37. The produce of two farms was as follows, viz: of the first, 785 bushels of wheat, and 250 of rye; of the second, 1000 bushels of wheat, and 113 of rye. What was the entire produce of the farms (§ 26)?

Ans. 1785 bushels of wheat, and 363 of rye. 38. A merchant bought 4 bales of cotton; the first and second contained 470 yards each; and the third and fourth, 532 yards each. What was the number of yards purchased? Ans. 2004 yards. 39. Bought live stock as follows, viz: of A 13 cows, 16 oxen, and 120 sheep; of B 24 cows, 30 oxen, and 153 sheep: and of C 100 cows, and 425 sheep. It is required to find the amount of stock purchased (§ 26).

Ans. 137 cows; 46 oxen; 698 sheep. 40. A has 2375 dollars; B 150 dollars more than A; and C as much as A and B together. What sum is possessed by C, and what by the three together? SC has 4900 dollars. The three 9800 dollars.

Ans.

41. A farmer has in store at one place 500 bushels of wheat, 325 of oats, and 50 of corn; and at another, 475 bushels of wheat, 75 of oats, and 83 of corn. What amount of produce has the farmer in store?

Ans. 975 bushels of wheat; 400 of oats; 133 of corn. 42. Bought a quantity of cloth for 386 dollars, of cotton for 200 dollars, and of silk for 150 dollars. The cloth was sold at a profit of 73 dollars, the cotton at a profit of 35 dollars, and the silk at cost. What was the whole sold for?

Ans. 844 dollars.

43. The population of each of the grand divisions of the Earth, is estimated as follows, viz: of Europe, at 238 millions, 473 thousand, nine hundred and fifty-seven; of Asia, at 390 millions; of Africa, at 65 millions; of North America, at 35 millions; of South America, at 15 millions, 240 thousand; and of Oceanica, at 20 millions. What then is the whole population of the several grand divisions of the Earth?

Ans. 763713957 inhabitants.

SUBTRACTION.

§ 29. SUBTRACTION consists in finding the difference between two numbers; that is, the remainder when the less number is taken from the greater.

The less number is called the subtrahend, and the greater the minuend.

Thus 4 from 9 leaves 5; then 4 is the subtrahend, 9 the minuend, and 5 the difference or remainder.

What is the difference between 5 and 8? Between 6 and 10? Between 9 and 15? Between 8 and 17? Between 10 and 19?

Addition and Subtraction.

§ 30. Addition and Subtraction are the reverse of each other. In Addition, the parts are given, to find the sum or whole; in Subtraction, the sum or whole, and one of its parts, are given, to find the other part.

The sum being 10, and one of its parts 7, what is the other part? The sum being 13, and one part 6, what is the other part? The sum being 19, and one part 12, what is the other part?

Sign of Subtraction.

§ 31. The sign

called minus, placed between two numbers, signifies that the one before which it stands, is to be subtracted from the other.

Thus 9-4, 9 minus 4, signifies 4 subtracted from 9.

How many is 8-5?

13-7? 15-4? 18-11? 20-10? How many is 10-3? 14-9? 17-8? 21-10? 25-15?

Difference of Concrete Numbers.

$ 32. The difference of two similar concrete numbers, is a concrete number of the same kind.

Thus the difference of 5 cents and 8 cents is 3 cents.

What is the difference between 12 pounds and 3 pounds? Between 18 days and 9 days? Between 20 dollars and 12 dollars?

§ 33. Two dissimilar concrete numbers cannot be subtracted, the one from the other.

Thus we cannot subtract 5 pounds from 8 days.

Constant Difference.

$ 34. The Difference of two numbers remains the same, when those numbers are equally increased or diminished.

What is the difference between 4 and 7? Between 4+1 and 7+1? Between 5 and 9? Between 5+2 and 9+2? Between 7 and 12? Between 7+10 and 12+10? Between 20-9 and 15-9?

RULE IV.

§ 35. To Subtract one Number from another.

1. Set the less number under the greater, with units under units, tens under tens, &c.

2. Proceeding from right to left, take each lower figure from the one above it, and underneath set the remainder.

3. If the lower figure exceed the upper, add 10 to the upper figure; from the sum subtract the lower, and then add 1 to the next lower figure before subtracting it.

EXAMPLE.

To find the Difference between 654739 and 80657.

654739
80657

574082

Having set the less number under the greater, with units under units, tens under tens, &c., and, drawn a line below them,

We begin at the right, and say 7 from 9 leaves two; the 5 being greater than the 3 above it, we say 10 and 3 are 13, and 5 from 13 leaves 8; then adding 1 to the 6, making 7, we say 7 from 7 leaves 0; 0 from 4 leaves 4; 10 and 5 are 15, and 8 from 15 leaves 7; there being no figure under the 6, the 1 to be added there makes 1 for that place,—then 1 from 6 leaves 5. The Difference required is 574082.

The 10 added to any upper figure is always equal to the 1 added to the next lower figure (§ 11); so that these additions preserve the same difference between the two given numbers (§ 34).

