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15. In example 11, how many times greater is the period to the left than the right-hand period? than the middle period? 16. The expenses of our government in one year were $1785687098. Separate this number into periods and read

it.

17. Write four other numbers expressing billions.

Write:

18. Ten thousand ten hundred two.

19. Six hundred millions six thousand six hundred.

20. Six billion sixty-six million ten thousand five.

21. Five hundred five billion ninety-eight thousand four hundred four.

22. Eight hundred million eight.

23. Six million five.

4. 4, 2, 6, 8

5. 3, 7, 1, 9

6. 5, 4, 6, 5

7. 2, 3, 8, 7

8. 5, 4, 1, 3

9. 6, 2, 4, 8

REVIEW OF ADDITION

1. Define addition; addends; plus; sum.

2. What must be observed in writing numbers to be added?

3. Add the numbers in examples 18-23 above.

Add:

10. 30, 60, 10, 5

11. 22, 30, 20, 19

12.

25, 14, 25, 30

13.

18, 32, 30, 20

14.

50, 25, 25, 60

15. 40, 15, 60, 25

Give sums at sight:

16. 40, 60, 50

21. 42, 18, 7

26. 21, 14, 15

17. 65, 35, 40

22.

16, 32, 22

27.

48, 22, 69

18. 92, 28, 31

23.

72, 18, 35

28.

50, 65, 15

19. 86, 14, 25

24.

16, 24, 39

29.

25, 15, 23

20. 40, 15, 65

25. 87, 13, 25

30. 37, 62, 38

A large number of problems may be made from the following numbers. Add horizontally or vertically to a certain point; subtract the numbers in one column from those in a column to the right; or multiply the numbers in the last column by those in the first column, etc. In adding, notice convenient combinations.

α

31. 594

32.

273

33.

634

34. 175

35. 439

36. 275

37.

684

38. 273

39.

619

40. 875

41. 267

42. 286

43. 394

44. 899

b

697

598

736

214

567

324

768

436

875

987

349

483

526

743

с

913

870

837

415

638

475

867

537

946

987

693

679

638

698

d

1043

1195

1375

2867

4298

5149

6238

2628

4153

1697

4278

4284

6953

8907

e

8697

7963

8674

3695

9369

6937

7245

8734

6928

7961

8639

5698

7293

5032

REVIEW OF SUBTRACTION

1. Define subtraction, minuend, subtrahend, remainder, minus, difference.

2. How may we test subtraction?

Give differences at sight:

3. 43-28

9. 31 14

6. 86-43 4. 65-32 7. 71-18 8. 69-27

10. 26-19

5. 94-77

11. 37-24

15. When the minuend and the difference are given, how may the subtrahend be found?

37. 10000.

Subtract in 3 minutes:

38. · 607008

448789

39.

16.

When the difference and the subtrahend are given, how may the minuend be found?

Take each number below from 1000:

17. 225 21. 216

25. 725

29. 715 33. 375

18. 314

22. 500

26. 946

30. 800

34. 814

19. 625

23. 499

27. 328

31. 125

35. 731

20. 374

24. 795

28. 613

32. 625 36. 656 Take each of the numbers in examples 17-36 from

40.

756008

398497

41. 180260

98775

[blocks in formation]
[blocks in formation]

12. 86-79

13. 96-93

14. 18-11

44. 800647900

98749897

45. 870009809 698058948

46. 906700983

798897497

REVIEW OF MULTIPLICATION

1. Show that multiplication is a short method of addition. 2. Define multiplication, multiplier, multiplicand, product, factors, an abstract number, a concrete number.

3. What kind of a number must the multiplier always be? 4. What does the multiplication sign show? Which term in multiplication is usually written before it?

5. At $2 a bushel, how much will 125 bushels of peaches cost? Which number is the multiplicand? Which one is the multiplier? 125 × $2 = ? How many times has the multiplicand $2 been taken? What is the product? Why is the product a concrete number?

6. Compare the product of 8 x 6 with the product of 6 x 8; the product of 2 × 14 with the product of 14 × 2. Either factor may be regarded as the multiplier.

The multiplicand may be either concrete or abstract. When it is concrete, the product will have the same name as the multiplicand. The multiplier is always abstract. Hence, when a concrete multiplicand is for convenience used as multiplier, it must be regarded as abstract.

Name two factors of:

7. 81; 125; 75; 64; 110; 108; 39; 72; 96; 80.

8. Multiply by 10, by 100, by 1000: (Do not use pencil.) 4; 8; 12; 15; 18; 25; 30; 35; 40; 50; 75.

9. State how the addition of one naught, two naughts, three naughts, etc., to the right of a number affects its value.

State products:

10. 40 x 20

11. 20 × 20

12. 30 x 15

13. 50 x 20

14.

18 x 30

15. 30 × 70

16. 64 × 40

17.

70 × 28

18. 40 x 70

[blocks in formation]

31. Find the amount of the following bills:

161 lb. butter at 18¢ a pound.
12 doz. lemons at 20¢ a dozen.

6 cans corn at 2 for 25¢.
12 lb. roast at 12 a pound.

32. 18 bu. potatoes at $0.65 a bushel. 25 bu. tomatoes at $0.55 a bushel.

27. 693 x $37.14

28.

245 x $64.59

29.

369 x $83.96

30.

248 x $39.81

3 boxes peaches at $1.75 a box.

15 qt. berries at 10 a quart.

33. Make a bill for 6 articles bought at a dry goods store.

34. Take the number 125, multiply it by 5, then this product by 5, and so on. Write only the products, not the multipliers. Continue for two minutes. How many successive products have been written?

REVIEW OF DIVISION

1. Define division, dividend, divisor, quotient, remainder. 2. What is the sign of division? Division is indicated in three ways; thus, 155, 15, and 5)15.

3. In problem 2, which number is the dividend? which is the divisor?

If the dividend and divisor are concrete, they must have the same The quotient is then abstract. Thus, $7 (divisor) is contained in $21 (dividend) 3 times (quotient).

name.

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