LESSON VII.

A UNIT is a single thing, or one.

A CONCRETE NUMBER is a number whose units have refer ence to some particular thing or quantity; as, 15 cents, 3 men. An ABSTRACT NUMBER is a number whose units have no reference to any particular thing or quantity; as, 5, 3.

A SIGN is a symbol employed to indicate the relations of quantities, or operations to be performed upon them.

The SIGN of EQUALITY is two short horizontal lines, = and signifies equal to; thus, 1 foot 12 inches, is read, 1 foot is equal to 12 inches.

The SIGN of Addition is an erect cross, +, which signifies plus, and, or added to; thus, 4+6=10, is read, 4 plus 6 are equal to 10.

1. Charles gave 15 cents for an arithmetic, 10 cents for a grammar, and 8 cents for a writing-book; what was the cost of the whole?

2. 15+10+8 are how many?

3. Bought 12 bales of cotton, 6 bags of rice, and 2 boxes of sugar; what is the number of articles purchased?

4. 12+6+ 2 are how many?

5. A lady purchased some silk for 25 dollars, and a shawl for 5 dollars; how much did she give for both? 6. A man bought a cow for 35 dollars, and a calf for 5 dollars; how much did both cost?

7. 355 are how many?

8. If a wagon is worth 50 dollars, a saddle 9 dollars, and a whip 1 dollar, what is the value of the whole?

9. A boy found 62 chestnuts under one tree, and 20 under another; how many did he find in all? 10. 62+10+10 are how many?

11. 34+26+6 are how many?

12. A gentleman gave 46 dollars for a watch, 7 dollars for a chain, and two dollars for a key; how many dollars did he pay for the whole?

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13. 4672 are how many?

14. Lucy had 70 pins in a cushion, and put in 20 more; how many had she then in the cushion? 15. I gave 80 apples to Peter, and had 20 apples left; how many did I have at first?

16. 6020 are how many?

17. 35 +20 +15 are how many ?

18. New York has 59 counties, Delaware has 3, and Rhode Island 5; how many counties have the three States ?

19. A man gave 64 dollars for a piece of land; it cost him 10 dollars to fence it, and 2 dollars to have it plowed; what was the whole cost?

20. A farmer raised 40 bushels of oats, 50 bushels of corn, and 20 bushels of turnips; how many bushels in all did he raise?

21. Rufus received 40 cents on his birthday; and 40 cents at Christmas; how many cents did he receive in all ?

22. A farmer kept his sheep in 4 pens; in the first there were 20, in the second there were 10, in the third there were 8, and in the fourth there were 6; how many sheep did he have?

23. My book-case has 4 shelves; the first shelf contains 16 books, the second 12 books, the third 7 books, and the fourth 6 books; how many books are there in the book-case?

24. A man started on a journey; the first day he traveled 30 miles, the second day 10 miles, and the third day 9 miles; how many miles did he travel?

25. Edward bought a vest for 98 cents, some buttons for 12 cents, and some thread for 6 cents; what was the whole cost?

26. 83+17+3+7 are how many?

27. 22+18+25+3 are how many?

28.

What examples of this lesson contain abstract numbers? What ones concrete?

LESSON VIII.

SUBTRACTION is the process of taking one number from another, to find the difference. The result obtained is also I called the remainder.

1. If you have 2 apples, and give 1 of them to your brother, how many apples will you have left? SOLUTION.If I have 2 apples, and give 1 of them away, I shall have left the difference between 2 apples and 1 apple, which is 1 apple.

2. James had 3 pencils, and gave 1 away; how many pencils did James then have?

3. Lucy had 4 books, and gave 2 of them to Jane; how many books did she then have?

4. If I have 5 peaches, and should eat 3 of them, how many should I have left?

5. Charles had 6 doves, but the cat caught 3 of them; how many did he then have?

6. Rufus caught 7 fishes, and threw 4 of them back into the water; how many had he left?

7. Lydia had 8 nuts, but has eaten 4 of them; how many has she left?

8. I had 9 sheets of paper, but have given 5 of them to Charles; how many have I left?

9. William had 8 pears, but has given 6 of them to his teacher; how many pears has he left?

10. William caught 10 squirrels, but 6 of them were allowed to escape; how many were retained? 11. Thomas had 12 cents, but has spent 7 of them; how many has he left?

12. Gave 13 dollars for a barrel of flour, and 8 dollars for a tub of butter; how much more did the flour cost than the butter?

13. A farmer sold 16 sheep, and 8 lambs; how many more sheep did he sell than lambs?

14. James had 13 chickens, but 6 were taken by the hawks; how many remained?

15. George planted 19 trees, but only 9 lived; how many died?

16. Gave 15 cents for oranges, and 9 cents for lemons; how much more did the oranges cost than the lemons?

17. Paid 20 cents for nails, and 10 cents for brads; how much did the one cost more than the other?

18. Bought a clock for 10 dollars, and sold it for 15 dollars; what was gained?

19. John found 12 eggs, and Samuel 8; how many more did John find than Samuel ?

20. A man engaged to labor 17 days, but left at the end of 11 days; how many more days had he agreed to labor?

21. Gave 11 dollars to Emily, and 7 dollars to Betsey; how many more dollars were given to Emily than to Betsey?

22. Paid 20 cents for a penknife, and 12 cents for an inkstand; how much more did the penknife cost than the inkstand?

23. Sarah is 17 years old, and Isabel is 9 years old; what is the difference of their ages?

24. A farmer raised 25 bushels of beans, and 11 bushels of peas; how many more bushels of beans did he raise than of peas ?

25. Henry had 35 pins, and lost 15 of them; how many had he left ?

26. Mary went a shopping with 40 cents in her purse, and when she returned she had only 10 cents remaining; how many cents had she spent?

27. I had 14 oranges, and sold 7 of them; how many had I left ?

28. Thomas had 18 birds, and 9 of them flew away; how many birds remained?

29. Henry had 12 quarts of berries, and sold 6 of them; how many had he left?

30. Thomas recited 25 perfect lessons, and William only 8; how many more did Thomas recite than William ?

31. Bought a cow for 27 dollars, and sold her for 24 dollars; how much did I lose by the bargain?

32. Sold a lot of wood for 20 dollars, and received in payment some cloth worth 7 dollars; how much was still due ?

33. Bought a wagon for 28 dollars, and sold it for 40 dollars; how much was gained by the bargain? 34. 40 less 28 are how many ?

35. A man paid 14 dollars to one man, and 4 to another; how much more did he pay to one than the other?

36. From a vessel containing 40 gallons, 15 gallons leaked out; how many gallons still remained?

37. A boy counted his chickens one night, and found he had 19; he counted them the next morning, and found he had but 14; how many were missing?

38. A horse traveled 40 miles one day, and 27 the next day; how many more miles did he travel the first than the second day?

39. Bought a carriage for 60 dollars, and a harness for 35 dollars; how much more did the carriage cost than the harness?

40. A cistern, which holds 90 gallons, was full in the morning, but at night there were but 30 gallons left; how many gallons had leaked out?

41. If a man is now 50 years old, what was his age 24 years ago?

42. John is 11 years old, and his father 40; how many years younger is John than his father : 43. How many are 80 less 62?