13. A. had 450 sheep, B. had 175 more than A., and C. had as many as A. and B. together minus 114. How many sheep had C.?

14. Mr. Swift has in cash $419.14, but he owes Mr. Brick $47.55, Mr. Quick $274.30, and Mr. Lick $97.29. After paying these gentlemen, how much will he have left?

15. A. paid $9000 for his farm, $8476 for a new house, and $873 for a barn, and then sold them for $29,600. What was his gain?

16. In 1890 the exports of the United States amounted to $857,828,684, the imports to $789,310,409. How much does the sum of these two amounts exceed their difference?

17. A farmer had 738 sheep. He sold 327 to A. and 234 to B. Disease carried off 90. How many re

mained?

18. I paid $2240 for some land. I sold coal for $116. a horse for $225, a wagon with a horse attached for $277, and collected a bill of $565.25 long due. How much more did I pay out than I received?

19. If February has 28 days, and April, June, September and November have 120 days, the remaining seven months supply how many days to make up 365 days?

20. If June (30 days), July (31 days), and August (31 days) are the summer months, and December (31 days), January (31 days), and February are the winter months, which is the longer, summer or winter, and how much?

21. I start out with $205.50 in one pocket and $43.25 in the other. I pay the grocer $63.69, the butcher $32.08

the shoemaker $10.70, the landlord $37.50, the tailor $17.50. How much have I left?

22. Margaret has 74 cents, Mary has 135 cents. Mary gave Margaret 28 cents. Which has then the greater sum, and greater by how much?

23. If the minuend is $4937 and the remainder is $1593, what is the subtrahend? The subtrahend being $3825 and the remainder $337.84, what is the minuend?

24. From what number must I subtract 10 to leave 14? 16 to leave 18? 2.586 to leave 4.098?

25. What sum must be subtracted from $1.00 to leave $.50? To leave $.625? To leave $.375? To leave $.875?

26. What number increased by 63,915 makes a million? 27. If in July 220,860 carriages visited Fairmount Park, 5575 equestrians, and 1,443,173 pedestrians, find the excess of pedestrians over the other two classes.

28. A lady bought a bonnet for $12, a pair of shoes for $4, and a fan for $1. She gave the salesman a $20 bill. What change did she receive?

29. Find the value of MCLX. + LXXXVIII. — DXL. + IX. + IV. - XC.

30. Find the value of MCMXCVIII. XCVIII. DCCC. M.

31. A man had in bank $15,000, deposited $3875, drew out $8725, and then put in enough to make his deposit $20,000. How much did he last put in?

32. $15,000 is divided among three children, the second of whom receives $2240 more than the first, and the third of whom receives the remainder. If the first receives $5000, how much does each of the others receive?

2 x 1 2 is read "two times one equal two"; the

word times being expressed by the sign.

The process of thus shortening addition is called Multiplication.

4. Proceeding in like manner with 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13, we construct the following table:

5. In the column beginning with 4 X 1= 4, show how all the results, 4, 8, 12, 16, etc., were obtained.

6. The multiplication table is an invention of the greatest value. If you do not yet know this table, learn it perfectly as soon as possible.

DEFINITIONS.

1. Multiplication is a short process of adding when the numbers to be added are all equal; or, it is the process of finding the result of repeating one number as many times as there are units in another.

2. The Multiplicand is the number to be repeated or multiplied.

3. The Multiplier is the number by which we multiply.

4. The Product is the result of multiplying.

5. The Multiplicand and Multiplier are called Factors of the product.

6. We may write 5 times 12 equal 60, or we may write 5 times 12 men equal 60 men, or five times $12 equal $60. In the first case, 12 and 60, having no application to men, or money, or other things, are called Abstract Numbers; in the second case, being applied to men, and in the third case to dollars, 12 and 60 are called Denominate Numbers.

The multiplier 5 is abstract in all the cases; showing no more than the number of times 12 is to be taken.

7. Since 5 × 12 = 60, and 12 × 5 = 60, we see that the product is the same whether 5 or 12 is used as the multiplier.