27. A man bought a keg of molasses for three dollars, sixtytwo cents, five mills. He gave the retailer a five dollar bill; how much should he receive?

28. A farmer sold a load of hay for 15 dollars, 75 cents, and received in pay a barrel of flour worth $7.375, and the rest in money. How much money did he receive?

29. A man is worth $1875.45. How much more must he lay up before he is worth $3000.00 ?

22. The number which must be added to another number to make it equal to a unit of the next higher order (6.) is called the complement of that number. Thus 3 is the complement of 7, it being what 7 wants of being one ten. So 37 is the complement of 53, being what 53 wants of 100. 374 is the complement of 626. Why? So 90 is the complement of 10; 88, of 12. Why? 1. What is the complement of 10? 20? 24 28? 23? 29? 30? 44 49? 50? 58? 53?

18?

47

76

12? 15? 17? 19? 13?

33? 35? 38? 40? 42? 60? 62? 68? 65? 70? 74?

93?

78 80? 84? 87? 90? 2. James buys a book for 28 cents. in exchange for a dollar bill

How much must he receive

3. A man buys 15 lbs. of sugar for $1.34. How much must he receive in exchange for a three dollar bill? (5.)

QUESTIONS. What is subtraction? What is the sign of subtraction? Give an example. What is the subtrahend? The minuend? The remainder? What if the same quantity be either added to or subtracted from two numbers? What does the difference between two numbers show? What is the rule for subtraction? What is the method of proof? Why? What is to be done when the subtrahend has more decimal places than the minuend?

Miscellaneous Examples in Addition and Subtraction.

23. 1. A farmer sells a merchant 7 bushels of potatoes at 78 cents a bushel, and takes in return 8 gallons of molasses at $0.375 per gallon. How much money must he receive besides?

2. A shoemaker sells a farmer 3 pairs of shoes at $0.875 a pair, and receives in exchange 4 bushels of corn at $0.625 a bushel. How much is the balance, and which must pay it?

3. A man bought a coat for $8.75, a vest for $1.75, and a pair of pants for $4.375. How much did they come to? He gave the tailor 2 ten dollar bills. How much change should he receive?

4. A man owed $864.95. He has paid one debt of $75.84,

another of $108.375, another of $15.17, and another of $5.625. How much does he still owe?

5. What is the difference between 318.067 +4000.91 and 184001.4501?

.6. A man owes to A $694.81, to B $354.17, to C $1000.075. How much does he owe in all? How much more to A than B? To C than B? To C than A?

7. The man spoken of in the last example owns a farm worth $3000. How much will he be worth after paying his debts?

8. What must be added to 1849017+3591 to make 3848108?

9. A man owes $346.50, which he is to pay in monthly payments of $57.75. How much will he owe after making the first payment? After the second? After the third? How many payments in all must he make to cancel the debt?

10. A man having $3467.85, invested $1018.25 in railroad stock, $387.95 in bank stock, and bought 5 acres of land at $125.00 per acre. How much had he left?

11. A man died, leaving an estate of 60187 dollars. He gave to his wife $10000, to his 4 daughters $5200 each, and to his 3 sons $7500 each; the remainder he gave to benevolent institutions. How much did his charities amount to?

12. A man bought a quantity of flour for $6184.58, a quantity of coffee for $584.75, and a quantity of sugar for $215.18. In exchange he gave 3725 dollars worth of corn, a quantity of butter worth $385.75, and a quantity of potatoes worth $548How much did he then owe?

.78.

24. 1. How many are 54 +16? (17.) 49+23? 83+17? 47-17? 4819? 45-14? 68- 32 55-23? 126-112? 384213? 684-243? 126+112?

2. How much is 42-18? Say 42 is equal to 30+ 12; 10 from 30 leaves 20, 8 from 12 leaves 4, which added to 20 makes 24; therefore, 42 less 18 is 24.

3. 63-37? Solution. 63 = 50+13; 50—3020; 13—7— 6; 20+6=26; therefore, 63 less 37 is 26. 4. How much is 48 - 29? 73-48? 58-34 67+248? 187-38?

65-47? 87 - 39?

100 54, to which

=

5. How much is 154- 68! Solution. 154 add the complement of 68, which is 32. 54 and 32 are 86; therefore, 154-68 is 86. 436-78 464-356? 146-47? 865-48? 6. How much is 436-278? 436 — 300 : = 136, to which add the complement of 78; = 158. How much is 567 — 384? 327-149? 564-237?

Solution.

136 +22

746-489? (5 and 19) note.

25. MULTIPLICATION is a short method of adding equal numbers. By it we find the amount of any number repeated a given number of times.

What will 5 bushels of corn come to at 67 cents a bushel?

To perform this question, we may write down 67 five times, and add as in addition. But as the same number is five times repeated, we may write it down as in the margin, and say 5 times 7 units are 35 units, or 3 tens and 5 units. Write down the 5 units, and 67 reserve the 3 tens to be added to the tens. 5 times 6 tens are 30 tens, and 3 tens are 33 tens, or 3 hundred and 3 tens. Answer, 335.

5

335

The terms used in multiplication are the multiplicand, the multiplier, and the product. The multiplicand is the number to be multiplied or repeated. The multiplier is the number to multiply by, and shows how many times the multiplicand is to be repeated. The product is the number resulting from the multiplication. The multiplier and multiplicand are called factors of the product. In the above example, 67 is the multiplicand, or the number to be repeated; 5 the multiplier, or the number of times the 67 is to be repeated; 335 is the product, or number resulting from the multiplication; and 67 and 5 are factors of 335.

