IS WE HAVE TO MULTIPLY IT
BY ANOTHER UNIT FRACTION
AND ONE YARD IS EQUAL TO THREE FEET.
SO WE'LL PUT FEET IN THE DENOMINATOR,
SO THAT WOULD SIMPLIFY OUT, YARDS IN THE NUMERATOR,
AND AGAIN THE CONVERSION IS ONE YARD EQUALS THREE FEET.
NOTICE THAT THE FEET WOULD SIMPLIFY OUT,
AND SO NOW WE'RE LEFT WITH, IN THE NUMERATOR,
6 x 5,280 YARDS DIVIDED BY 1 x 1 x 3 OR 3.
SO NOW WE'LL USE OUR CALCULATOR, MULTIPLY 6 x 5,280
AND THEN DIVIDE THAT BY 3.
AND THAT GIVES US 10,580 TOTAL YARDS.
OKAY, LET'S GO AHEAD AND TAKE A LOOK AT SOME CONVERSION NOW
THAT DEAL WITH WEIGHT.
ON NUMBER ONE WE WANT TO CONVERT TONS TO POUNDS.
SO FIRST STEP, WRITE 6.3 TONS/1 SO IT'S IN FRACTION FORM.
NOW WE'RE GOING TO LOOK FOR A CONVERSION FROM THE TABLE.
NOTICE THAT 1 TON IS EQUAL TO 2,000 POUNDS.
SINCE WE WANT TONS TO SIMPLIFY OUT,
WE'LL PUT TONS IN THE DENOMINATOR
AND POUNDS IN THE NUMERATOR.
AND THE CONVERSION IS 1 TON EQUALS 2,000 POUNDS.
NOTICE TONS SIMPLIFIES OUT,
THIS LEAVES US WITH A DENOMINATOR OF 1
AND A NUMERATOR OF 6.3 x 2,000 POUNDS.
SO WE MULTIPLY 6.3 x 2,000 AND IT GIVES US 12,600 POUNDS.
ON NUMBER TWO WE'RE CONVERTING OUNCES TO POUNDS.
SO WRITE 86 OUNCES/1, LOOK FOR A CONVERSION.
WE HAVE 16 OUNCES EQUALS 1 POUND.
SO OUR UNIT FRACTION WE WANT OUNCES IN THE DENOMINATOR,
POUNDS IN THE NUMERATOR.
AGAIN, WE KNOW THAT BECAUSE WE WANT THE OUNCES TO SIMPLIFY OUT,
BUT BEFORE WE DO THAT,
THE CONVERSION IS 1 POUND EQUALS 16 OUNCES.
SO 1 POUND IN THE NUMERATOR, 16 OUNCES IN THE DENOMINATOR,
AND NOW WE MULTIPLY.
OUR NUMERATOR IS 86 POUNDS, OUR DENOMINATOR IS 16.
SO ON THIS PROBLEM WE HAVE TO DIVIDE 86 DIVIDED BY 16
WILL GIVE US 5.375 POUNDS.
AND THEN THE LAST EXAMPLE FOR WEIGHT,
WE HAVE 6,400 OUNCES CONVERTING TO TONS.
SO FIRST STEP, WRITE IT IN FRACTION FORM
AND IT LOOKS LIKE WE'RE GOING TO HAVE TO HAVE TWO UNIT FRACTIONS
THIS PROBLEM BECAUSE WE CAN CONVERT OUNCES TO POUNDS
USING THIS EQUATION.
LET'S DO THAT FIRST,
OUNCES IN THE DENOMINATOR,
CONVERSION IS 16 OUNCES EQUALS ONE POUND.
NOTICE NOW WE'VE CONVERTED TO POUNDS,
BUT WE WANT TONS.
SO WE HAVE TO MULTIPLY IT BY ANOTHER UNIT FRACTION
WHERE WE WANT POUNDS IN THE DENOMINATOR
AND TONS IN THE NUMERATOR.
NOTICE HOW THE POUNDS WILL SIMPLIFY OUT.
THE CONVERSION, ONE TON IS EQUAL TO 2,000 POUNDS.
SO THE POUNDS SIMPLIFY OUT.
OUR NUMERATOR IS GOING TO BE 6,400 TONS.
OUR DENOMINATOR IS GOING TO BE 16 x 2,000.
LET'S GO AHEAD AND GO TO OUR CALCULATOR.
WE HAVE 64,000 DIVIDED BY 16 x 2,000.
SO THIS IS EQUAL TO .2 TONS.
LET'S GO AHEAD AND TAKE A LOOK AT A FEW MORE.
ON THIS ONE WE WANT TO CONVERT QUARTS TO CUPS.
SO THE PROCESS IS EXACTLY THE SAME
3 QUARTS/1 x A UNIT FRACTION.
LOOKING AT CAPACITY, ONE QUART IS EQUAL TO TWO PINTS.
THAT'S THE ONLY CONVERSION WE HAVE SO LET'S DO THAT FIRST.
WE DON'T WANT QUARTS THAT GOES IN THE DENOMINATOR.
CONVERT IT TO PINTS,
AND THE CONVERSION IS ONE QUART EQUALS TWO PINTS.
NOTICE HOW THE QUARTS ARE NOW GONE,
BUT NOW WE'RE LEFT WITH PINTS WE WANT TO CONVERT TO CUPS.
WE HAVE TO MULTIPLY IT BY ANOTHER UNIT FRACTION
WHERE WE DON'T WANT PINTS BUT WE DO WANT CUPS.
AND THE CONVERSION IS ONE PINT EQUALS TWO CUPS.
SO WE HAVE ONE PINT, TWO CUPS.
NOTICE HOW THE PINTS ARE NOW SIMPLIFIED OUT,
SO WE'RE LEFT WITH A NUMERATOR OF 3 x 2 x 2 = 12 CUPS/1.
SO WE HAVE 12 CUPS.
ON NUMBER TWO, TO CONVERT 72 FLUID OUNCES TO PINTS.
WE ONLY HAVE A CONVERSION FROM FLUID OUNCES TO CUPS
SO WE'LL DO THAT CONVERSION FIRST.
WE DON'T WANT FLUID OUNCES IN OUR ANSWER
SO WE'LL CONVERT THAT TO CUPS.
SO IT'S EIGHT FLUID OUNCES TO ONE CUP.
SO NOW THE FLUID OUNCES ARE OUT,
SO NOW WE'LL CONVERT CUPS TO PINTS.
THE CONVERSION IS ONE PINT TO TWO CUPS.
SO WE'LL PUT TWO CUPS HERE TO ONE PINT HERE.
NOW THE CUPS ARE GONE, SO NOW WE CAN MULTIPLY ACROSS THE TOP.
THAT'D BE 72 PINTS DIVIDED BY 16.
SO 72 DIVIDED BY 16 EQUALS 4.5 PINTS.
WE'RE RUNNING OUT OF TIME
SO WE'RE GOING TO GO AHEAD AND STOP HERE,
BUT HOPEFULLY YOU FOUND THESE EXAMPLES HELPFUL.
THANK YOU FOR WATCHING AND HAVE A GOOD DAY.