the following: Reduce of a bushel to pecks. Any number of bushels is reduced to pecks by multiplying by 4. Any fraction of a bushel is reduced to pecks in the same way. 3. .75 of a foot reduced to inches? 4. Reduce SOLUTION: × 4 equals how many inches? How are feet Apply the process. of a gallon to lower denominations. = 31, the number of quarts.qt. reduced to pints = 1 × 2 = 1, the number of pints. The answer is 3 qt. 1 pt. 5. Reduce of a yard to lower denominations. SOLUTION: × 3 = 2, the number of feet. x 12=43, the number of inches. Ans. 2 ft. 4 in. 6. Reduce of a day to lower denominations. 7. In of a cord, how many cubic feet are there? 8. Reduce of a barrel to lower denominations. 9. Reduce of a yard to lower denominations. 10. Reduce of a gallon to lower denominations. 11. Reduce .7 of a pound to ounces. 16 In .7 of a pound there are .7 of 16 oz., or 11.2 oz. .7 11.2 16 .2 3.2 In 2 of an ounce there are 2 of 16 drams, or 3.2 drams. Ans. 11 oz. 3.2 drams. 12. What decimal of an hour is .07 of a day? .15 of a day? 13. What decimal of a quart is .75 of a peck? .45 of a peck? 14. Reduce of a quart to the fraction of a gallon. How are quarts reduced to gallons? Apply the process in the above example. SOLUTION: ÷ 4 = %, the fraction of a gallon. 15. What part of a gallon is of a pint? The answer is gal. SOLUTION: First find what part of a quart of a pint is, then find what part of a gallon the resulting fraction is. 16. How can you reduce days to weeks? What decimal of a week is .21 of a day? 17. 30.8 rd. is what decimal of a mile? 18. What part of a gallon is 2 qt. 1 pt.? The question now becomes, 5 pt. is what part of 8 pt.? Ans. §. The question now becomes, 8 ft. is what part of 16 ft.? Ans. §. 20. What part of a day is 12 hr. 30 min.? 12 hr. 30 min. how many minutes? 1 day = = how many minutes? How may the question now be stated? 22. What part of 51 yd. is 2 yd. 2 ft.? 23. What part of a ton of hay is 1800 lb.? What decimal? ADDITION AND SUBTRACTION OF COMPOUND DENOMINATE NUMBERS 142. In adding compound numbers, as in simple numbers, the numbers to be added must be of the same denomination. In adding simple numbers, the sum of the numbers of any denomination is divided by ten, the quotient is added to the next higher denomination, and the remainder is written under the numbers added. In adding compound numbers, the sum of the numbers of any denomination is divided by the number of units of that denomination it takes to make one of the next higher denomination; the remainder, if any, is written under the numbers added, as in simple numbers, and the quotient is added to the number of the next higher denomination, as in simple numbers. the 4 under the days added. weeks; the sum is 26 wk. Adding the hours, gives the sum 46 hr. Dividing 46, the number of hours, by 24, to reduce to days, gives 1 da. and the remainder 22 hr. Write the remainder 22 under the hours added. Add the 1 da. to the numbers representing days; the sum is 18 da. Dividing 18, the number of days, by 7, to reduce to weeks, gives 2 wk. with 4 da. remainder. Write Add the 2 wk. to the numbers representing The entire sum is 26 wk. 4 da. 22 hr. ing 4 yd., the sum may be written 4 yd. 1 ft. 6 in., the entire sum being 16 rd. 4 yd. 1 ft. 6 in. bu. pk. qt. 7. From 8+1+5 take 5+3+7 7 qt. cannot be taken from 5 qt. Add to the 5 qt., 8 qt., the number of quarts in 1 pk.; from the sum, 13 qt., subtract 7 qt., and write the remainder, 6 qt., underneath. We have added 1 pk. to the minuend. We must, therefore, either take 1 pk. from it or add 1 pk. to the subtrahend, in order that the result may be correct. Add 1 pk. to the 3 pk. in the subtrahend; the sum is 4 pk. 4 pk. cannot be taken from 1 pk.; add 4 pk., the number of pecks in a bushel, to the 1 pk., and from its sum, 5 pk., subtract 4 pk. The remainder is 1 pk. Write the 1 pk. underneath. Add 1 bu. to the 5 bu. in the subtrahend, making it 6 bu.; subtract 6 bu. from 8 bu. The remainder is 2 bu. The entire answer is 2 bu. 1 pk. 6 qt. If there is a fraction in the remainder, reduce it to lower denominations, and write the numbers of the lower denominations as a part of the remainder. 143. Finding the difference between dates. In finding the difference between two dates, treat the number of the year as so many years, the number of the month as so many months, and the day of the month as so many days. In subtracting, count thirty days to the month and twelve months to the year. Find the difference in time between Sept. 8, 1901, and Nov. 21, 1896. yr. mo. da. 1. 19019+ 8 1896 +11 + 21 4+9+17 The later date is written as 1901 yr. 9 mo. 8 da. The earlier date is written as 1896 yr. 11 mo. 21 da. The subtraction is performed in the same way as in other cases of subtraction in compound numbers. 2. A man was born Nov. 3, 1844; he died Jan. 18, 1900. At what age did he die? 3. What was the date of your birth? What is your age to-day? 4. If you have a brother who is 4 yr. 6 mo. 10 da. older than you are, what was the date of his birth? 5. A man gave a note Aug. 10, 1904; he paid it June 7, 1906. How long did the note run? |