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Review Problems.

ORAL EXERCISES. ART. 48.-1. A merchant gave $32 for goods, and paid $5 for freight : at what price must he sell them to gain $7?

Solution.—The goods with the freight added cost the sum of $32 and $5, or $37; and to gain $7, he must sell them for the sum of $37 and $7, or $44.

2. John had $15, earned $7, and then spent $11 : how much had he left ?

3. A girl having 13 apples, bought 8, and then gave away 12 : how many remained ?

4. A man bought a cow for $40, and paid $9 for her keeping : for what must he sell her to gain $12?

5. A lady bought needles for 12 cents and thread for 18 cents : what change should she receive from 50 cents ?

6. Susan having 15 cents, spent 5 cents, and her mother gave her 6 cents : how much had she then ?

7. John having 9 pears, picked 11, and then gave his mother 14 : how many had he left ?

8. A gentleman bought a watch for $25 and a chain for $8. He sold them both for $42 : how much did he gain ?

9. A man bought a vest for $6 and a pair of trousers for $12 : what change should he receive from a twentydollar bill ?

10. A street car contained 18 passengers ; 10 got out ; after which 8 entered : how many were then in the car ?

11. A man earned $15 one week and $13 another week. His expenses for the two weeks were $17: how much did he save ?

12. How much less than 38 pounds is the sum of 14 pounds and 7 pounds ?

13. How much less than 60 feet is the sum of 25 feet and 30 feet?

14. What number must be added to 32 to make the sum 6 less than 49 ?

15. From the sum of 12 plus 10 subtract 13. 16. From 10 plus 5 plus 4 subtract 4. 17. From 8 plus 6 plus 5 subtract 13. 18. From 7 plus 4 plus 6 subtract 3 plus 8. 19. How much is 8 plus 6 minus 5 plus 4 minus 3 ? 20. How much is 14 plus 4 minus y plus 5 minus 2 ?

WRITTEN EXERCISES.

ART. 49.–1. Easter in 1886 fell on April 25, its latest possible date. It will not so fall again until 1943 : how great is the interval ? 2. Mr. Jones bought a house for $8,000.

He paid $1,500 for alterations and then sold it for $9,400: did he gain or lose, and how much ?

3. A horse cost $1,500; a set of harness $200; a carriage $275: how much does the amount lack of being $2,000 ?

4. A merchant paid $75 for some goods and they cost $6 for transportation : for what must he sell them so as to gain $13 ?

5. George Washington was born in 1732 ; how many years was that before you were born ?

6. The area of France is 200,705 square miles and the area of Texas is 265,780 square miles : how many more square miles does Texas contain than France ?

7. A merchant's profits on his sales for one year were $8,450 ; out of this he paid $1,000 rent, $120 insurance, for salaries $2,800, and his incidental expenses were $148: how much had he left ?

8. An estate worth $28,000 has two mortgages upon it, one for $9,000, and the other for $6,500 : what is it worth above encumbrances ?

9. Mr. Harris deposited in bank $785 on Monday, $385 on Tuesday, and $650 on Wednesday. During the same time he checked out $1,184 : how much did his deposits exceed the amount checked out ?

10. A gentleman distributed $4,800 among his three children. To one he gave $1,400, and to another $1,500 : how much did he give to the third ?

11. A merchant having $2,368 on deposit, gave checks for $385, for $428, and for $299 : how much remained on deposit ?

12. A man having $11,284, invested $4,200 in railroad stock, $1,800 in a house, $3,800 in bank stock, and $1,300 in government bonds : how much had he left ?

13. What number is that from which if you take 38,526, the remainder will be 13,250 less than 16,250 ?

14. The sum of three numbers is 24,256; the first is 8,256, and the second is 894 more than the first : what is the third ?

15. The area of Dakota is 149,100 square miles, of Indian Territory 64,690 square miles, and of New Mexico 122,580 square miles : how much does their united area lack of equaling the area of all the territories, which is 1,509,770

square miles ?

16. A man paid $3,250 for a lot, on which he erected a house costing $5,713. He sold his property for $9,224 : how much did he gain ?

17. Mr. Brown bought a watch for $103.50 and a chain for $27.25. He gave his note for $100 and paid the rest of the debt in cash : how much cash did he pay?

18. Illustrate by an original problem addition and subtraction of numbers.

Multiplication. Progressive Oral and Written Drills. SUGGESTION.-Multiplication grows out of addition, and is a short method of adding a number to itself. The numbers only that result from adding one to itself are called prime numbers, such as 1, 2, 3, 5, 7, 11, 13, 17, 19, etc. When a number larger than one is added to itself, the resulting number is called a multiple of that number. The multiples that arise from multiplying a digit by a digit, are the facts to be learned in multiplication, of which there are 36 only, as will be shown in the following drills.

DEVELOPMENT OF THE TABLE.

Take columns of 2's and bring out the 8 facts of the multiplication of 2's. Thus :

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REMARK.—The examples are graded, so that the multiplicand has no higher figure than the number treated, but the multiplier may be any of the nine digits. The pupil must be taught how to carry when the product is more than 9.

SUGGESTION.-Develop the table of 3's from columns of 3's. Thus:

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REMARK.--As 3 x 2 is the same as 2 x 3, this combination educes no new fact, and it is therefore omitted. Only the seven new combinations with 3 are given.

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REMARK.-It is an excellent exercise to write a long line of 1's, 2's and 3's, and require pupils to multiply in class.

SUGGESTION.-Since 2 x 4 is the same as 4 x 2, and 3 x 4 as 4 x 3, there are only six new facts to be learned. Thus :

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