Changing Units of Measure

Fractions always show what part you have out of the whole thing:

  part    
  whole    

The part can be any amount. The whole always specifies the number of pieces in each whole thing.

For example, if you have 75 pennies and want to write it as a fractional part of a dollar:

  part
  whole
=   75 pennies
  100 pennies
  (your part)  
(one whole dollar)
=   75
  100
=   3
  4

75 pennies is what fractional part of a dollar?
EXPLANATION:   Put the part (the 75 pennies) in the numerator (on top) of the fraction; the number of those SAME units in each WHOLE (dollar) is the denominator (on the bottom). You now have 75/100 (which can be simplified).   75/100 = 3/4 (of a dollar)

Notice that the fraction is always simplified completely (reduced to lowest terms). The part can be more than one whole thing -- divide to change the improper fraction to a mixed number, then simplify (reduce) if possible.




Change 20 feet to yards.   There are 3 feet in one yard.

  part
  whole
=   20 feet
  3 feet
  (your part)  
(one whole yard)
=   20
  3
= 6 2/3

Change (convert) 20 feet to yards.
EXPLANATION:   Put the part (the 20 feet) in the numerator (on top) of the fraction; the number of those SAME units in each WHOLE (yard) is the denominator (on the bottom). Notice that 20 feet is MORE THAN one whole yard; the fraction is "improper" (the numerator -top- is greater than the denominator). You now have 20/3 (which can be simplified).   20 divided by 3 = 6 2/3 (yards)


Answers to the following problems are also printed at the bottom of the page.
SAMPLE PROBLEM #1:
  One hour equals 60 minutes. Change 45 minutes to hours.
Look at the set-up.
 
  See the solution.



SAMPLE PROBLEM #2:
  There are four quarters in a dollar. Change 10 quarters to dollars.
Look at the set-up.
 
  See the solution.




Remember the PART is the number of pieces you're given; the WHOLE is the number of those pieces in each whole thing:
  12 inches in a foot:   ONE WHOLE = 12 inches
a yard equals 36 inches: ONE WHOLE = 36 in.
ten dimes in a dollar: ONE WHOLE = 10 dimes
100 centimeters = one meter ONE WHOLE = 100 cm.

fractional part (on the top) out of the whole(on the bottom).



PRACTICE. Reduce fractions and mixed numbers to lowest terms.

1) Change 10 inches to feet.   There are 12 inches in a foot.




2) Change 80 inches to yards.   There are 36 inches in a yard.




3) Change 10 inches to yards.   There are 36 inches in a yard.





4) Change 150 minutes to hours.   One hour equals 60 minutes.



ANSWERS:

Sample Problem #1   45 minutes = 3/4 hour
45 minutes out of 60 minutes in one WHOLE hour = 45/60

Sample Problem #2   10 quarters = 2 1/2 dollars
10 quarters is MORE THAN one whole dollar
10/4   (10 divided by 4 quarters per dollar) = 5/2 = 2 1/2 dollars

1)   10/12 = 5/6 ft.    
2)   80/36 = 2 2/9 yd.    
3)   5/18 yd.    
4)   2 1/2 hr.




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