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Add 1 and }, here 4 and 8 make 12

j Ans. and 4 x 8 4)32 { and

1 and RULE—Add the denominators together for a new numerator, and multiply them together for a new denominator.

CASE VII.

When the numerators are alike and more than a unit.

RULE.-Add the denominators together, and multiply their sum by the common numerator, and the product will be a new numerator; also, the product of the denominators will be a common denominator.

Add i and , here 4 and 7 make 11, which multiply by the numerator 3, which is common to both.

FIRST METHOD.
Thus: 11 x 3 = 33

15g Ans.
And 4 x 7 = 28

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SECOND METHOD.

X 8

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* *7 = $t, here & and t= , as above.

THIRD METHOD.

X by multiplying the numer- 3 x 8 = 24 ators alternately by the denominators. 3 x 7= 21

and 7 x 8 Add } and its

Ans. 186. Add and s,

Ans. 1% s. Add and 1

Ans. 1, . Add 1 and 1. Here the ratio between the denominators is as 1 to 7; therefore, 1 x 7

14 and make if or answer.

Add 1 and 15)
Add i and 1962
Add and
Add and

Ans. 15.
Ans. 1
Ans, is
Ans. 11

CASE VIII.

To add mixed fractions.
RULE.—Find a common denominator by reducing the
fractions to the lowest terms.
Add $178

194
133

5)1 5 2

5 5 1844

2)1 1

2 1 1

191%

1 1 1 1 1 $89386 Multiply all the divisors together 4 X 5 X 2 = 40 common denominator.

CASE IX.

To add mixed fractions whose numerators and denomina

tors are unlike.
Add $152
Add 195

$35% () The operation can be performed thus, by cross multiplication & + $, 24 + 20 = t = 1f reduced, from whence the following Rule is deduced: multiply each numerator by all the denominators, except its own, for a new numerator, and all the denominators together for a new denominator. Example.- Add

621 373 194 171

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$13747 Add 1, \, k, and 16 together, (say dollars.)

By Reduction 1 is equal to 50 cents.

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CASE X.

To add mixed or compound fractions. 1. Add s of a day of an hour, and I of a minute together?

Ans. 16h. 48m. 18s. 2. Add f of a year, 4 of a month, ļ of a week, j of a day, i't of an hour, and of a minute together?

Ans. 4m. 1w. 1d. 8h. 5m. 48s. 3. Add f of an eagle, i of a dollar, To of a dime, and 4 of a cent?

Ans. $8.821. 4. Add of a week, į of a day, and of an hour together?

Ans. 2d. 14 h. 5. Add of a dollar, f of a dollar, and of a dime together?

Ans. $1.451. 6. Add į of a yard, ß of a foot, and f of an inch together?

Ans. 1 ft. 4 in. 1 barley corn.

CASE XI.

To add compound fractions together, connected by the pre

position of (see Def. 9.)

GENERAL RULE. Multiply the numerators together for a new numerator, and the denominators together for a new denominator. Reduce the fractions, and then add them together agreeably to Case VIII. or IX.

1. Example. Add of á of , and of f of together?

Ans. 17.

1

Operation, f XX = reduced is . Now, it is plain, that of of of the first compound is equal to t, and ; x 3 x 1 of the second compound is equal to To reduced is equal to 31, which added to į the sum is 37 as required.

2. How much is of of a dollar? Ans. 5c. 3. How much is of 1% of a dollar Ans. Zo or 18c.

4. How much is the į of , the į of ả, and the į of } of a dollar?

Ans. 111, or $1.00c. 8fm. 5. Add 1 of į of of a dollar, to šof sof of a dollar?

Ans. $25 or 24c. Operation, 1 x * xf = 40 = 1'o of a dollar or 10c. And } x x = 0 zo of a dollar or 14c.

Adding fractions together,

24c. 1. How much is the k and į of į of a dollar? Ans. 50c. 2. How much is the 4 and į of of a dollar? Ans. 650. 3. How much is ž of i of g of a yard? Ans. 1 ft. 3 in. 4. How much is of of} of $5.00? Ans. 124c. 5. How much is the į and í of off of a year? “ 7m. 6. How much is the to and of is off off of an Eagle?

Ans. $1.02.

CASE XII.

To reduce mixed fractions to parts, or to an improper

fraction. (See 11th Definition.) Rule.-Multiply the whole number by the denominator of the fraction, and add the numerator to the product for the numerator of the fraction sought, under which will be the given denominator.

Example.Reduce 171 dollars to half dollars.

ILLUSTRATION.

It is well known that two half dollars are equal to one dollar; consequently, as 1 dollar is = to 2 halves, 17 units or 17 dollars will contain 17 times as much, to which if we add one-half we get 35 halves for the required answer.

Ans. Y

81

1. Bring $193 to quarters?
2. Bring $204 to quarters?
3. Bring 33} cts. to thirds?
4. Bring $167 to eighths?
5. Bring $87ļ to halves?
6. Bring 14ş to an improper fraction?

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TO MULTIPLY FRACTIONS,

CASE I.

When the fractions are proper. Rule.—Multiply the numerators together for a new numerator, and the denominators together for a new denominator,

ILLUSTRATION.

It is manifest, that when a number is multiplied by 1, the product is equal to the multiplicand; therefore, when a number is multiplied by a fraction, which is less than 1, the product must be less than the multiplicand. Example 1.-Multiply į by ?

Ans. . From the analysis of Geometry, we find, that if a line be divided into 2 equal parts, the square of the whole line is 4 times the square of half the line: thus, let the

1

B be one mile, yard, &c. The square of 1 is 1, because 1 x 1 is 1, and squared is , hence, i x = 1 of 1.

line A

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CASE II.

When the multiplier and multiplicand are both mixed

numbers. RULE.-Bring them to improper fractions, agreeably to Case XII. (Addition,) this done, multiply the numerators together as before, for a new numerator, and the denominators together for a new denominator; divide the new numerator (so called) by the new denominator, and the result will be the product of the mixed numbers.

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