In the preceding example, the 10 tens added to the 3 tens, are equal to the 1 hundred added to the 6 hundreds; in like manner the 10 added to the 5 in the upper number is equal to the 1 added to the lower number, and subtracted from the 6.

The several figures in the remainder express the differences between the corresponding units, in their several orders, in the two given numbers, or those numbers equally increased in the process of subtracting.

The Operation Proved.

$ 36. Subtraction may be verified or proved, by adding the difference to the less number; the sum must be equal to the greater number.

EXERCISES.

1. William had 325 chestnuts, but gave James 148 of them. How many chestnuts had William left?

The number left is the difference between 325 and 148.

Ans. 177 chestnuts.

2. A person who undertook a journey of 735 miles, has traveled 93 miles of the distance. What distance has he yet to travel? Ans. 642 miles. 3. From a farm which contained 2350 acres, 1234 acres were sold. How many acres remained of the original farm?

4. A young man received from his which he paid 2500 dollars for a house. the first sum had he remaining?

5. A merchant deposited 5800 dollars made a draft upon it for 3270 dollars.

6. Suppose a farmer who has 4000 granary, should take out 2100 bushels how many bushels would remain ?

Ans. 1116 acres. father 5325 dollars, of

How many dollars of

Ans. 2825 dollars. in bank, but afterwards What sum remained?

Ans. 2530 dollars. bushels of wheat in his to be sent to market; Ans. 1900 bushels.

7. A vintner bought 4036 gallons of wine, and afterwards sold at different times to the amount of 2373 gallons. How many gallons had he remaining? Ans. 1663 gallons.

8. Suppose I should borrow of my neighbor 1000 dollars, and three months afterwards should pay him 385 dollars of the debt; what balance would still be owing? Ans. 615 dollars. 9. A drover bought cattle for 1495 dollars, and sold the same at a loss of 270 dollars. For what sum did he sell them?

10. A gentleman sold a farm for 6700 530 dollars more than he gave for it. farm?

Ans. 1225 dollars. dollars, which sum was What did he pay for the

Ans. 6170 dollars. cotton, containing 1200

11. A weaver made 30 pieces of yards; of which he has sold 17 pieces, containing 875 yards. How many pieces, and how many yards remain ?

Ans. 13 pieces; and 325 yards.

12. Bought of A 385 barrels of flour, and 2805 bushels of corn; of which I sold to B 109 barrels of flour, and 936 bushels of corn. What quantity of each remains unsold?

Ans. 276 barrels of flour; 1869 bushels of corn.

13. A salter bought 35850 pounds of beef, and 150000 pounds of pork. Having exported 20500 pounds of the beef, and 75900 pounds of the pork, what quantity of each has he still on hand? Ans. 15350 pounds of beef; 74100 of pork.

14. A farmer raised 1200 bushels of wheat, and 213 bushels of oats. He sold to A 835 bushels of wheat, and 179 of oats, and the remainder of the crop to B. What amount of produce did the farmer sell to B?

Ans. 365 bushels of wheat; and 34 of oats. 15. A merchant bought 375 yards of cloth, for 1645 dollars; of which he has sold 103 yards, for 685 dollars. How many yards of the cloth remain on hand, and for what sum must the remainder be sold, to lose nothing?

Ans. 272 yards; and 960 dollars. 16. A grocer bought coffee for 420 dollars, and sugar for 545 dollars. He sold the coffee for 500 dollars, and the sugar for 603 dollars; what did he gain on each ?

Ans. 80 dollars on the coffee; and 58 on the sugar.

17. Sold a lot of hams for 275 dollars-which made a profit of 43 dollars; and a lot of cheese for 305 dollars-which made a profit of 39 dollars. What did each kind cost me?

Ans. The hams, 232 dollars; the cheese, 266 dollars. 18. Four persons contribute towards the founding of a literary institution; A gave 2500 dollars, B 3300, C 375 less than A, and D 283 less than B. What were the sums contributed by C and D respectively?

Ans. 2125 dollars by C; and 3017 by D.

19. Find the Difference 230469-85340. 20. Find the Difference 349130-94131. 21. Find the Difference 400500-80973. 22. Find the Difference 739745-76378. 23. Find the Difference 511839-84674. 24. Find the Difference 601813-13834. 25. Find the Difference 803460-45009. 26. Find the Difference 910311-87300. 27. Find the Difference 999830-99001.

Ans. 145129.

Ans. 254999.

Ans. 319527.
Ans. 663367.
Ans. 427165.
Ans. 587979.
Ans. 758451.
Ans. 823011.
Ans. 900829.

28. A borrowed of B 8794 dollars; of which he paid to B at one time 2340 dollars, and at another time 1375 dollars. What balance remains to be paid?

From the whole debt subtract the first payment, and from the remainder subtract the second payment. Ans. 5079 dollars. 29. A person who set out on a journey of 900 miles, traveled the first week 255 miles, and the second 233 miles. How many miles then remained to be traveled? Ans. 412 miles.