is it a week, allowing 52 weeks to the year; and how much a day, there being 7 days in a week. Ans. $48 a week, $6 a day. 8. If you have a journey to perform of 1260 miles, and travel on an average, 36 miles a day: how many days will be requisite to perform the journey? Ans. 35 days.

9. In a solid foot there are 1728 cubic inches: how many solid feet in 207360 cubic inches?

Ans. 120 10. How many hogsheads would be required to contain 2646 gallons of molasses; one hogshead containing 63 gallons.

II. When the divisor does not exceed 12

Ans. 42.

The multiplication and subtraction may be made in the mind, without the formality of setting down the whole process. In this case, the quotient is placed under the dividend with a line drawn between.

7. A yard is 3 feet: how many yards are there in 5292 feet? Ans. 1764.

8. At 4 dollars a head, how many sheep can be purchased with 2684 dollars? Ans. 671. 9. How many yards of cloth, at 7 dollars a yard, can be purchased with 441 dollars?

Ans. 63. 10. If a man's income be 1248 dollars a year; how much is it per calendar month?

Ans. $104.

difficulty lies in determining of what denominations the quotient consists.*

When the divisor is a whole number, the quotient may be regarded as consisting wholly of the lowest denomination of the dividend. If that be dollars and cents, the quotient may be considered as so many cents.

If there be dollars only, the remainder (if any) may be reduced to cents, by adding 2 ciphers, and continuing the division; or, it may be reduced to mills by adding 3 ciphers.

1. The cost of 61 bushels of barley, being $ 45.75; how much is it a barrel ? Ans. 75 cts. 2. If 15 sheep cost $ 33.75; how much is it a head?

3. Divide $611, equally among 5 men.

To the remainder (1) in this

example, two ciphers are annexed for cents.

5)611.

122.20

Ans. $122.20.

4. Divide $171.55 by 47.

5. Divide $7913.576 by 209.

Ans. $3.65.
Ans. $37.864

6. A bunch of quills, consisting of 25, is sold for $.625;

how much is it a piece?

Ans. 25m. or 2 cents.

Federal Money will be treated of more at large, under the head of Decimals, to which it properly belongs.

1

QUESTIONS.

What does the quotient in division show?

Why must the remainder always be less than the divisor?
Define the three principal parts in division.

How do we know what number of figures in the dividend to take at each step of the operation?

Division "is a concise way of performing several subtractions :". work the following question by both methods, and show which is the shortest

There are in a vessel 17 quarts of water, how many times could a gallon measure be filled full from the vessel?

Can a less number be divided by a greater?

If a number be divided by unity, (1) what will be the quotient? If a number be divided by less than unity, (for example,) ought the quotient to be more or less than the dividend?

Of two numbers as divisors, with the same dividend, which gives the largest quotient, the greater or the less divisor?

In proving division, why is the remainder added to the product of the divisor and quotient?

SUPPLEMENT TO

MULTIPLICATION AND DIVISION.

I. When the multiplier has a fraction united to it, as 6, 62, &c.

Take the parts of the multiplicand denoted by the fraction, and add them to the product of the whole number.

Multiplying by 1, gives us the multiplicand for a product; therefore, multiplying by,, &c., must give,1, (according as the fraction may be,) of the multiplicand. 1. What will 720 barrels of flour come to, at $ 6 per barrel ?

2. 48 men were to receive $ 53 a piece; how many dol lars paid them?

3. What will 15 tons of hay come to, at $73 a ton ? 4. A farm of 156 acres was sold for $ 343 an acre: how much did it come to?

To divide by a mixed number, as 5, 53, &c.

Multiply the whole number by the lower term of the fraction, add the upper term to the product for a divisor; then multiply the dividend by the lower term of the fraction and divide.

1. There being 5 yards in a rod, how many rods in 682 yards?

5X2+1=11

682X2=1364÷11-124 Answer.

2. How many barrels of flour at $53, can be bought with $500?

Ans. 862. 3. 31 gallons to the barrel, how many barrels in 485 gallons? Ans. 152.

II. Operations in arithmetic, may often be considerably shortened, by a little attention to the relations of numbers. A few examples are adduced of contractions in multiplication. Suppose it were required to multiply a number-say 746382-by 999.

Multiply it by 1000
Subtract the multiplicand.

746382000

746382

Ans. 745635618

Here it is evident, that the product of 1000 exceeds the product of 999, by once the multiplicand.

In both the foregoing examples, we multiply the product of 9 by 7: because 63 is equal to 7 times 9. But, because the 9 in the last example, stands in the place of hundreds, the product of the other two figures is set two places toward the right.

It will be perceived, that it is indifferent in what order the figures of the multiplier stand, or which one of them is first multiplied by; the value of the products depending alone on their local position.

Whenever the multiplier has in it a figure, and the multiple* of that figure, this contraction may be used.

The following combinations will exhibit multiples of 6, 126, 186, 246, 306, 366, 426, 486, 546, &c.; or placing the 6 first: 612, 618, 624, 630, 636, 642, 648, &c.

* By multiple is meant, the exact product of any number by another.