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The American Tutor's Guide, &c.

PART I.

Arithmetic in Whole Numbers.

THE INTRODUCTION.

ARITHMETIC is the art of calculating by numbers, and

is comprised in the five following fundamental Rules, viz: NUMERATION, ADDITION, SUBTRACTION, MULTIPLICATION and DIVISION.

NUMERATION

Teacheth to read or write any number by these ten characters, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, and their values differ acording to the place they stand in, as may be seen by the folwing

TABLE.

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43.

Fom

Berio Periake
137486

4780

19.

3/4859607182.

2000000000 -99999999999.

QUESTIONS FOR EXERCISE.

at number added to 853791, will make the sum to 12!

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TO WRITE NUMBERS.

RULE. Write down the figures as their values are expressed and supply every deficiency in the order with ciphers.

EXAMPLES.

Ans.

Write down in proper figures the following numbers. 1. Twenty-three. Ans. 23 | 3. One hundred and six. 2. Fifty-seven. 4. Seven hundred and eighty-nine. 5. Nine thousand three hundred and ten. Ans. 6. Six hundred and thirty thousand five hundred and eighty

two.

Ans. 7. Three million two hundred and sixty thousand, one hundred and five. Ans.

To express in words at length any number proposed in figures. RULE. To the value of each figure, write the name of its place, beginning at the left and reading towards the right.

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Teacheth to add two or more sums together, to make on

whole or total sum.

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QUESTIONS FOR EXERCISE.

8. A merchant is indebted to A. $1205; to B. $738 to C. $71; to D. $19; and to E. $3874. I demand the amount of his debts?

Ans.

9. A merchant has received the following sums, 8117. 5177. 243/. 137. 1857. and 35187. Idemand the whole sum. Ans.

10. Bought 6 pipes of brandy containing as follows, viz. No. 1. 120; No. 2. 118; No. 3. 125; No. 4. 121; No. 5. 127; and No. 6. 119 gallons. How many gallons in the whole? Ans. 11. The difference between two numbers is 307, the lesser is 479. What is the greater number?

Ans.

12. Add together 3 times 48351; 5 times 87004; 4 times 7482 and 6 times 12345.

Ans.

13. In the city of Pekin in China, is a bell weighing 120000lbs. at Nankin in the same empire, another of 50000lbs. and at Erfort in Upper Saxony, the great bell weighs 25400lbs. Quere, the weight of the three ?

Ans.

14. The Roman emperor Julius Cæsar, was killed by Brutus, 44 years before Christ, and Louis the XVI. King of France was beheaded, Anno Domini 1793; the distance of time between the events is required?

Ans.

15. The distance from Portland in the province of Maine to Boston is 125 miles, from Boston to New-York 250, from New-York to Philadelphia 95, from Philadelphia to Baltimore 102, from Baltimore to Richmond in Virginia 176, from Richmond to Charleston, S. Carolina, 540, and from Charleston, to Savannah, in Georgia 119; what is the distance from Portland to Savannah? 16. Money was first made of gold and silver at Argos 894 years before Christ. How many years has it been in use?

SIMPLE SUBTRACTION

Ans.

Ans.

Teacheth to take a less number from a greater, and shews the remainder or difference,

EXAMPLES.

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QUESTIONS FOR EXERCISE.

at number added to 853791, will make the sum to

99999999999.

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Ane.

8. What number subtracted from 2745301 will make the remainder to be 1785392? Ans.

9. America was discovered by Columbus in 1492, and its independence declared in 1776. How many years have elapsed between those æres?

Ans.

10. In the city of Pekin in China, is a bell weighing, it is said, 120000lbs. and at Nankin, in the same country, is another weighing 50000lbs. the first exceeds the great bell at Erfort, in Upper Saxony, by 94600lbs. How much then is the Ger

man bell inferior in weight to the second?

Ans.

11. General George Washington was born in 1732, and died in 1799; what was his age when this event took place, and how many years since ? Ans. his age, and since.

12. A merchant has to receive $817, $512, $601, $21 and $1358; and has to pay rent $150, and bis note at the bank for $3352; whither will he have money to borrow or to spare, and how much?

Ans.

13. You were born 34 years after me; how old shall I be when you are 17? and how old will you be when I am 70 years of age? Ans. I shall be and you

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SIMPLE MULTIPLICATION

years.

Teacheth how to increase the one of two numbers given as often as there are units in the other, and compendiously performs many additions.

The number to be multiplied is called the multiplicand.

The number by which you multiply is called the multiplier. The number produced by the operation is called the product. Also, the multiplicand and multiplier are called factors. MULTIPLICATION TABLE.

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