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2. Reduce of a shilling to its proper value. 2 fifths of a shilling.

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4. Reduce of a mile to its proper quantity.

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Ans. 6 fur. 16 poles. of a cwt. to its proper quantity,

5. Reduce

Ans. 2 qrs.

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value.

Ans. 2R. 20P.

7. Reduce of a day to its proper value.

CASE X.

Ans. 7 hours 12 min.

To reduce any given quantity to the fraction of a greater denomination of the same kind.

RULE.

Reduce the given quantity to the lowest denomination mentioned for a numerator, and the integer into the same denomination for a denominator.

EXAMPLES.

1. Reduce 16s. 8d. to the fraction of a pound.

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2. Reduce 6 furlongs and 16 poles to the fraction of a mile Ans.. 3. Reduce of a farthing to the fraction of a pound. ៖ Ans. To

4. Reduce dwt. to the fraction of a pound Troy.

Ans.

5. Bring 80 cents to the fraction of a dollar. A dollar is 100 cents, then 80 cents are equal to of a dollar; which, being reduced, is equal to Ans. 6. Bring 16 cents 9 mills to the fraction of an eagle. 16 cents 9 mills = 169

1 eagle

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Ans.

7. Bring 2 quarters 33 nails to the fraction of an ell Fnglish.*

2 quarters 33 nails.

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Add all the numerators together, and place the sum over the common denominator, which will give the sum of the fractions required.

EXAMPLES.

1. Add §, ‡ and together.

XX=1 Answer.

*When the sum contains a fraction, as in the seventh example, multiply both parts of the sum by the denominator thereof, and to the numerator add the numerator of the given fraction.

2. Add, and together.

1+$+3+5=4=14 Answer.

CASE II.

To add fractions having different denominators.

RULE.

Find the common denominator by Case VI. in Reduction; then add, as in the preceding examples.

: EXAMPLES.

1. Add and together.

4X5=20)

3x9=27

numerators.

2. Add and &

47 sum.

4x9-36 com. denom. 471 Ans. together.

CASE III.

To add mixed numbers.

RULE.

Ans. 14

Add the fractions as in Case I, in Addition, and the whole numbers as in Simple Addition; then add the fractions to the sum of the whole numbers. . If the fractions have different denominators, reduce them to a common denominator, and then add the fractions to the integers or whole numbers.

EXAMPLES.

1. Add 13, 9, 37 together.

13+9+3=25 whole numbers.

√ + $+7=}}=1. Thus, 254 Ans.

2. Add 53, 67 and 41 together.

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5+6+4=15 whole numbers.

Then, 2x8x2=32

7×3×2=42

1X3X8=24

98 sum of the numerators.

3x8x2=48 common denominator.

Then, 21=24. Thus, 15+2=17, Answer.

3. Add 14, 23 and 35 together.

Ans. 7103.

CASE IV.

To add compound fractions.

RULE.

Reduce them to simple ones, and proceed as before.

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Ans. 1.

Ans. 113.

2. Add 2 of 7, and 4 of 18 together. 3. Add of, and of together. 4. Add, 9 and of together. Note. The mixed number of 93-46; the compound fraction of. Then the fractions are,, 4 and ; which must be reduced to the fractions of a common denominator and added. Ans. 918. 5. Add 1, 67, of and 7 together. Ans. 167.

CASE V.

When the given fractions are of several denominations.

RULE.

Reduce them to their proper values, or quantities, and add them according to the following examples.

EXAMPLES.

1. Add of a pound to of a shilling.
Thus, of a pound=13s. 4d.

and of a shilling= Os. 4d. 31qr.
3

13s. 8d. 31qr. Ans.

2. Add 7 of a pound and of a shilling together.

Ans. 15s. 10d.

3. Add of a week, of a day, and of an hour together. Ans. 2d. 14th.

4. Add of a yard, of a foot, and

of a mile toAns. 1100vds. 2ft. 7in.]

of a dollar,

of a cent,

of a cent, and

gether.
5. Add
of a mill together.

6. Add of a pound, of a shilling,

ny together.

Ans. 20c. 9m.

and of a pen-
415
Ans. 2s. 8,4d.

SUBTRACTION OF VULGAR FRACTIONS.
CASE I.

When the fractions have a common denominator.

RULE.

Subtract the less numerator from the greater, and set the remainder over the common denominator, which will show the difference of the given fractions.

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When fractions, or mixed numbers, are to be subtracted

from whole numbers.

RULE.

Subtract the numerator from its denominator, and under the remainder place the denominator; then carry one to be deducted from the whole number.

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