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Exam. 1. The compound Fraction of

35

160

leaves Anf.

19 189

is reduced to by Art. 3; reduce that and the fimple Fraction to the fame Denominator, by Art. 4, and they are and 128; then fubtracting the Numerator 35 from the Numerator 128, the Remainder is 93, to be placed over the common Denominator 160: Thus is the Difference fought.

160

The fecond Example is done in the fame Manner.

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Article 20. To fubtract fimple Fractions from mixed Numbers.

Rule. Reduce the mixed Number to an improper Fraction, by Art. 2; and reduce this and the given Fraction to the fame Denominator, by Art. 4; then fubtract the leffer Numerator from the greater, and place the Difference over the common Denominator, as at Art. 18.

Exam. I.

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Now the two Fractions are Now the two Fractions are

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3 and 5.
55

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21

from 275 leaves 267 Anf. 2 from 288 leaves 267 Anf.

Exam. 1. The mixed Number 13 proper Fractions, by Art. 2; then

28

is reduced to the imthis Fraction and the

8

20

given fimple Fraction are reduced to and 275, Fractions of the fame Denominator, by Art. 4: Subtract 8 from 275 and there remains 267, to be placed over the common Denominator 20; fo is 267 the Difference fought.

Exam. 2. The mixed Number 10 is reduced to the improper Fraction, by Art. 2; then the Fraction, and the given fimple Fraction, reduced to the fame Denominator, by Art. 4, are 2 and 238: The Difference of the Numerators 21 and 288 is 267, which placed over the Denominator 28 is 257, the true Difference fought.

The two following Examples are done in the fame Manner.

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Article 21. To fubtract compound Fractions from mixed Numbers.

Rule. Reduce the compound Fraction to a fimple Fraction, by Art. 3, and the mixed Number to an improper Fraction, by Art. 2; then reduce these two new Fractions to the fame Denominator, by Art. 4: Laftly, fubtract the leffer Numerator from the greater, and place the Remainder over the common Denominator, for the Difference fought.

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Hence the two fingle Fractions Hence the two fingle Fractions

are 28 and 20.

are

and 98.

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445

280

280

Exam. 1. The compound Fraction of is reduced to the fimple Fraction 28, by Art. 3, and the mixed Number 6 to

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the improber Fraction, by Art. 2: Reduce these to the fame Denominator, by Art, 4, and they make 4 and 1200 : Laftly, fubtracting the leffer Numerator from the greater, and placing the Remainder over the common Denominator, 1116 is the Difference fought.

180

The other Example is done in the fame Manner.

Article 22. To fubtract fimple Fractions from Integers.

Rule. Subtract the Numerator of the given Fraction from the Denominator, place the Remainder over the Denominator, and join this Fraction to the Integers leffened by 1: This is the Anfwer fought.

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Exam. 1. The Numerator 2 being fubtracted from the Denominator 5, there remains 3; which placed over the fame Denominator makes, the Remainder of the Fraction from an Unit: Then taking I from the Integer 7, for the I borrowed in fubtracting the Fraction from I or Unity, the Remainder is 6, to be annexed to the aforefaid: So is 6 the Remainder.

The other Example is done in the fame Manner.

The Reason of the Rule may be beft understood by an Example taken from common Arithmetick: If it be required to fubtract 31. 6s. 8d. from 71. as there are no Shillings or Pence in the Subtrahend, or Sum given for the other to be fubtracted from, it is performed in the following Manner, viz.

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In this Example, there being no Pence in the Sum given to be fubtracted from, we borrow 12 Pence, or I Shilling, to fubtract the 8 from, and the Remainder is 4; this borrowed Shilling is then carried to the Shiilings, which increases the

6 Shil

8

6 Shillings to 7 Shillings; then, there being no Shillings to fubtract the 7 from, we again borrow I from the next Article of Pounds; from which I Pound, or 20 Shillings, borrowed, the 7 is fubtracted; after which, that borrowed Pound is carried to the Place of Pounds. Now this is the fame that is done in this Rule, for 8 Pence is of a Shilling; and this 8 fubtracted from the Denominator 12 leaves, i. e. 4 Pence; but then is carried to the Place of Shillings, which is fubtracting from the Integer, of which the Fraction was a Part. So here of an Integer were to be fubtracted from 7 Integers: Now, of an Integer fubtracted from I of thofe Integers, the Remainder must be ; because and added together make, or I Integer; then, as this I was borrowed to fubtract the from, it must be carried as in common Subtraction; the Operation being in Effect thus, from nothing I cannot, but from, or I, there remains; then I fay, I that borrowed from 7, there remains 6; to which I annex the before remaining, and find the whole Remainder to be 63.

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Exam. 3.

Subtract from 5.

5

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Exam. I.

Subtract of from 29.

Article 23. To fubtract compound Fractions from Integers. Rule. Reduce the compound Fraction to a fimple Fraction, by Art. 3; then proceed as in the last Article.

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