39. The real estate of James Dow is valued at 3,769 dollars, and his personal estate at 2,648 dollars; he owes John Smith 1,728 dollars, and Job Tyler 1,161 dollars; how much is Dow worth?

40. If a man receive 5 dollars per day for labor, and it cost him 2 dollars per day to support his family, what will he have accumulated at the close of one week?

41. The city of New York owes 9,663,269 dollars, and Boston owes 1,698,232 dollars; how much more does New York owe than Boston?

*

42. From five hundred eighty-one thousand take three thousand and ninety-six.

43. E. Webster owns 6,765 acres of land, and he gave to his oldest brother 2,196 acres, and his uncle Rollins 1,981 acres; how much has he left?

44. It was ascertained by a transit of Venus, June 3, 1769, that the mean distance of the earth from the sun was ninetyfive millions one hundred seventy-three thousand one hundred twenty-seven miles, and that the mean distance of Mars from the sun was one hundred forty-five millions fourteen thousand one hundred forty-eight miles. Required the difference of their distances from the sun.

ART. 33.

IV. MULTIPLICATION.

MENTAL EXERCISES.

WHEN any number is to be added to itself several times, the operation may be shortened by a process called Multiplication.

Ex. 1. If a man can earn 8 dollars in 1 week, what will he earn in 4 weeks?

ILLUSTRATION. It is evident, if a man can earn 8 dollars in 1 week, in 4 weeks he will earn 4 times as much, and the result may be obtained by addition; thus, 8 +8 +8 +8= 32; or, by a more convenient process, by setting down the 8 but once, and multiplying it by 4, the number of times it is to be repeated; thus, 4 times 8 are 32. Hence in 4 weeks he will earn 32 dollars.

The following table must be thoroughly committed to memory before any considerable progress can be made in this

2. What cost 5 barrels of flour at 6 dollars per barrel?

ILLUSTRATION. If 1 barrel of flour cost 6 dollars, 5 barrels will cost 5 times as much; 5 times 6 are 30. Hence 5 barrels of flour at 6 dollars per barrel will cost 30 dollars.

3. What cost 6 bushels of beans at 2 dollars per bushel? 4. What cost 5 quarts of cherries at 7 cents per quart? 5. What will 7 quarts of vinegar cost at 12 cents per quart? 6. What cost 9 acres of land at 10 dollars per acre? 7. If a pint of currants cost 4 cents, what cost 9 pints? 8. If in 1 penny there are 4 farthings, how many in 9

pence? In 7 pence? In 8 pence? In 4 pence?

pence ?

In 3

9. If 12 pence make a shilling, how many pence in 3 shillings? In 5 shillings? In 7 shillings? In 9 shillings?

10. If 4 pecks make a bushel, how many pecks in 2 bushels? In 4 bushels? In 6 bushels? In 7 bushels ?

In 3 bushels?

In 9 bushels?

11. If 12 inches make 1 foot, how many inches in 3 feet? In 4 feet? In 5 feet? In 7 feet? In 8 feet? In 9 feet? In 10 feet? In 12 feet?

12. If there be 9 feet in a square yard, how many feet in 4 yards? In 5 yards? In 6 yards? In 8 yards? In 9 yards? În 12 yards?

4

13. What cost 3 yards of cloth at 5 dollars per yard? yards? 5 yards? 6 yards? 7 yards? 8 yards? 9 yards? 10 yards? 11 yards? 12 yards?

14. If 1 pound of iron cost 7 cents, what cost 2 pounds? 3 pounds? 5 pounds? 6 pounds? 7 pounds? 8 pounds? 9 pounds? 12 pounds?

15. If 1 pound of raisins cost 6 cents, what cost 4 pounds? 5 pounds? 6 pounds? 7 pounds? 8 pounds? 9 pounds? 10 pounds? 12 pounds?

16. In 1 acre there are four roods; how many roods in 2 acres? In 3 acres? In 4 acres? In 5 acres? In 6 acres?

In 9 acres?

