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A o Thousands
There is another mode, shorter and more practical, for performing subtraction, when figures in the 'subtrahend are larger than corresponding figures in the minuend.
Take the same example. We cannot subtract 7 from 3. Therefore we add 10 to the 3 and say, 7 from 13 leaves 6. Having thus increased the minuend figure
5 3 minuend. 3, by 10 units, we balance
4 9 6 7 subtrahend. that excess by adding 1 ten to the 6 of the subtrahend,
3 0 8 6 difference. making 7 tens. But the 7 tens cannot be subtracted from the 5 tens. Add, then, 10 tens to the 5, making 15 tens, and then say 7 from 15 leaves 8; having added 10 tens to the 5 of the minuend, we restore the balance by adding 1 hundred to the 9 of the subtrahend, making 10. But we cannot subtract 10 from 0. Then we add 10 hundred to the 0, and say 10, from 10 leaves 0. Before subtracting the thousands, we must add 1 to the 4 thousands to compensate for the 10 hundred added to 0, then say 5 from 8 leaves 3. From 9034 subtract 7941.
Ans. 1093. From 8087 subtract 4759.
Ans. 3328. From 87315 subtract 19848.
Ans. 67467. From 64281 subtract 38796.
Ans. 25485. From what has been lone, we deduce this
I. Place the subtrahend under the minuend, so that units may stand directly under units, tens under tens, &c.
11. Then commencing at the right, subtract each figure of the subtrahend from the corresponding figure of the minuend ; observing, when a figure of the subtrahend is greater than the curresponding figure of the minuend, to increase the minuend figure by 10 before subtracting, and then to carry 1 to the next figure of the subtrahend.
How do you place the numbers for subtraction? Where do you commence to subtract ? Explain the method of subtracting when the figure in the subtrahend exceeds the corresponding figure of the minuend.
PROOF OF SUBTRACTION. 13. If the operation is rightly performed, the differreica added to the subtrahend must equal the minuend.
10. From seven million three hundred and sixty-five thousand, two hundred and thirty-nine, take three hundred and forty-two thousand and thirteen.
Ans. 7023226. :1. From one million and eleven, subtract thirteen.
. Ans. 999998. • 12. From three hundred and sixty-five thousand, take three hundred and sixty-five
- Ans. 364635. 13. America was discovered in 1492. How many years from that time to the year 1844 ?
Ans. 352 years. 14. If a man receive 11345 dollars, and pay out of it 9203 dollars, how much will he have remaining ?
Ans. 2142 dollars. 15. In 1842 the Onondaga Salt Springs yielded 2291903 bushels of salt, and in 1826 they yielded 827505 bushels. How many more bushels were produced in 1842 than in 1826 ?
Ans. 1464398 bushels. 16. In 1842 the United States shipped to England 205154 barrels of flour, to Scotland 3830 barrels. How many more barrels were sent to England than to Scotland?
Ans. 201324 barrels. 17. Two men start together from the same place, and travel in the same direction; one goes 63 miles each day, and the other goes 37 miles. How far apart will they be at the end of the first day?
Ans. 26 miles. 18. George Washington was born in the year 1732; he died in the year 1799. To what age did he live?
Ans. 67 years.
19. At an election 12572 votes are taken, of which the successful candidate received 7391. How many votes did the other candidate receive?
Ans. 5181 votes. 20. And what was the first one's majority ?
Ans. 2210 votes. 21. The coinage of the Uniteå States mint for 1843 was in value 11967830 dollars, and in 1846 it was 6633965 dollars. How much greater in value wås the coinage in 1843 than in 1846?
Ans. 5333865 dollars. 22. The total number of pieces coined in 1843 was 114640582, and in 1844 it was 9051834. How many more pieces were coined in 1843 than in 1844 ?
Ans. 105588748 pieces. 23. In the year 1846, the value of the gold coin produced at the mint was 4034177 dollars; the value of the silver coin was 2558580 dollars; and the copper coin, was 41208 dollars. How much greater was the value of the gold than the silver, and how much greater the copper ? Also, how much did the silver exceed the copper ?
Gold exceeded silver by 1475597 dollars. Ans. " 6 copper“ 39929696
1 Silver 66 66 66 2517372 66 24. In 1835, the number of post offices in the United States was 10770; extent of post roads 112774 miles; in 1845, the number of offices was 14183; and extent of roads 143940 miles. How many offices were added during these 10 years, and how many additional miles of road were added ?
5 3413 post offices.
31166 miles of road.
25. In 1840 the population of New York was 2428921, and in 1830 it was 1913006. What was the increase during this 10 years ?
QUESTIONS INVOLVING ADDITION AND SUBTRACTION,
1. A lets B have 60 bushels of wheat, worth 70 dollars, a fine horse worth 150 dollars, and 37 dollars' worth of butter. B in turn gives A his note for 110 dollars, and the rest in cash. What is the amount of cash?
Ans. 147 dollars. 2. A borrows of B, at one time, 375 dollars; at a second time he borrows 95 dollars, and at a third time he borrows 413 dollars; he has paid him 319 dollars. How much does he still owe him ?
Ans. 564 dollars. 3. A person left a fortune of 10573 dollars to be divided between two sons and one daughter; the first son received 4309 dollars, the other son had 4987 dollars. How much did the daughter receive ?
Ans. 1277 dollars. 4. Two persons are 375 miles apart; they travel towards each other; at the end of one day, one has travelled 93 miles, and the other 57 miles. How far apart are they?
. Ans. 225 miles. 5. A farmer sold a span of horses for 150 dollars, a cow for 27 dollars, some cheese for 83 dollars, and 7 tons of hay for 56 dollars. He purchased 10 yards of broad. cloth worth 45 dollars, a cook stove for 23 dollars, and a pleasure carriage for 80 dollars. How much money will he have left?
Ans. 168 dollars. 6. In the year 1840, the coinage of the United States mint was as follows: 1675302 dollars of gold, 1726703