The oblique cross X is the sign of multiplication; as, 8 x 4 32, which is read, 8 multiplied by 4 equals 32, or 4 times 8 are 32.

Let the learner copy upon paper the following table, supplying the product of each combination of factors.

The pupil should be taught to recite the above table, not only as it is written, as 2 times 0 are 0; 2 times 1 are 2; 2 times 2 are 4; 2 times 3 are 6, &c., but also to recite it by using the figures in the several columns as multipliers, and the number at the top as a multiplicand; thus, 0 times 2 are 0; once 2 is 2; 2 times 2 are 4; 3 times 2 are 6; 4 times 2 are 8; 5 times 2 are 10, &c. So, times 6 are 0; once 6 is 6; 2 times 6 are 12; 3 times 6 are 18; 4 times 6 are 24, &c.

26. 1. If 1 pound of sugar is worth 8 cents, how much are 5 pounds worth?

Ans. 5 pounds are worth 5 times as much as one pound; 5 times 8 cents are 40 cents. How many are 5 times 8? 8 times 5?

2. How much will 6 pounds of beef come to at 9 cents a pound? How many are 6 times 9 9 times 6?

3. At 12 cents a dozen, how much will 4 dozen of eggs come to? How many are 4 times 12? 12 times 4? 5 times 9? 9 times 5?

4. How many are 3 times 9? 9X7? 7X9? 9×11? 11X9? 8X7 7X8? 8X5? 5X8? 8X9? 9X8?

5. At 17 cents a pound, how much will 4 pounds of butter cost? Ans. 4 pounds will cost 4 times as much as 1 pound. 4 times 10 are 40; 4 times 7 are 28, or 2 tens and 8, which added to 40 makes 68; therefore, 4 pounds of butter at 17 cents a pound will cost 68 cents. 6. How many are 3 times 14? 4 times 13? 5 times 15? 6 times 4 times 16? 5 times 19? 6 times 17? 9 times 15? 8 times

14?

19?

7. How many are 2 times 20? 3 times 20? 4 times 20! 20 X 5? 20 X 6 20 X 7? 20 X 8? 20 X 9? 20 X 10?

8. How many are 3 times 21?

4 times 27? Ans. 4 times 20 are 80; 4 times 7 are 28, or 2 tens and 8, which added to 80 makes 108; therefore, 4 times 27 are 108. 5 times 37? 6 times 34? 8 times 56? 38 X 9?

9. How many are 45 X 9? 36 X 7! 69 X 7? 85X6? 93X7? 87 X 5? 58 X4? (5.)

27. If 1 acre of land is worth 243 dollars, how many dollars are 6 acres worth?

243

6

To perform this question, write the multiplier, 6, under the right hand figure of the multiplicand, and draw a line underneath. Then say, 6 times 3 units are 18 units, or 1 ten and 8 units. Write the 8 units, and reserve the 1 ten. 6 times 4 tens are 24 tens, and one ten added make 25 tens, or 2 hundreds and 5 tens. Write the 5 tens, and reserve the 2 hundreds. 6 times 2 hundreds are 12 hundreds, and 2 hundreds added make 14 hundreds, or one thousand and 4 hundreds, which write. The product of answer is 1458 dollars.

1458

RULE FOR MULTIPLICATION WHEN THE MULTIPLIER HAS BUT ONE SIGNIFICANT FIGURE. Write the significant figure of the multiplier under the right hand significant figure of the multiplicand. Multiply each figure of the multiplicand by the multiplier, beginning at the right hand, and write the result as in addition.

EXAMPLES FOR PRACTICE.

1. Multiply 123 by 2; by 3; by 4; by 6; by 8; by 9. 2. Multiply 2345 by 3; by 4; by 5; by 6; by 7; by 8. 3. Multiply 56789 by 2; by 4; by 5; by 7; by 8; by 9. 4. How much is 617 x 4? 843 X 5? 7016 X 6? 3917 X7? 84167 × 11? 50800905 by 12?

5. Multiply 36.5 by 5.

Say 5 times 5 tenths are 25 tenths, or 2 units and 5 tenths. Write the 5 tenths, and reserve the 2 units. 4 times 6 units are 24 units, and 2 units added make 26 units, or 2 tens and 6 units, &c.

Ans.

36.5

5

182.5

6. Multiply 35.6 by 4; 6.3 by 8; 17010.8 by 7. Multiply 180109.15 by 5. Say 5 times 5 hundredths are 25 hundredths, or 2 tens and 5 hundredths. 5 times 1 tenth are 5 tenths, &c. Ans. 900,545.75.

RULE. If there are decimal places in the multiplicand only, point off as many figures for decimals in the product as there are decimals in the multiplicand.

7. Multiply 301.87 by 8; 40180.901 by 6; $145.19 by 7. 8. What will 5 barrels of flour come to at $7.875 a barrel? 9. What will 8 loads of wood come to at $6.35 a load? 10. A man sold 5 barrels of apples at $1 875 a barrel, and 5 bushels of potatoes at 75 cents a bushel. What did the whole come to?

How much is 4 multiplied by 2? by 2? by .02? by .002? If 4 be multiplied by 2, the product will be 8. If it be multi