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6. Exercises for practice in addition. Find the sums of these short columns on five successive days. Record the time required and note your improvement. Do not copy the examples. Place a paper below them and write the sums upon it. Add consecutive numbers when their sum is 10. Thus, in the first column think 7, 17, 26, 31.

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Practice for speed and accuracy in finding the following To check your results add once beginning at the

sums.

bottom of the column and once beginning at the top.

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Write the sums of the following numbers as rapidly as possible. In the first exercise get the sum by adding 42 and 30 and 5. Think 42, 72, 77.

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7. Cash accounts. It is important for every one who receives and spends money to be able to keep a cash account. In a cash account are recorded the amount and the date of each sum received and of each sum paid out. ence between the sum of the receipts and the payments is called the balance.

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EXAMPLE. Write and balance the following account : Receipts July 1, cash on hand, $2.85; July 6, picking berries, 45¢; July 15, errands, 25¢; July 20, mowing lawn, 50; July 30, birthday present, $1. Payments : July 2, fishing line, 25¢; July 4, expenses for picnic, 40¢; July 18, cap, 75¢. Find the balance July 31.

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Write and balance each of the following accounts, ruling the paper as in the example above:

1. Receipts: Jan. 1, 1923, cash on hand, $3.56; Jan. 1, gift, 50; Jan. 10, shoveling snow, 25¢; Jan. 17, errands, 20¢ ; Jan. 26, shoveling snow, 25¢; Jan. 31, selling papers this month, $3. Payments: Jan. 2, sharpening skates, 25¢; Jan. 8, moving pictures, 20¢; Jan. 12, mittens, 50¢; Jan. 18, car fare, 15é; Jan. 25, relief fund, 25¢. Balance, Jan. 31.

2. Receipts: May 1, cash on hand, $1.75; May 4, caring for children, 25; May 6, washing dishes, 30¢; May 12, delivering milk, $1.15; May 20, picking strawberries, 40¢ ; May 28, errands, 15¢. Payments: May 6, ribbon, 40¢; May 9, car fare, 10¢; May 12, ice cream soda, 20¢; May 18, pencil, 10; May 30, picnic expenses, 50¢. Balance, May 31.

3. Receipts Aug. 1, cash on hand, $57; Aug. 7, week's salary, $20; Aug. 14, week's salary, $20; Aug. 21, week's salary, $20; Aug. 21, overtime, $3.50; Aug. 28, week's salary, $20. Payments: Aug. 3, shirts, $3.50; Aug. 9, trip, $4.80; Aug. 31, room rent, $10; Aug. 31, board, $20. Balance, Aug. 31.

4. Receipts Sept. 1, cash on hand, $937.40; Sept. 5, J. H. Sims, $89.60; Sept. 12, R. S. Myers, $32.48; Sept. 26, J. Minnick, $148.29; Sept. 30, C. B. Jones, $200. Payments Sept. 9, J. J. Fitch, $38.65; Sept. 15, Felix Post, $9.83; Sept. 20, K. G. O'Neil, $60. Balance, Sept. 30.

5. For part of one year a boy kept an account of the receipts and expenditures for his cow as follows :

Expenditures: Sept. 9, 100 lb. dairy feed at $1.65; Oct. 1, 100 lb. dairy feed at $1.75; Oct. 20, 100 lb. cracked corn at $2; Oct. 20, 100 lb. bran at $1.65; Oct. 20, 50 lb. oil meal at $2.30 a hundred; Nov. 7, 25 lb. salt, $.25; Nov. 7, pasture, $5.15, hay, $4.80; Nov. 18, 100 lb. oil meal, $2.50, 200 lb. cracked corn, $4.50, 200 lb. bran, $3.40, 1025 lb. hay at $.75 a hundred, 2 bu. oats, $1; Dec. 3, clover, 4 bales, $3.

Receipts Nov. 1, milk sold to date, 780 lb. at $4.35 a hundred; Nov. 29, 552 lb. milk at $4.35; Dec. 6, 121 lb. milk at $4.35; Dec. 13, 125.3 lb. at $4.35; Dec. 20, 117 lb. 103 lb. at $4.35;

at $4.35; Dec. 31, 125 lb. at $4.35; Jan. 5,

Jan. 12, 118 lb. at $4.35; Jan. 19, 115 lb. at $4.35.
Balance the account Jan. 20.

8. Finding averages. If Tom earned 30¢ on Monday, 45¢ on Tuesday, and 33¢ on Wednesday, how much-did he earn in the three days?

If he had earned equal amounts on each of the three days, how much must he have earned each day to have earned the $1.08?

This 36¢ is called the average amount that he earned for the three days.

A girl saved 15¢ one week, 35¢ the second week, 28¢ the third week, and 13¢ the fourth week. Find the average amount per week saved for the four weeks.

The average of several numbers is found by dividing their sum by the number of them.

Exercise 4

1. A cow gives 22 lb. of milk on Monday, 18 on Tuesday, 19 on Wednesday, 21 on Thursday, 23 on Friday, 21 on Saturday, and 19 on Sunday. Find her average daily yield.

2. Ask the age of each pupil in your room. Find the average age of the pupils in your room.

3. Ask the teacher to tell you the number of pupils present in your room each day for the past month. Find the average daily attendance in your room for the past month.

4. Mrs. Brown's hens have the following daily record of eggs produced: 54, 32, 60, 41, 56, 28, 63, 38, 50, 39, 64, 29, 55, 34, 58, 42. Find the average daily number of eggs.

5. The average daily number of eggs for Mrs. Brown's hens for the next 20 days was 42 eggs. How many eggs did they lay in the 20 days?

6. A train ran 30 miles the first hour, 35 miles the second hour, 24 miles the third hour, 28 miles the fourth hour, and 31 miles the fifth hour. What was its average rate per hour

for the five hours?

7. The annual rainfall for a certain place for the years 1904 to 1913 inclusive was 26.14 in., 35.36 in., 30.37 in., 35.10 in., 34.83 in., 43.22 in., 26.86 in., 33.83 in., 29.67 in., and 27.11 in. How much below the average was the rainfall of the year having the least rainfall? How much above the average was that of the year having the greatest rainfall?

8. In his examinations Arthur has made the following grades arithmetic 80, geography 70, grammar 77, and spelling 68. He is still to be examined in history. What grade must he make in history in order to have an average of 75? 9. Practice giving the sums in the first 15 exercises of page 9.

Exercise 5. Problems of the farmer

1. Mr. Henry purchased 13 tons of fertilizer of Mr. Shubert at $18.50 a ton. He sold Mr. Shubert 246 bushels of potatoes at 45¢ a bushel and paid the balance in cash. How much cash did he pay?

2. Mr. Black bought 160 acres of land at $120 an acre. His taxes for the year are $1 an acre and the repairs cost him $1 an acre. He can rent the farm to a tenant for $8 an acre cash rent, but chooses to rent it for crop rent. He gets one-half of the corn, one-third of the broom corn, one-third of the oats, one-third of the wheat, one-half of the hay, and $5 an acre for the pasture. The tenant raises 40 bushels of corn per acre on 40 acres ; one-fourth of a ton of broom corn per acre on 20 acres ; 20 bushels of wheat per acre on 30 acres ; 40 bushels of oats per acre on 25 acres ; 2 tons of hay per acre on 25 acres. He uses 18 acres for pasture. The corn is sold at 60¢ a bushel, the broom corn at $150 a ton, the oats at 42¢ a bushel, the wheat at $1.10 a bushel, and the hay at $12 a ton. How much more does Mr. Black receive than if he had rented the farm for cash rent?

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