A quarter of a cent can be written thus, $,0025 (for < of a cent is 25 tens of thousandths of a dollar.) At 12} cents per hour, in how much time will a man earn $46. At 64 cents per pint, how much molasses may be bought for $2 ? At 8,06 an ounce, how much camphor can be bought for $3? At $,12} a bushel, how much coal could be bought for $5 ? Divide ,032 by ,005. EXERCISES IN DECIMAL MULTIPLICATION AND DIVISION. Multiply ,25 by ,003. Divide ,25 by ,003. If you buy 24 bushels of coal, at $09 per bushel, what does the whole cost ? If a man's wages be fifty hundredths of a dollar a day, what will it be a month ? What will be the cost of 25 thousandths of a cord of wood, at $2 a cord ? What will be the cost of twelve hundredths of a ton of hay, at $11 a ton ? If a man pays a tax of two mills on a dollar, how much must he pay if he is worth $350 ? If a man pays $,06 a year for the use of each dollar he borrows of his neighbor, how much must he pay in a year if he borrows 264 dollars? How much in two years ? REDUCTION. Reduction is changing units of one order, to units of another order. Reduction Ascending, is changing units of a lower to a higher order. What is reduction? What is reduction ascending ? descending ? Reduction Descending, is changing units of a higher to a lower order. EXAMPLES FOR MENTAL EXERCISE. In 4 gallons how many quarts ? NOTE. Let each sum be stated thus. One gallon con. tains four quarts, and four gallons four times as much. times 4 is 16. In 4 gallons how many pints? In 8 yds. 3 qrs. how many quarters ? In 8 feet how many inches ? In 4 bushels how many quarts? In 5 hours how many minutes ? . Are the above sums in Reduction Ascending or De. scending? In 32 quarts how many gallons ? Let such sums be stated thus. One gallon contains 4 quarts. In 32 quarts therefore, there are as many gallons as there are 4's in 32. In 42 pints how many gallons ? bushels ? : 2379 farthings. We first change the pounds to shillings, by multiplying by 20, and add the 9 shillings to them, making 49 shil. lings. We then change the 49 shillings to pence, by multiply. ing by 12, and add the 6 pence to them, making 594 pence. We then change the 594 pence to farthings, by multiplying by 4, and add the 3 qrs. and thus we obtain the an. swer, 2379 qrs. This is Reduction Descending, because we have changed units of a higher order to those of a lower. Why did we multiply by 20, 12, and 4 ? £. 2 S. d. qr. We first change the 2379 farthings to pence, by divi. ding by 4, and the answer is 594 pence, and 3 farthings (or qr.) over, which is put in the quotient with qr. over it. We then change the 594 pence to shillings, by dividing by 12, and the answer is 49 shillings, and six pence over, which is put in the quotient with d. written over. We next change the 49 shillings to pounds, by dividing by 20, and find there is £2 and 9s. over, which are both put in the quotient with their signs written over them. Why did we divide by 4, 12, and 20 ? Let the following sums be performed and explained in the same way: Change 2486 farthings to pounds. RULE FOR REDUCTION. To reduce from a higher to a lower order. Multiply the highest order by the number required of the next lower order, to make a unit of this order. Add the next lower order to this product, and multiply it by the num. ber required of the next lower order, to make a unit of this order, adding as before. Thus through all the orders. To reduce from a lower to a higher order. Divide the amount given, by the number required to make a unit of the next higher order. Divide the answer in the same way, and continue thus till the answer is in units of the order demanded. The remainders are of the same order as the dividend, and are to be put as a part of the answer. EXERCISES. Bought a tankard of silver weighing 5 lb. 3 oz. for which I paid $1,12 an ounce, how much did it cost? Reduce 2 lb. 8 oz. 11 pwt. to grains. per lb. many cwt. ? What is the rule for reduction ? In 63469542 drams, how many tons ? How many barley corns will reach round the globe, it being 360 degrees? How many miles in 836954621 barley corns ? REDUCTION OF FRACTIONS TO WHOLE NUMBERS. 1. In ten fifths, how many units ? 4. Change thirteen fourths to units, and what is the an. swer? 5. Change eighteen fourths to units, and what is the an. swer ? 6. Change fourteen sixths to units. It will be perceived, that in answering these questions, the pupil divides the numerator by the denominator. Thus in changing twelve fourths to units, the numerator twelve is divided by the denominator four. The above sums are to be performed mentally first, and the answers given, and then they are to be written, thus, 7. Change fourteen sixths to units. Ans. La 14 - 6 24. Let the pupil be required to perform all the above sums, in this manner. |