17. A good pair of boots is worth 5 dollars; what must I give for 5 pairs? For 6 pairs? For 7 pairs? For 8 pairs?

18. A cord of good walnut wood may be obtained for 8 dollars; what must I give for 4 cords? For 6 cords? For 9 cords?

19. What cost 4 quarts of milk at 5 cents a quart, and 8 gallons of vinegar at 10 cents a gallon?

20. If a man earn 7 dollars a week, how in 3 weeks? In 4 weeks? In 5 weeks? 7 weeks? In 9 weeks?

much will he earn

In 6 weeks? In

21. If 1 thousand feet of boards cost 12 dollars, what cost 4 thousand? 5 thousand? 7 thousand? 9

thousand? 12 thousand?

6 thousand?

22. If 3 pairs of shoes buy 1 pair of boots, how many pairs of shoes will it take to buy 7 pairs of boots?

23. If 5 bushels of apples buy 1 barrel of flour, how many bushels of apples are equal in value to 12 barrels of flour? 24. If 1 yard of canvas cost 25 cents, what will 12 yards cost?

ILLUSTRATION.

The number 25 is composed of 2 tens and 5 units; 12 times 2 tens are 24 tens; and 12 times 5 units are

60 units, or 6 tens; 24 tens added to 6 tens make 30 tens, or 300. Therefore, 12 yards will cost 300 cents, or 3 dollars.

25. In 1 pound there are 20 shillings; how many shillings in 3 pounds? In 4 pounds? In 6 pounds?

26. A gallon of molasses is worth 25 cents; what is the value of 2 gallons? Of 3 gallons? Of 4 gallons? Of 5 gallons? Of 6 gallons? Of 9 gallons?

27. If 12 men can do a piece of work in 16 days, how long will it take 1 man to do it?

28. If a steam-engine runs 28 miles in 1 hour, how far will it run in 4 hours? In 6 hours? In 9 hours?

29. If the earth turns on its axis 15 degrees in 1 hour, how far will it turn in 7 hours? In 11 hours? In 12 hours?

30. In a certain regiment there are 8 companies, in each company 6 platoons, and in each platoon 12 soldiers; how many soldiers are there in the regiment?

ART. 34. The learner, having performed the foregoing questions, will perceive that

MULTIPLICATION is the repetition of a number any proposed number of times, and is therefore a compendious method of addition.

In multiplication, three terms are employed, called the Multiplicand, the Multiplier, and the Product.

The multiplicand is the number to be multiplied or repeated.

The multiplier is the number by which we multiply, and denotes the number of repetitions to be made.

The product is the answer, or number produced by the multiplication.

The multiplicand and multiplier are often called factors.

ART. 35. SIGNS. The sign of multiplication is formed by two short lines crossing each other obliquely; thus, X. It shows that the numbers between which it is placed are to be multiplied together; thus, the expression 7 x 5 = 35 is read, 7 multiplied by 5 is equal to 35.

QUESTIONS. Art. 34. What is multiplication? What three terms are employed? What is the multiplicand? What is the multiplier? What is the product? What are the multiplicand and multiplier often called? - Art. 35. What is the sign of multiplication? What does it show?

EXERCISES FOR THE SLATE.

ART. 36. Method of operation, when the multiplier does

not exceed 12.

Ex. 1. Let it be required to multiply 175 by 7.

OPERATION.

Multiplicand 175

Multiplier

Product

17

1225

Ans. 1225.

After having written the multiplier under the unit figure of the multiplicand, and drawn a line below it, we multiply the 5 in the multiplicand by 7, saying, 7 times 5 are 35, and set down the 5 units directly under the 7, and reserve the 3 tens in the mind We then multiply the 7 in the multiplicand, saying 7 times 7 are 49, and, adding the 3 tens which were reserved, we have 52 tens, or 5 hundreds and 2 tens. Setting down the 2 tens, and reserving the 5 hundreds, we multiply 1 by 7, and, adding the reserved 5 hundreds, we have 12 hundreds, which, as it completes the multiplication, we set down in full, and the product is 1225.

15. What cost 8675 barrels of flour at 7 dollars per barrel ?

QUESTIONS. Art. 36. How must numbers be written for multiplication? At which hand do you begin to multiply? Why? Where do you write the first or right-hand figure of the product of each figure in the multiplicand? Why? What is done with the tens or left-hand figure of each product? How, then, do you proceed when the multiplier does not exceed 12?