enough to make the larger number at the top. We read, 6 and 9 are 15, writing in the 9 and carrying the 1 as in addition; 8 and 4 are 12, writing in the 4 and carrying the 1; 5 and 4 are 9. We prove our work by adding from the bottom, 9 and 6 are 15; 5 and 7 are 12; 5 and 4 are 9.

Note. The additive plan for subtraction is of special value, as it constantly strengthens addition. It has been carefully tested in the class room and in business and found to be the easiest and surest way of subtracting.

42. Copy, subtract, and prove:

43. In writing decimal parts for subtraction, write the decimal points under each other, as this will place units of the same order in the same vertical columns. The operation of subtraction is the same as that of whole numbers.

44. 1. Only like numbers may be subtracted.

2. In subtraction, the larger number is called the minuend, the smaller number the subtrahend, and the result the difference or remainder.

3. The sign of subtraction is a short horizontal line (-). It is called "minus," and means less.

4. In the subtraction of decimals, if there are less decimal places in the minuend than in the subtrahend, we annex ciphers to the right of the decimal places of the minuend. This does not alter the value of the minuend.

5. Subtraction is the converse process of addition.

APPLICATION OF ADDITION AND SUBTRACTION

45. 1. A man bought some goods for $750 and sold them for $ 825. How much did he gain?

2. Bought some hay for $65, some straw for $10, and paid cash $50. How much do I still owe?

3. Bought a farm for $3500, paid $750 for improvements, and then sold it for $5000. How much did I gain?

4. Bought shoes for $2.50, a hat for $2.75, a suit of clothes for $ 25, a tie for $.75, and gave the man $35. How much change should I receive?

5. Mr. Smith had $1000 in the bank. He drew out $250 to pay his rent and $75 to buy some sheep. How much had he left in the bank?

6. From a farm containing 50 acres, 12.5 acres were sold. How many acres remained?

7. A man had 100 sheep, which he kept in three fields. There were 25 sheep in the first field, 35 in the second. How many sheep in the third field?

8. Some boys wish to raise $10 for a ball club. They have $7.50. How much more do they need to raise ?

9. I owe Mr. Smith $500 and have $350. How much must I draw from the bank that I may pay him? If I had $ 400 in the bank, how much will be left after I have paid Mr. Smith?

10. A merchant gave his note for $5200. He paid at one time $2500 and at another $1525. How much remained to be paid?

11. Borrowed from my neighbor at one time $150, at another $ 75, and at another $ 125. Having paid him $275, how much do I still owe?

12. Mr. Smith owns 1215 sheep, Mr. Jones owns 150 more than Mr. Smith. How many sheep do both gentlemen own?

13. A merchant had 7520 barrels of flour. He sold 1200 barrels to one man, 750 to another, and 1350 to another. How many barrels of flour had he left?

14. A farmer raised 1575 bushels of wheat and 900 bushels of corn. After using 750 bushels of wheat and 350 bushels of corn, how many bushels of each remained?

15. A man sold some hay for $50, some grain for $25, and some potatoes for $12.50. With the money received he bought a wagon for $ 65. How much money had he left?

16. There are 15 acres in a field. After a man has plowed 10.25 acres, how much remains to be plowed?

17. A man measures the sides of his garden, and finds them to be 40.5 feet, 25.25 feet, 40.25 feet, and 24.75 feet. How many feet of fence will it take to fence this garden?

CHAPTER IV

MULTIPLICATION

46. The process of taking one quantity as many times as there are units in another is called multiplication.

47. The sign of multiplication is an oblique cross (x). It means that the numbers between which it is written are to be multiplied together.

INTRODUCTION TO MULTIPLICATION

48. 1. A boy measures a fence with a stick 4 feet long. He finds that the fence is 20 times as long as his stick. How long is the fence?

2. A man takes a pailful of water 4 times from a tank of water. If the pail holds 10 quarts, how much water does he take from the tank?