108. A merchant bought 500 yards of silk for $375, 3500 yards of muslin for $175, and 600 yards of linen for $235; he sold the whole for $1000. How much did he gain?

109. An estate of $12,350 was divided among a widow and two children. The widow's share was $6175, the son's, $2390 less than the widow's, and the rest fell to the daughter. What was the daughter's share?

110. A drover bought 300 horses for $32,150, and 150 cows for $4265, and sold them all for $37,000. the gain?

What was

111. Mr. E bought two farms. For one he paid $4560, and for the other $6000. He spent on each $537 for improvements, and paid taxes which amounted to $78. He sold both farms for $12,450. Did he gain or lose on the sale, and how much?

112. If a ship was bought for $43,650, and sold for $45,000, what was the gain?

113. A gentleman gave $13,465 for a house and some land. The house alone was worth $8978. What was the value of the land?

114. If two candidates for office received in the aggregate 93,565 votes, and the successful one had 47,659 votes, how many did the other have?

115. A lumberman, having 632,000 feet of boards, sold 328,582 feet of them. How many feet remained unsold?

116. A man is worth $16,425, of which $3750 is invested in bank stock, $ 2746 in mortgages, and the rest in` land. How much has he invested in land?

MULTIPLICATION.

57. 1. How many cents are there in 3 five-cent pieces? 2. How many blocks are there in 3 piles containing 3 blocks each?

3. How many are two 4's? Two 3's?

Three 3's?

4. What have you been doing with the numbers given above?

5. When numbers are used without reference to any particular thing, what name is given to them? Abstract Numbers.

6. What name is given to numbers used in connection with some thing? Concrete Numbers.

7. How many trees are 3 times 3 trees? What is taken 3 times in this example?

8. How many ponies are 4 times 3 ponies? What is taken 4 times in this example?

9. How many cents are 3 times 4 cents? What is taken 3 times in this example?

10. In each example, is the number in the answer like the number taken or like the number which tells how many times the number is taken?

11. Is the number which tells how many times the other number is taken concrete or abstract?

12. How does 3 times 2 compare with 2 times 3? 4 times 2 with 2 times 4? 3 times 4 with 4 times 3?

58. The process of taking one number as many times as there are units in another is called Multiplication; or,

Multiplication is a short process of adding equal numbers.

59. The number taken or multiplied is called the Multiplicand.

60. The number showing how many times the multiplicand is taken is called the Multiplier.

61. The result obtained by multiplying is called the Product.

62. The multiplicand and multiplier are called the Factors of the Product

63. The Sign of Multiplication is an oblique cross X. It is read multiplied by when the multiplicand precedes it and times when the multiplier precedes it.

Thus, 4 × 3 is read 4 multiplied by 3 when 4 is the multiplicand, but it is read 4 times 3 when 4 is the multiplier.

64. A number used without reference to any particular thing is called an Abstract Number.

Thus, 4, 7, 9, etc., are called abstract numbers.

65. A number used in connection with some thing is called a Concrete Number.

Thus, 4 books, 7 days, 9 dollars, are concrete numbers.

66. PRINCIPLES.-1. The multiplier must be regarded as an abstract number.

2. The multiplicand and product must be like numbers.

3. Either factor may be used as multiplier or multiplicand when both are abstract.

In practice, for convenience, the smaller number is generally used as the multiplier.

EXPLANATION.

The numbers in the left-hand column may be regarded as the multipliers, and the numbers across the top as the multiplicands. The products will be found in the horizontal columns opposite the multipliers.

Thus, 2 ones are 2; 2 twos are 4; 2 threes are 6; 2 fours are 8, etc. The order may be changed so that the numbers in the upper hori. zontal line may be regarded as the multipliers, and the numbers on the left as the multiplicands. The products will then be found in columns under the multiplier.

68. 1. At 8 cents each, what will 5 pencils cost? 2. What will 4 pairs of shoes cost at $6 a pair? 3. A boy received $4 per week for his wages. much did he earn in 8 weeks? 8 times 4 = ?

How

4. How far can a man walk in 9 hours, if he walks 4 per hour? 9 times 4 ?

miles

=

5. An orchard contained 8 rows of trees, and there were 7 trees in each row. How many trees were there?

6. A girl attended school every school-day for 9 weeks. How many days was she at school?

7. There are 8 pints in a gallon. How many pints are there in 8 gallons? 8 x8 = ?

8. A teacher assigned as a lesson 9 written problems each day for 6 days. How many did she assign altogether? 9. How much must I pay for 9 quires of paper at 8 cents per quire? 9 times 8

= :?