QUESTIONS FOR REVIEW. Into what classes are numbers divided? What is a simple number? A compound number? When are two numbers of the same denomination? When of different denominations? What is the simplest class of Compound Numbers? Why? What is Federal Money? The denominations? How many units of each denomination make one of the next higher? Give the table. What is a coin? Of what are the coins made? Which are made of silver? Which, of nickel? of the copper cent? The mill? Of gold? What is said How is Federal Money written? Why? What place do mills occupy? Cents? Dollars? Eagles? Dimes? How are the dollars separated from cents? How are cents and dimes read? How many places do they occupy? How are dollars and eagles read? What is the rule for numeration? What is done when the cents are less than 10? rule for notation. When there are no cents? Give the What is reduction? How many kinds of reduction? What are they? What is reduction descending? Reduction ascending? Give the rule for addition of Federal Money. Proof. The rule for subtraction. Proof. The rule for multiplication. Proof. How divide one sum of money by another? How divide a sum of money into any number of equal parts? What does + mean when placed after the quotient? What is a bill? What is Arithmetic? What is a number? How are numbers expressed? What is numeration? What is addition? What does the amount represent? What is the sign of addition? What is the sign of equality? What is a proof? How many figures make a period? Name the periods. What is subtraction? Give the rule. What is the subtrahend? The minuend? The remainder? How is subtraction proved? What is multiplication? What are the factors? What is the multiplier? The multiplicand? The product? Of what denomination is the product? What is division? What is the difference between long and short division? What is the dividend? The divisor? The quotient? The remainder? Of what denomination is the remainder? Give the rule for long division. 64. DRY MEASURE. Dry Measure is used in measuring grain, vegetables, fruit, coal, etc. TABLE. 2 pints (pt.) make 1 quart, marked qt NOTES.-1. The standard of dry measure is the bushel, which is 18 inches in diameter, 8 inches deep, and contains 2150% cubic inches. 2. The English quarter contains 8 bushels of 70 pounds each, and is used in measuring grain. 3. The chaldron, used for measuring coal, is employed in England and some of the United States. It contains 36 bushels. MENTAL EXERCISES. EXAMPLE.-How many pints are there in 4 quarts? SOLUTION. Since in 1 quart there are 2 pints, in 4 quarts there are 4 times 2 pints, which is 8 pints. CONCLUSION.-Therefore, in 4 quarts there are 8 pints. 1. How many pints in 3 quarts? In 5 qts.? In 6 qts.? In 7 qts.? 2. How many quarts in 2 pecks? In 3 pks.? In 4 pks.? In 5 pks.? 3. How many pecks in 2 bushels? In 4 bu.? In 3 bu.? In 5 bu.? 4. How many pints in 8 quarts, or 1 peck? In 2 pks.? In 4 pks.? 5. How many pecks in 6 bushels? In 9 bu.? Ir 8 bu.? In 10 bu.? SOLUTION. Since 2 pints equal 1 quart, 6 pints equal as many quarts as 2 is contained times in 6, which is 3. CONCLUSION.-Therefore, in 6 pints there are 3 quarts. 6. How many quarts in 4 pints? In 8 pt.? In 12 pt.? In 16 pt.? 7. How many pecks in 8 quarts? In 32 qt.? In 64 qt.? In 24 qt.? 8. How many bushels in 8 pecks? In 32 pk.? In 16 pk.? 9. How many bushels in 12 pk.? In 20 pk.? In 64 qt.? MODEL SOLUTION. EXAMPLE. Reduce 4 bu. 1 pk. 7 qt. 1 pt. to pints. OPERATION. Since in 1 bu. SOLUTION. there are 4 pk., in 4 bu. there are 4 times 4 pk., which are 16 pk.; 16 pk. +1 pk. = 17 pk. Since in 1 pk. there are 8 qt., in 17 pk. there are 17 times 8 qt., which are 136 qt.; 136 qt. +7 qt. 143 qt. Since in 1 qt. there are 2 pt., in 143 ot. there are 143 times 2 pt, which are 286 pt.; 286 pt. +1 pt.287 pt. CONCLUSION.-Therefore, in 4 bu. 1 pk. 7 qt. 1 pt. there are 287 pt. EXAMPLE.-Reduce 177 pints to higher denomina tions. SOLUTION.-Since 2 pt. make 1 qt, 177 · pt. make as many qt., as 2 is contained times in 177,88 qt and 1 pt. remaining. Since 8 qt make 1 pk., 88 qt make as many pk. as 8 is contained times in 88, = 11 pk. = Since 4 pk. make 1 bu., 11 pk. make OPERATION. 2)177 pt. 8)88 qt.+1pt 4)11 pk. 2 bu. +3 pk. as many bu. as 4 is contained times in 11,=2 bu. and 3 pk. remaining. CONCLUSION.-Therefore, in 177 pt. there are 2 bu. 3 pk. 1 pt. Hence, the GENERAL RULES. For Reduction Descending.-Multiply the highest denomination given, by that number which it takes of the next lower denomination to make one of this higher; add to the product the number, if any, of the next lower denomination. Proceed in like manner with the result obtained, until the whole is reduced to the required denomination. For Reduction Ascending.-Divide the given quantity by the number of units of its own denomination which makes one of the next higher. Proceed in like manner with the quotient thus obtained, till the whole is reduced to the required denomination. The last quotient, with the several remainders, if any, annexed, will be the answer. PROOF.-Reverse the operation; that is, reduce the answer back to the denomination from which it was derived. EXAMPLES FOR PRACTICE. 1. Reduce 2 bu. to pints. 2. Reduce 172 pt. to bushels. 3. Reduce 5 bu. 1 pk. to pints. 5. Reduce 1 bu. 1 pk. 1 qt. to quarts. 8. Reduce 12 bu. 1 pk. 3 qt. to pints. 10. Reduce 24188 pt. to pecks. 11. Bought 10 bushels of plums at 5 cents a quart. what did they cost? 12. Bought 8 bu. 3 pk. of blackberries at 8 cents a quart, and sold them for 10 cents a quart: how much did I gain? 13. A man sold 108 bu. 3 qt. of corn at the rate of one cent a pint: what did it bring? 14. How many bushels of wheat can be purchased for $17.30, at 2 cents a pint? 65. TROY WEIGHT. Troy Weight is used in weighing gold, silver, jewels, etc. TABLE. 24 grains (gr.) make 1 pennyweight, marked pwt. 1 ounce, OZ. lb. NOTE.-Th standard unit of weight in the United States is the Troy pound, containing 5760 grains. |
