TWO HEADS OF WHEAT

1. Henry has 5 heads of wheat containing, respectively, 28, 36, 24, 37, and 39 grains. How many grains are there in all?

2. How many grains of wheat are there in 26 heads if each head has an average of 39 grains?

3. If each grain when planted produces 6 stalks, how many stalks will 87 grains produce?

4. If one bushel of wheat produces 18 bushels, what will be the yield of 39 bushels?

5. One bushel of wheat weighs 60 pounds. Find the weight of 6 bushels.

6. How many grains of rice are there in 7 heads if each head has 135 grains?

7. If 8 heads of oats have 360 grains, what is the average number per head?

8. A bushel of oats weighs 32 pounds. Find the weight of 8 sacks of oats, each containing 3 bushels.

9. How many bushels of wheat will 36 acres of land produce at the rate of 16 bushels per acre?

10. A farmer gathered from 9 acres 324 bushels of oats. How much was that per acre?

11. If 5 sacks of rough rice weigh 930 pounds, what is the average weight per sack?

12. How much more will 12 bushels of wheat weigh than 19 bushels of oats?

VI. BILLIONS, MILLIONS, THOUSANDS, AND ONES

1000 ones a thousand, written 1,000.

1000 thousands a million, written 1,000,000.

1000 millions = a billion, written 1,000,000,000.

If a large number, expressed in figures, is separated into periods of three figures each, beginning at the right, the first period expresses ones, the second thousands, the third millions, and the fourth, billions.

Thus, separating 37809063 into periods, we have 37,809,063, which means 37 millions 809 thousands 63 ones, and is read, thirty-seven million eight hundred nine thousand sixty-three.

Notation is writing a number in figures, and numeration is naming or reading a number in words.

In the following the pupil should show, by periods, how the numeration comes from the notation, and vice versa. 1. 8420; eight thousand four hundred twenty.

2. 25,012; twenty-five thousand twelve.

3. 601,005; six hundred one thousand five.

4. 3,010,049; three million ten thousand forty-nine. 5. 42,000,800; forty-two million eight hundred.

6. 500,050,005; five hundred million fifty thousand five.

7. 645,000,002; six hundred forty-five million two.

8. 324,905,628; three hundred twenty-four million nine hundred five thousand six hundred twenty-eight.

The word “and” should never be used in reading whole numbers.

13. Three hundred seventy-four thousand eighty-nine. 14. Eight hundred eighty-three thousand seventy-one. 15. Sixty-seven thousand three hundred ninety-eight. 16. Five hundred thousand four hundred thirty-three. 17. Forty-eight thousand eight hundred seventy-nine. Write in words:

30. 63 millions 408 thousands 21 ones. 31. 125 millions 41 thousands 307 ones. 32. 209 millions 3 thousands 500 ones. 33. 460 millions 17 ones.

34. 9 millions 9 thousands 9 ones.

35. Fifteen million three hundred thousand five." 36. Twelve million seven hundred eighty-nine. 37. Six hundred twenty million fifteen thousand. 38. Eight hundred six billion one thousand ten.

REVIEW

1. Name the first ten multiples of 7; of 8; 9.

2. Count by 8's from 6 to 70.

3. Count by 21's from 5 to 25.

4. Find, by addition and by multiplication, the first nine multiples of 24.

Thus, 1st, 24; 2d, 24+ 24 = 48, 2 x 24 = 48; and so on.

5. Find, in like manner, the first nine multiples of 86. 6. Find, by addition, the first nine multiples of 31. Thus, 1st, 34; 2d, 31+ 34 = 61; 3d, 61+34 = 9; etc.

7. Find, in like manner, the first nine multiples of 21. 8. The weights of four boys are 721 lb., 84 lb., 76₫ lb., and 65 lb. Find their total weight.

9. A man asked $160 for a horse, but sold it for $123 less. How much did he receive for it?

10. How many inches are there in 3 yards?

11. A train ran from station A to station B in 43 minutes. If it left A at 8:37 o'clock, what were the positions of the hands of the clock when it reached B?

12. How many hours and minutes are there between 9:35 A.M. and 4:15 P.M.?

13. Find the sum of the quotients 896 + 7 and 945 + 9.

14. How many pints are there in 79 gallons?

15. How many bushels are there in 928 quarts?

16. If 6 hats cost $21, how much will 8 hats cost?

17. Mary bought a book for 45, a tablet for 10%, a bottle of ink for 5%, and a pencil for 34, and gave the clerk three quarters of a dollar. How did the clerk make change?

ADDITION

In this game of "tug-of-war" the boys who pull together are said to be united.

1. How many boys are united on each side?

2. Two boys united with 2 boys are how many boys?

3. Five men united with 4 men are how many men?

4. If a 6-pound weight and a 4-pound weight were united into one weight, what weight would it be?

5. What sum of money is equal to $8 united with $7?

6. What is the result of uniting 9, 4, and 3 into one number?

Addition is the operation of uniting two or more numbers into one number.

The addends are the numbers added.

7. What is the sign of addition?

8. What is the result of addition called?

PRINCIPLES.

The addends may be taken in any order.

Thus, 6 + 4 + 3 = 6 + 3 + 4 = 3 + 4 + 6.

Only like numbers can be added.

Tell how the following may be added:

9. 3 quarts and 2 gallons; 2 yd. and 1 ft. 10. 3 halves and 2 eighths; and 1.