sions of No. 1 will be ,1, and one of the small squares in No. 2 is ,01.

Particular attention should be paid to this diagram, in order to understand perfectly the nature of enumeration.

EXAMPLES FOR PRACTICE.

1. Add 224,001; 33,125; 34,125; 275,625; 545,875; 36,35. Ans. 1149,101.

2. Add twenty-nine and seven thousandths; thirty-five and one hundred twenty-five thousandths; eighty-four and four tenths. Ans. 148,532.

3. A man sold a horse for seventy-five dollars; a saddle for nine dollars and seventy-five cents; a bridle for one dollar, thirty-seven and a half cents. How much money did Ans. $86,125.

he receive?

4. A man bought a lot of land for ninety-seven dollars, eighty-seven cents and five mills; a yoke of oxen for one hundred and twelve dollars; a horse for seventy-nine dollars and ninety cents; a wagon for thirty-two dollars and twenty-five cents; and a harness for nineteen dollars, sixtytwo and a half cents. How much money did he pay?

Ans. $341,65.

5. Add ,003; 44,351: 3,12; 87,0001; 36,07; 34,0036; 36,00875; 365,375. Ans. 605,93145. 6. Add 47,875; 36,001; 375,375; 45,375; 670,625. Ans. 1175,251.

7. Add 87,25; 39,875; 46,45; 150,89; 360,75; 81,94; 175,365; 422,755.

Ans. 1365,275.

8. Add one hundred and one hundredth; three hundred seventy-five thousand and three hundred seventy-five thou sandths; two hundred and two hundredths.

Ans. 375300,405.

9. A man sold three hundred and sixty-five dollars, eightyseven and a half cents' worth of cattle, one hundred and seventy-nine dollars, sixty-two and a half cents' worth of pork, eighty-seven dollars and five dimes worth of hay, thirty-seven dollars and two dimes worth of other articles; what was the amount of the whole? Ans. $670,2.

10. A man sold a horse for seventy-five dollars; a saddle for nine dollars and seventy-five cents; a bridle for one dollar, thirty-seven and a half cents. How much money did he receive? Ans. $86,125.

11. A man bought a lot of land for ninety-seven dollars, eighty-seven cents and five mills; a yoke of oxen for one hundred and twelve dollars; a horse for seventy-nine dollars and ninety cents; a wagon for thirty-two dollars and twentyfive cents; and a harness for nineteen dollars, sixty-two and a half cents. How much money did he pay?

Ans. $341,65.

IV. Subtraction.

Subtraction is taking a less number from a greater. The greater number is called the minuend, the less number is called the subtrahend, and the result is called difference, or remainder.

RULE.-Write the numbers according to their local value, units under units, tens under tens, hundreds under hundreds, tenths under tenths, hundredths under hundredths, &c. Draw a line under them, and beginning at the right hand, subtract the figure of the subtrahend from the figure above it in the minuend, and write the difference below. If there be no figure in the minuend, from which to subtract the figure in the subtrahend, or, if the figure in the minuend be less than the figure below it in the subtrahend, suppose 10 to be added to the minuend, and from that amount subtract, observing to add 1 to the next left-hand figure in the subtrahend before subtracting.

PROOF. Add the remainder to the subtrahend, and if the amount agree with the minuend, the work may be supposed

to be right.

SIGN. A short, horizontal line, thus, -, placed between

two numbers, shows that the number at the right hand is to be subtracted from the number at the left. As, 8—6—2.

Ex. 1 17,25 minuend. 14,375 subtrahend.

2,875 remainder.

In this example, I place the larger number, 17,25, uppermost, and call it the minuend. Under the minuend, I write the smaller number, 14,375,

calling it the subtrahend. Beginning at the right hand, I subtract 5 from 10, according to the rule, and add 1 to 7 before subtracting it. I subtract 8 from 15, and add 1 to 3 before subtracting it. I subtract 4 from 12, and add 1 to 4 before subtracting it. To prove this sum, add the remainder to the subtrahend, and the amount will agree with the minuend.

