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CASE IV.

To reduce an improper fraction to its proper terms.

RULE. Divide the numerator by the denominator, the quotient is the whole number; the remainder is the numerator of the fraction.

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To find the least common denominator. RULE.-Divide the given denominators by any number that will divide two, or more of them without a remainder; then divide the undivided numbers and last quotients, by any number that will divide two or more of them, without a remainder; and thus continue dividing till no two numbers can be divided without a remainder; then multiply the divisors and remainders together, the product is the common denominator required.

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Examples

1. What is the least common denominator of 3, 3, 1 10 18. ?

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2. What is the common denominator of 3, 4, Ans. 1008.

12, and 4?

CASE VI.

To reduce fractions to a common denominator. RULE. Find the common denominator by case 5th, and use it as a dividend; use each given denomi-.: nator as a divisor; divide, multiply the quotients by the respective numerators, and the product placed over the common denominator will form the fractions required.

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Examples.

Reduce 2, %, and to common denominators.

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Com. denom. 40 410×3-30 1st numerator. 405 8×216 2d numerator. 408 5×7 35, 3d numerator. 40÷10 4x936 4th numerator.

The new numerators being written over the common denominator, the fractions appear thus 18, 18, thus, 25, 6 Answers.

35 36

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2. Reduce, 14, 16, and to common denominators.

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To reduce compound fractions to simple ones. RULE.-Multiply all the numerators together for a new numerator; and all the denominators together for a new denominator, and it is done.

Examples.

1. Reduce of 4 of 5 of 4 of g to a simple frac

tion.

Den.

Num. 1 X 3 X 5 X 4 X 6
2 X 4 X 6 X 7 X 82688

360

Ans.

1 2

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2. Reduce of of 3 of of to a simple fraction, and to its lowest terms.

CASE VIII.

27

1600

Ans.

To reduce a fraction of a lower denomination to the fraction of a higher, retaining the same value.

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RULE. Reduce the fraction to a compound one, by comparing it with all the denominations between itself, and the denomination, to which you would reduce it; then reduce it to a simple fraction by case seventh.

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Examples.

1. Reduce of a mill, to the fraction of a doll.

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2. Reduce of a grain to the fraction of a pound, Troy weihgt.

1 of 1 of 1 of 1 of 11520 Ans.

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3. Reduce of a day the fraction of a year, containing 365 days.

Ans.

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RULE 2. Reduce the Integer to the same denomination with the denominator of the fraction, for a denominator; over which place the numerator of the given fraction, and it will form the fraction required,

Examples.

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1. Required to reduce of a mill, to the fraction of a dollar.

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dolls. d. C. m. tenths.

1x10x10x10x10 10000 denominator.
Ans. Todo

2. Reduce of a day to the fraction of a year.

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Ans. 160.

CASE IX.

To reduce the fraction of a higher, to the fraction of a lower denomination, retaining the same value.

RULE. Multiply the numerator of the given fraction, into the denominators of the compound ones between itself and the denomination to which you would reduce it, for a new numerator; which being placed over the given denominator, will form the fraction required.

RULE 2.-Invert the denominations between the given denomination, and the one to which you would reduce it; then multiply all the numerators together for a new numerator, and the denominators, for a new denominator.

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Examples.

1. Reduce 10000 of a dollar, to the fraction of a

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2. Reduce 1 of a year to the fraction of a day.

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To express the value of a fraction in the several denominations of the Integer.

RULE. Multiply the numerator of the fraction into the known denominations of the Integer, and divide the product by the denominator, the quotient is the value of the fraction, in the denominations of the Integer.

Examples.

1. What is the value of a dollar.

1 Dol. 100×9900÷1090 cts. Ans.

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4. What is the value of of a yard ?

Ans. 3 qr. 2 na.

CASE XI.

To reduce parts of an Integer which are expressed in several denominations, to the fraction of a

RULE.

greater of the same kind.

Reduce the several denominations to the lowest denomination mentioned, for a numerator; and reduce the integer to the same denomination for a denominator.

Examples.

1. It is required to reduce 1 dime, 6 cts. and 9 mills, to the fraction of an Eagle.

1 dime 6 cts. 9 m.

1 Eagle

169 10000

Ans.

2. Reduce 2 rods, 12 feet to the fraction of a mile, and to its lowest terms.

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1. Reduce 10 feet 100 inches to the fraction of a

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cord, wood measure.

Ans. 221184.

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