« ΠροηγούμενηΣυνέχεια »
In this example, we say, 7 from 14 leaves 7: 1 carried to 2 is 3, 3 from 5 leaves 2: 6 from 13 leaves 7: I carried to 4 is 5, 5 from 6 leaves 1. The remainder therefore is 1727.
Ex. 4. From 60204 take 32861.
60204 Micüend 1 from 4 leaves 3: 6 from 32861 Subtrahend 10 leaves 4:1 carried to 8 27343 Remainder. is 9, 9 from 12 leaves 3 : 1 carried to 2 is 3, 3 from 10 leaves 7 : 1 carried to 3 is 4, 4 from 6 leaves 2.
From these examples, we may deduce the following general
$ 25. I. Set down the less number under the greate er, so that units shall fall under units, tens under tens, hundreds under hundreds, doc. and draw a line beneath them.
II. Then, beginning at the right hand, subtract each figure from the one directly over it, and set down the remainder.
III. But if the upper figure be the least, suppose it to be increased by 10 : then make the subtraction, set down the remainder, and carry 1 to the next figure of the subtrahend.
PROOF. $ 26. Add the remainder to the subtrahend. If their sum is equal to the minuend the work may be regarded as right.
QUESTIONS. 20. What is Subtraction ?
§ 21. What is the larger of the two numbers called? What is the lesser called ? What is their difference called ?
$ 22. What is the sign of subtraction? What is it called ? What does the term signify? When placed between two num. bers what does it denote?
$23. When the numbers are small how do you read them, as God?
$24. When a figure of the subtrahend is greater than the one above it, what do you do? What is this called ?
$ 25. How do you set down the numbers for subtraction? Where do you begin to subtract? How do you subtract?
926. How do you prove subtraction ?
(3.) Minuends, 8592678 67942139 219067803 Subtrahends, 1078953 9756783 104202196 Remainders, 7513725 58185356 104865607 Proofs. 8592678 67942139 219067803
4 Rem. 9996
(6.) 67987 40000 27987
9. From 2637804 take 2376982.
Ans. 260822. 10. From 3762162 take 826541.
Ans. 2935621. 11. From 78213606 take 27821890.
Ans. 50391716. 12. From thirty thousand and ninety seven, one thousand six hundred and fifty four.
Ans. 28443. 13. From one hundred million two hundred and forty seven thousand, take one million four hundred and nine.
Ans. 99246591. 14. Subtract one from one million. .
APPLICATIONS. 1. Suppose John were born in eighteen hundred and fifteen, and James in eighteen hundred and twenty five : what is the difference of their ages?
Ans. 10 years.
2. A man was born in 1735; what was his age in 1830 ?
Ans. 45 year's.
3. Suppose I lend a man 1565 dollars, and he dies, owing me 450 dollars : how much had he paid
Ans 1115 dollars. 4. In five bags are different sums of money to the amount in all of 1000 dollars. In the first there are 100 dollars ; in the second, 314 dollars ; in the third, 143 dollars; and in the fourth, 209 dollars; how many dollars does the fifth contain?
Ans. 234 dollars. 5. America was discovered by Christopher Columbus in the year 1492. What number of years has since elapsed ?
6. George Washington was born in the year 1732, and died in 1799: how old was he at the time of his death?
Ans. 67 years."
7. The declaration of independence was published July 4th, 1776: how many years to July 4th, 1832?
Ans. 56. 8. By the census of 1830, it appeared, that the white population of the United States was 10,526,248, and the number of blacks 2,328,642. How much did the white population exceed the black ?
Ans. 8,197,606. 9. In 1830 there were in the State of New York
SUBTRACTION OF SIMPLE NUMBERS.
1,918,608 inhabitants, and in the State of Pennsylvania 1,348,233 inhabitants : how many more in. habitants were there in New York than in Pennsylvania ?
Ans. 570,375. 10. The revolutionary war began in 1775; the late war in 1812: what time elapsed between their commencements ?
years. :11. In 1830 there were in New York, (which is the largest city in the United States,) 207,021 in. habitants, and in Philadelphia, (the next largest city,) 161,412: how many more inhabitants were there in New York, than in Philadelphia ?
Ans. 45,609. 12. A man dies worth 1200 dollars ; he leaves 504 to his daughter, and the remainder to his son : what was the son's portion ?
Ans. 696 dollars. 13. Suppose a gentleman has an income worth 3090 dollars a year, and pays for taxes 150 dollars, and expends besides 253 dollars : how much does he lay up?
Ans. 2687 dollars. 14. A merchant bought 500 barrels of flour for 3500 dollars; he sold 250 barrels for 2000 dollars; how many barrels remained on hand, and how much must he sell them for, that he may lose nothing ?
Ans. 250 barrels remained, and he must sell for 1500 dollars.
APPLICATIONS IN ADDITION AND
SUBTRACTION. 1. A merchant buys 19576 yards of cloth of one
»7580 yards of another, and 375 yards of a
MULTIPLICATION OF SIMPLE NUMBERB. 31 third : he sells 1050 vards to one customer, 6974 yards to another, and 10462 yards to a third : how many yards has he remaining? Ans. 29045.
2. A person borrowed of his neighbour at one time 355 dollars, at another time 637 dollars, and 403 dollars at another time: he then paid him 977 dollars. How much did he owe him ?
Ans. 418. 3. I have a fortune of 2543 dollars to divide among my four sons, James, John, Henry, and Charles. "I give James 504 dollars, John 600 dol. lars, and Henry 725. How much remains for Charles ?
Ans. 714 dollars.
MULTIPLICATION OF SIMPLE
NUMBERS. $ 27. If a number be added to itself, the sum will be two times greater than that number. Thus, 2+2=4: the number 4 is 2 times greater than 2.
If 2 be repeaced 3 times, we shall have 2+2+2=6. The number 6, is three times greater than 2: and if 2 be written four times, the sum will be 8, a number four times greater than 2.
Any number may be repeated, as many times as we please, by adding it continually to itself.
$28. Multiplication is a short method of repeating one number asguny times as there are units in another,
The number to be repeated is called the multipli. cand.
The number denoting how many times the multiplicand is to be repeated, is called the multiplier.
The number arising from repeating the multiplicand as many times as there are units in the multiplier, is called the product.
6.29. The multiplicand and multiplier are o factors, or producers, of the product.