DENOMINATE NUMBERS 



1767 



DENOMINATE NUMBERS 



(3) Change to higher units 5963 pints. 

 Number qt. =5^=2981, and 1 pt. 



A 

 OOQ1 



Number pk.==^-=372, and 5 qt. 



O 

 Q79 



Number bu.=^==93. 

 4 



5963 pt. = 93 bu. 5 qt. 1 pt. 

 It may be done in this concise form: 



2|5963 



8 1 2981+ remainder 1 



4 1 3 72 + remainder 5 



93 

 5963 pt. = 93 bu. 5 qt. 1 pt. 



(4) Change 56 cwt. to T. 



Number T.= 



56X100 

 2000 



(5) Express in bu. 3 pk. 5 qt. 1 pt. 

 Number qt. =5^ 



t 



Number pk.=3^=3y| 



3H 59 

 Number bu - = ~7~ = 64 



Note 1 pt.= % qt., so there are 5% qt. ; It 

 requires 8 qt. to make a pk. ; 5 % qt. n of a 

 pk. ; multiply numerator and denominator of the 

 complex fraction by 2, thus; =- There 



are 3 pk. and Hie pk. or 



3 ii 

 pk., which is 



of a bu. Reduce fraction by multiplying both 



terms by 16, thus ; 



3&X16 59 



4X16 64' 



Addition and Subtraction of Compound De- 

 nominate Numbers. In the following para- 

 graphs the principles underlying the addition 

 and subtraction of denominate numbers are 

 explained. Addition : 

 Add: 



Sum: 

 Reduced sum : 



8 gal. 3 qt. 1 pt. 

 1 gal. 2 qt. 3 pt. 



9 gal. 5 qt. 4 pt. 



10 gal. 3 qt. pt. 

 Add at first; then reduce: 



4 pt. = 2 qt. 



(5 + 2) qt. = 7 qt. = l gal. 3 qt. 



9 gal. + l gal. = 10 gal. 



Reduce as you add, as below: 



sq. yd. 

 6 

 2 



sq. ft. 

 4 



sq. in. 

 20 



200 



9 4 76 



Note Out of 220 sq. in. we get 1 sq. ft. (which 

 is 144 sq. in.), and have -left 76 sq. in.; (4+8 + 

 1) sq. ft. = 13 sq. ft.; out of 13 sq. ft. we get 1 

 sq. yd. (which is 9 sq. ft.) and have left 4 sq. 

 ft.; (6 + 2 + 1) sq. yd. = 9 sq. yd. 

 Add: 



mo. da. hr. min. 

 4 12 18 40 



3 15 12 50 



1 20 25 52 



Sum: 8 47 55 



Reduced sum: ~9 19 9 



142 



(1) Add each set. 



(2) Divide 142 by 60 (the number of minutes 

 in an hour), which gives 2 and a remainder 22. 

 This means that 142 minutes=2 hours and 22 

 minutes. 



(3) Add 2 to 55 and divide 57 by 24 (the 

 number of hours in a day) ; this division shows 

 there are 2 days and 9 hours in 57 hours. 



(4) Add 2 to 47, and divide 49 by 30 (the 

 number of days in 1 month) ; this division 

 shows there are 1 month and 19 days in 49 days. 



(5) Add 1 to 8. 



We find the sum to be 9 months 19 days 9 

 hours 22 minutes. Reduce each set as we go 

 along and get the final answer at once, as 

 below : 



gal. qt. 



4 3 



1 2 



2 1 



Pt. 

 1 

 1 

 1 



gi- 

 3 



2 



1 



9002 



Adding the gills we get 6 gills, which equals 1 

 pint 2 gills. Place 2 gills in gills' place, add 



1 pint to the pints, and get 4 pints, which 

 equal 2 quarts and no pints. Add the 2 quarts 

 to the quarts and get 8 quarts, which equal 



2 gallons. Add the 2 gallons to the gallons 

 and have 9 gallons. The answer is 9 gallons 

 quarts pints 2 gills. 



Subtraction: 



(1) A boy weighed on Monday 118 Ib. and 

 7 oz.; on Thursday 116 Ib. and 13 oz. What 

 did he lose in the time? 



118 

 116 



oz. lb. 



7 = 117 

 13 = 116 



oz. 



=23 



13 



1 10 



Note We cannot take 13 oz. from 7 oz., so we 

 take 1 It), from 118 It), and add it (16 oz.) to 7 

 oz. and have 23 oz. Subtracting, we have 1 lb. 

 10 oz. 



(2) From a piece of ground containing 78 

 acres and 90 sq. rd., a piece is sold containing 

 15 acres and 140 sq. rd. What is left? 



acres sq. rd. acres sq. rd. 



78 90 = 77 250 (160 + 90) 

 15 140 = 15 140 



62 



110 



(3) Subtract the following: 



gal. qt. 

 6 2 



4 3 



Pt. 



1 

 1 



gi. 



1 



3 





1212 



Note Change 1 pt. to 4 gi. ; then subtract 3 gi. 

 from 5 gi. and have 2 gl. left. Change 1 qt. to 

 2 pt. and subtract 1 pt., having 1 pt. left ; then 

 change 1 gal. to 4 qt. and add that to 1 qt. ; 

 from the sum take 3 qt., leaving 2 qt. ; finally 

 take 4 gal. from 5 gal. and have 1 gal. left. 



