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EXAMPLES. 1. If 37 yards of cloth cost £.40 4.9, what will 1 yard cost ?

£. S.

d. £ d.
37) 40
4 9

1 9. Answer.
37

O

33 20

37)64(1

37

27 12

37)3339

333 2. If 47 bags of Indigo weigh 12Cwt. 1qr: 2616. 402. what does each weigh?

Ans. 1gr. 1lb. 12oz. 3. If 19 degrees on the earth's surface be 1321 miles, 2fur. 26 rods, what is the length of 1 degree?

Ans. 69m. 4fur 14 rods. 4. If 135 solar years be 49307 days, 17h. 8m. 15s. how long are the years ?

Ans. 365d. 5h. 48m.-57s. 5. Divide £.184 34, between 12 men, and 16 women ;

and give the men twice as much as the women. Men.

d.
12 8)184 3
2

5)23 0 5
24
16 £.4 12 1 A woman's share.

2
40

6.9 2 A man's share.

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In the last example, I divided the sum by the num. ber of simple shares, which was 40 ; (for the men had 12 double shares, and the women: 16 single shares which make 40 single shares) and the quotient. was a woman's share ; which being doubled, gave a man's share.

DECIMAL FRACTIONS. Decimal Fractions are set down in the same form; and managed in the same manner, as whole numbers.

The denominator of a decimal fraction is always 10, 100, 1000, &c. that isz an'unit with a number of cyphers annexed; therefore, the denominator needs not to be set down, for the numerator; with a point at the left hand, to distinguish it from a whole number, is sufficient to express the value of a decimal ; thus,

is written ,5 ; Tong is written ,42, &c.—But if the numerator has not so many places, as the denominator has cyphers, prefix.so many cyphers at the left hand as will make up the defect; thus, tér is written ,92 7oSon is written ,00036, &c.

Decimal fractions decrease from the left hand towards the right, in the same proportion as whole numbers increase towards the left; as may be seen in the following Table :

po 5 4 3 2 1, 2 3 4 5 6 7

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Millions.
* Thousands.
c) Hundreds.
ö Tens.
Units.
6 Hundreds of thousands.
is Tens of thousands:

â Tenth parts.
» Hundredth parts.
* Thousandth
in Ten thousandth parts.
w Hundred thousandth pårts.
Millionth parts.

parts.

From this table it is evident, that, in decimals, as. well as in whole numbers, each figure takes its value by its distance from units' place : if it be in the first place after units, it signifies tenths.; if in the second place, hundredths, &c. therefore every single figure, expressing a decimal, has, for its denominator, an unit with so many cyphers as its place is distant from units ; thus, ;2 (in the decimal part of the table) is ii ,03 is io, &c. And if a decimal be expressed by several figures, the denominator is 1, with so many cyphers as the lowest figure is distant from units' place ; thus, ,146 is 448 ; ,0083 is &c.

100009 The value of decimals cannot be altered, by placing: eyphers at the right hand, because every significant. figure possesses the same place it did before : thus, 95 ,50 ,500 are all of the same value, .or equal to But cyhers placed at the left hand of a decimal, alter its.value, by removing the significant figures farther from units place ; every cypher depressing it to to of the value it had before ; thus, ,3 ,03 ,003 express decimals of different values, ,3 being to ,03

8.3

3

and ,003 170.0

100.

A mixed number, viz. a whole number with a decimal annexed, is equal to an improper fraction, whose numerator is all the figures of the mixed number tak.. en together, and the denominator, that of the decimal part; thus, 23,764 is equal to 1667

Addition of Decimals.

RULE. t. Place the numbers, whether mixed or pure de-cimals, in such order, that figures of the same value may stand directly under each other.

Add them together, as in whole numbers, and point off so many figures in the sum, for decimals, as.

are equal to the greatest number of decimal places in any of the given numbers.

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4. Required the sum of 7268,45321-3,600599 -20--,00010094276,3375, and 3,8.

7268,45321

3,600599 20,

,00010094 276,3375

3,8

Note. The vacant places, in the decimal parts of these numbers, are suppose ed to be supplied with cy: phers.

7572,19140994

5. What is the sum of 8000,2368--800,04342 80,00963–64,86634, and 1,7369 ?

Ans. 8888,89309. 6. What is the sum of 21_67-0001--12,83 and: 29,87654321 ?

Ans. 130,70664321. 7. Required the sum of 10407,305-639,2501 and 33778,2.

Ans. 44824,7551.

Subtraction of Decimals.

RULE. Place each figure of the less number directly under those of the same value in the greater ; then subtract. as in whole numbers, and point off the decimals, as: in addition

EXAMPLES.

1. From 716,358 Take 295,426

2. 11864,3

139,54329

Rem. 420,932.

11524,75671

3. From 88726 take 9999,2222

Rem. 78726,7778..
From 1000 také 99,993

Rem. 900,01. 5. From 73690,27 take 364,50873.

Rem. 73325,76127. 6. From 8,00035 take ,01036.

Rem. 7,98999...

Multiplication of Decimals.

RULE. 1. Place the factors, whether they be pure décimals or mixed numbers, in the same order, and multiply them in the same manner as whole numbers.

2. Point off so many figures at the right hand of the product, for decimals, as there are decimal places in both factors ;, but if there be not so many places, supply the defect by prefixing, cyphers at the left hand

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