DEFINITIONS.

The process of finding the difference between two numbers is called Subtraction.

The greater of the two numbers is called the Minuend.

The lesser of the two numbers is called the Subtrahend.

The result obtained by subtracting is called the Remainder or Difference.

The Sign of Subtraction is a short horizontal line: called minus.

1. From 768 subtract 425.

PROCESS.

768

425

343

EXPLANATION.-For convenience the less number is written under the greater, units under units, tens under tens, etc.

Beginning at the right hand, each figure of the subtrahend is subtracted from the corresponding figure of the minuend.

8 units minus 5 units equal 3 units, which are written under the units.

tens.

6 tens minus 2 tens equal 4 tens, which are written under the

7 hundreds minus 4 hundreds equal 3 hundreds, which are written under the hundreds. Hence the remainder is 343.

the corresponding figure of the minuend.

Since 6 units can not be subtracted from 5 units, 1 ten is united with the 5 units. 1 ten is equal to 10 units. 10 units and 5 units are 15 units. 6 units from 15 units leave 9 units. The 9 is written in units' place.

Since 1 of the tens was united with the units, there is but 1 ten left. Because 3 tens can not be subtracted from 1 ten, 1 hundred is united with the 1 ten. 1 hundred is equal to 10 tens. 10 tens and 1 ten are 11 tens. 3 tens from 11 tens leave 8 tens. The 8 is written in tens' place.

Because 5 hundreds can not be subtracted from 3 hundreds, 1 thousand is united with the 3 hundreds. 1 thousand equals 10 hundreds. 10 hundreds and 3 hundreds equal 13 hundreds. 5 hundreds from 13 hundreds leave 8 hundreds. The 8 is expressed in hundreds' place.

Since 1 thousand was added with the hundreds, there are but 6 thousands left. 2 thousands from 6 thousands leave 4 thousands. The 4 is written in thousand's place in the remainder.

12. A paid 8,728 dollars for his farm, and B paid 5,935 dollars for his. How much more did A's farm cost than B's?

13. There were manufactured in a cotton factory 1,857 yards on Monday, and 2,139 yards on Tuesday. How many yards more were manufactured on Tuesday than on Monday?

14. A man who owned 8,754 acres of land, sold 3,215 acres to one company, and 2,154 acres to another. How many acres were unsold?

15. From eight thousand, five hundred sixteen, subtract three thousand, six hundred twenty-four. 16. A mill was purchased for 13,850 dollars, and afterward sold at a loss of 2,175 dollars. How much was received for it?

Copy and subtract the following:

MULTIPLICATION

LESSON LXXII.

1. What will 9 sheep cost at 6 dollars a head? 2. What will 10 quarts of milk cost at 6 cents a quart?

3. What will be the cost of 4 wagons at 30 dollars apiece?

4. Since 12 inches make one foot, how many inches are there in 3 feet?

5. At 11 cents a quart, what will 9 quarts of berries cost?

6. If a laborer can work but 13 days per month, how many days can he work in 3 months?

7. In one week there are 7 days. How many days are there in 12 weeks?

8. If one hogshead of sugar is worth 40 dollars, what are 2 hogsheads of sugar worth?

9. If one apple-tree yields 14 bushels of apples, how many bushels will 2 such trees yield?

10. If a man plants 20 apple-trees in one row, how many trees will he plant in 5 such rows?

11. When loaf-sugar is worth 15 cents a pound, how much will 4 pounds cost?

12. What will 9 dozen of peaches cost at 10 cents per dozen?

13. What will be the cost of 3 copy-books at 20 cents each?

14. What will be the cost of 4 yards of muslin at 30 cents a yard?

15. If you give 25 cents to each of 3 beggars, how much will you give them?

DEFINITIONS.

The process of taking one number as many times as there are units in another, is called Multiplication. The number to be taken or multiplied is called the Multiplicand.

The number which shows how many times the multiplicand is taken is called the Multiplier. The result obtained by multiplying is called the Product.

The Sign of Multiplication is an oblique cross: X. It is read times or multiplied by.

1. Multiply 421 by 3.

PROCESS.

3

Multiplicand 421

Multiplier

Product

1263

EXPLANATION. For convenience the multiplier is written under the multiplicand. Beginning at the right hand each figure of the multiplicand is multiplied by the multiplier.

Thus 3 times 1 unit are 3 units. The 3 is written in units' place in the product. 3 times 2 tens are 6 tens. The 6 is written in tens' place in the product.

3 times 4 hundreds are 12 hundreds, which equal 1 thousand and 2 hundreds. The 1 thousand is written in thousands' place and the the 2 hundreds in hundreds' place in the product.

Hence the product is 1263.