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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.

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:
4. 4, 2, 6, 8

10.30, 60, 10, 5
5. 3, 7, 1, 9

11. 22, 30, 20, 19 6. 5, 4, 6, 5

12. 25, 14, 25, 30 7. 2, 3, 8, 7

13. 18, 32, 30, 20 8. 5, 4, 1, 3

14. 50, 25, 25, 60 9. 6, 2, 4, 8

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. 6

d 31. 594

697
913
1043

8697 32. 273

598
870
1195

7963

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REVIEW OF SUBTRACTION 1. Define subtraction, minuend, subtrahend, remainder, minus, difference.

2. How may we test subtraction? Give differences at sight: 3. 43 - 28 6. 86 - 43 9. 31 - 14 12. 86–79 4. 65 – 32 7. 71 – 18 10. 26 – 19

13. 96 - 93 5. 94 - 77 8. 69 – 27 11. 37 – 24 14. 18-11 15. When the minuend and the difference are given, how may the subtrahend be found?

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

Take each number below from 1000 :

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37. Take each of the numbers in examples 17–36 from 10000.

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REVIEW OF MULTIPLICATION

IPLICATION 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 x 14 with the product of 14 x 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 13. 50 x 20

16. 64 x 40 11. 20 x 20 14. 18 x 30

17. 70 x 28 12. 30 x 15 15. 30 x 70

18. 40 x 70

Find the products : 19. 309 x 785 23. 386 x $41.72 20. 597 x 900 24. 648 x $65.39 21. 987 x 109 25. 269 x $73.36 22. 500 x 690 26. 845 x $69.47

27. 693 x $37.14 28. 245 x $64.59

29. 369 x $83.96 30. 248 x $39.81

31. Find the amount of the following bills :

161 lb. butter at 18¢ a pound.
124 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.
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, 15+5, 1, 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).

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