49. Albert Smith sold in one year goods to the amount of 58692 dollars, which was 5863 dollars more than he gave for them. How much did he give for the goods? Ans. 52829 dollars.

50. If the mean distance of the sun from the earth is ninety-five million one hundred seventy-three thousand one hundred twenty-seven miles, and that of the moon two hundred thirty-eight thousand six hundred fifty miles, how much farther is the sun than the moon from the earth?

REVIEW.

1. A man having 7839 dollars, paid away at one time 317 dollars, and at another 2163; what did he then have left?

OPERATION.

He had left the difference between 7839 dollars and the sum of 2163 dollars and 317 dol

2163 7839 lars; the sum of 2163 dollars and 317 dollars 317 2480 is 2480 dollars; and the difference between 7839 dollars and 2480 dollars is 5359 dollars.

2480 5359 He had left 5359 dollars.

2. Bought flour to the amount of 256 dollars, cloth to the amount of 317 dollars, and paid down 373 dollars. How much remained to be paid?

3. Henry Smith went out with 435 dollars to settle accounts. He paid 115 dollars to one man, received 119 dollars from another, and paid 316 to another. How much had he left? Ans. 123 dollars.

4. A boy had 216 apples; he sold 34 of them one day, 72 another day, and afterwards 29; how many had he left?

What is Subtraction? How does it differ from Addi

tion? Ans. It is the reverse of Addition.

5. Bought a house for 3165 dollars, laid out for repairs on it 593 dollars, and sold it for 3500 dollars. How much was lost by the bargain? Ans. 258 dollars.

6. Sold cloth for 10 dollars, sugar 17 dollars, pork 43 dollars, beef 19 dollars, and fish 13 dollars; and in payment received a check for 75 dollars, and a 50-dollar note. How much change should be paid back? Ans. 23 dollars.

7. A farmer buys a yoke of oxen for 163 dollars. He exchanges them for others, paying 27 dollars, and then sells for 200 dollars. Did he gain or lose? - and how much?

8. Dana estimates that there are workable coal measures in the United States to the extent of 130000 square miles; and in Great Britain and Ireland of 12000, in Spain of 4000, in France of 2000, and in Belgium of 518. How much do those of the United States exceed those of the other countries named? Ans. 111482 square miles.

MULTIPLICATION.

48. 1. If a boy can earn 5 dollars in one week, how many dollars can he earn in 4 weeks?

2. How many are 4 times 5?

3. Susan has 6 books and Mary has 3 times as many. many books has Mary?

How

4. How many are 3 times 6?

5. If you obtain 7 merit marks in 1 day, how many will you obtain in 6 days?

Of what name or kind is the answer in Subtraction? Ans. The same as that of the Minuend and Subtrahend. What is the Rule for Subtraction? Proof?

49. Multiplication is the process of taking one number as many times as there are units in another number. The PRODUCT is the result of the multiplication.

The MULTIPLICAND is the number to be multiplied.

The MULTIPLIER is the number by which the multiplicand is to be multiplied.

50. The Factors are the multiplier and multiplicand.

What is Multiplication? The Product?

The Multiplier? The Factors? Recite the Tables.

The Multiplicand?

how many? how many? how many? how many? how many? how many? how many?

51. The Sign of Multiplication is an inclined cross,

X, and is read multiplied by.

Thus, 5X4 is read, 5 multiplied by 4.

EXERCISES ON THE TABLES.

1. 3 times 8 are 2. 2 times 7 are 3. 4 times 2 are 4. 5 times 3 are 5. 4 times 5 are 6 7 times 3 are 7. 6 times 7 are

1. What will 3 oranges cost at 6 cents apiece?

SOLUTION. ·At 6 cents apiece, 3 oranges will cost 3 times 6 cents, or 18 cents.

2. If a boat will carry 7 men, how many men will 4 boats of the same size carry?

What is the sign of Multiplication?

3. If a quart of berries can be bought for 8 cents, how many cents will be required to buy 6 quarts?

4. How much will 8 melons bring, at 12 cents each?

5. By reading 9 pages a day, how many pages can you read in 9 days?

6. What cost 12 tons of coal, at 5 dollars a ton?

7. What cost 11 pencils, at 10 cents apiece?

8. If a boat sails at the rate of 9 miles an hour, how far will it sail in 12 hours?

9. When flour is 8 dollars a barrel, how much must be paid for 7 barrels ?

10. How many are 4 times 24?

SOLUTION.

As many as the product of 24 by 4. 4 units; 4 times 2 tens are 8 tens, or 80 units, and 4 are 16 units; which added to 80 units equal 96 units. 4 times 24 are 96.

24 is 2 tens times 4 units Therefore,

11. How many are 3 times 16? 3 times 35? 12. How many are 5 times 18? 4 times 27? 13. What cost 7 pounds of butter, at 41 cents a pound?

A PRINCIPLE OF MULTIPLICATION.

52. The product of two or more factors is the same in whatever order they are taken.

0000 ۵۵۵۵ ۵۵۵۵

For the product of 4 by 3, or 3 by 4, is 12. This is shown by the illustration. The number of pears in the picture are the same, whether we consider them 4 in a row and 3 rows, or 3 in a row and 4 rows.

Show that the product of two factors is the same in whatever order taken.