48. From 7000 subtract 4565.

69 9 10

7000

EXPLANATION.-We cannot subtract 5 units from 0 units, and since there are no tens nor hundreds, 1 thou and must be changed 4565 into hundreds, leaving 6 thousand; 1 of the hundreds must be 2435 changed into tens, leaving 9 hundreds; and one of the tens into units, leaving 9 tens. The expression 6 thousands, 9 hundreds, 9 tens, and 10 units is thus equal to the minuend. 5 units from 10 units leave 5 units, which we write under the units; 6 tens from 9 tens leave 3 tens, which we write under the tens; 5 hundreds from 9 hundreds leave 4 hundreds, which we write under the hundreds; 4 thousands from 6 thousands leave 2 thousands, which we write under the thousands. Hence, the result is 2435.

70. 1. A man had 380 bushels of corn, and sold 165 bushels. How many bushels had he left?

380

SOLUTION.-If a man had 380 bushels of corn and sold 165 bushels, 165 there remained the difference between 380 bushels and 165 bushels, which is 215 bushels. 215

2. A farmer who owned 750 acres of land, sold 275 acres. many acres remained?

How

3. A merchant sold for $4563 goods which cost him $3645. How much did he gain?

4. A ship that cost $35742 was sold for $40000. What was the gain?

5. George Washington was born in 1732, and died in 1799. How old was he at his death? How long since he died?

6. Galileo was born in 1564, and invented the telescope in 1610. How old was he when he invented it? How long since the telescope was invented?

7. A man owned property valued at $65475, and owed $18869. How much was he worth more than he owed?

8. In 1900 the population of New York was 3437202, and that of Chicago 1698575. How much greater was the population of New York than that of Chicago?

9. A man having a fortune of $18000, willed $7500 to his wife, $4500 to his daughter, and the remainder to his son.

did he leave to his son?

How much

10. A merchant having $12360 in a bank, drew out $3475, and afterward put in $4720. How much had he then in the bank ? 11. Mr. A bought a farm for $8450. He spent $2340 for improvements, paid $87 for taxes, and then sold it for $12000. What was the gain?

12. A grocer's profits last year were on fruits $350; on sugars $227; on potatoes $420; on syrups $165; on fish $137; on general merchandise $3785, He paid for rent $300, insurance $125, salaries $775, and incidental expenses $195. What was his net profit? 13. I went to a store and bought a hat for $1.75, tie for $0.45, 6 collars for $1.25, 6 linen handkerchiefs for $1.87, and a cane for $2.25. I handed the clerk a twenty-dollar bill. What change was given back?

14. A firm's total resources are $27350, and the total liabilities $9875. What is the net capital of the firm?

15. I had in bank on Monday morning $750. On Tuesday I deposited $230; on Wednesday I deposited $475; Thursday I checked out $322.60; Friday I checked out $172.25. How much remained in bank?

16. A farmer received $750 for his wheat, $145.85 for his oats, $190 for his rye, and $213.75 for his corn. He paid $115 for taxes, $80 for labor, and $165 for other expenses. How much did he save?

17. A merchant bought goods of a manufacturer amounting to $3465, and paid him cash $1637.85. How much did the merchant still owe?

18. Mr. H. began business with $4000. The first year he lost $1450, the second year he gained $675, the third year he gained $2285.68, and the fourth year he gained $1750. What was his capital at the end of the fourth year?

MULTIPLICATION.

71. Multiplication is a short process of finding the result where equal numbers are added together a given number of times. Multiplication is a short way of adding equal numbers.

72. The Multiplicand is the number to be multiplied.

73. The Multiplier is the number by which to multiply.

74. The Product is the result of the multiplication.

75. The Factors of the Product are the multiplicand and the multiplier.

76. The Sign of Multiplication is an oblique cross X. It is read multiplied by when the multiplicand precedes it, and times when the multiplier precedes the sign.

Thus, 52 is read 5 multiplied by 2 when 5 is the multiplicand, but it is read 5 times 2 when 5 is the multiplier.

77. PRINCIPLES.-1. The multiplicand may be an abstract or a concrete number.

2. The multiplier must always be regarded as an abstract number. 3. Either factor may be used as the multiplier when both are ab

'ract.

4. The product is always similar to the multiplicand.

In practice, the smaller number is generally used as the multiplier.

EXPLANATION.-The numbers across the top may be regarded as the multiplicands, and those in the left-hand column as the multipliers. The products will be found in the column under each multiplicand.

Thus, 3 ones are 3; 3 twos are 6; 3 threes are 9, etc.

The pupil should make the multiplication table for himself, work out the products, and commit it to memory. Study, recitation, and frequent repetition, are necessary to fix it in the mind. The pupil must repeat each line of the table over and over, and be drilled upon it until he knows it. Writing the table frequently will assist the pupil in committing it.

79. 1. Multiply 385 by 7.

Multiplicand, 385

Multiplier,

7

Product,

2695

EXPLANATION.—For convenience, we write the multiplier under the multiplicand, draw a line beneath, and begin at the right to multiply.

7 times 5 units are 35 units, or 3 tens and 5 units. We write the 5 units in units' place in the product, and reserve the 3 tens to add to the tens.

7 times 8 tens are 56 tens, plus the 3 tens are 59 tens, or 5 hundreds and 9 tens. We write the 9 tens in tens' place in the product, and reserve the 5 hundreds to add to the hundreds.

7 times 3 hundreds are 21 hundreds, plus the 5 hundreds, are 26 hundreds, or 2 thousands and 6 hundreds, which we write in the thousands' and hundreds' places in the product.

Hence, the product is 2695.

In practice, we say: 7 fives are 35; write 5 and carry 3. 7 eights are 56 and 3 are 59; write 9 and carry 5. 7 threes are 21 and 5 are 26; write 26. Answer, 2695.

RULE. Write the multiplier under the multiplicand, so that units may stand under units, tens under tens, etc. Draw a line beneath.

Begin at the right, and multiply each figure of the multiplicand by the multiplier, writing the result and carrying as in addition.