Ans. 34999,965.

6. From thirty-five thousands take thirty-five thousandths.

7. From 21 take 19,777.

Ans. 1,223.

8. From 8 and 8 hundredths take 3 and 3 tenths.

9. A man bought a dollars and 75 cents. horse than the wagon?

Ans. 4,78.

horse for 60 dollars; a wagon for 35 How much more did he give for the

Ans. 24,25.

V. Multiplication.

"When a number is added to itself once, it is said to be doubled; when it is added to itself twice, it is said to be tripled; or, in general, the operation of adding a number to itself a certain number of times, is called multiplication. The number which is added to itself is called the multiplicand, and the one which expresses the number of additions, the multiplier; both are called factors."* The result, or answer, is called the product.

SIGN. The sign of multiplication is two lines crossing each other in the form of the letter X, and shows that the number at the left hand of the cross is to be multiplied by the number at the right hand of it. As, 8X4=32.

The scholar should now make himself familiar with the following

MULTIPLICATION TABLE.

6

12 times 3 times 4 times] 5 times 6 times 7 times 8 times) 9 times 10 times 11 times] 12 times 12 13 14 15 16 17 18 1 9 1 10 1= 11| 1= 12 24 26 28 2-10 2-12 2-14 2-16 2 18 2 20 2 22 2 24 36 39 3-12 3-15 3-18 3-21 3-24 3 27 3= 30 333 336 4 8 4 12 4 15 4-20 4-24 4-28 4-32 4 36 4 40 4 44 4 48 5= 5 15 5 20 525 530 5-35 540 5 45 550 5 55 560 6-12 6-18 6-24 6-30 636 642 6=48 6= 60 6 66 672 7-14 7-21 7-28 7-35 7-42 7=49 7-56 7= 7 70 777 784 8-16 8-24 8-32 8=40 8-48 8=56 8 64 8=72 8 80 8 88 8 96 9-18 9-27 9-36 9=45 9-549-63 9=72 981 9 90 999 9-108 10-20 10-30 10-40 10-50 10-6010-70 10-80 10 90 10-100 10-110 10-120 11-2211-33 11-4411-55 11=6611=77 11-88 11 99 11 11011=12111=132 |12=24|12=36|12-48 12-60 12-7212-8412-96|12=108 12=120 12-132 12-144

RULE.--Place the multiplier under the multiplicand, without regard to the local value of the figures. Beginning at the right hand, multiply each figure in the multiplicand by each figure in the multiplier, and place the first figure of each product directly under the multiplying figure, setting down the right-hand figure, and adding the left-hand figure to the next figure in the product. Having gone through in this manner with all the figures in the multiplier, add their several products, and cut off as many figures from the right hand as there are decimal places in both factors.

*Ed. Ency. in loco.

Ex. 1. Multiply 82 by 12.

82

82 In this example, having set down the 12 figures according to the rule, I begin with the right-hand figure in the multi164 plier, and by it multiply each figure in the multiplicand, setting down the first figure of the product under 2' in the multiplier. I then begin with the next figure in the multiplier, and multiply each figure in the multiplicand by it, placing the first figure of the product under the multiplying figure. Having multiplied by both figures in the multiplier, I add the two products, and their sum is the required product, or answer.

Product. 984

Ex. 2. Multiply 18,25 by 6,25.

18,25

6,25

9125

3650

10950

Product. 114,0625

Ex. 3. A man bought 8 bushels and a half of wheat, at one dollar and a half per bushel; how much did he give for the wheat?

1,5

8,5

75

120

Ans. $12,75

4. A man sold six calves for five dollars and fifty cents each, how much did he obtain for the calves? Ans. $33.

5. Multiply,09875 by ,0625. 6. Multiply,99999 by ,99999.

7. Multiply,5 by,5.

8. Multiply,25 by ,25.

Ans. ,006171875.

Ans. ,9999800001.

Ans.,25.

Ans. ,0625.