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IX. To find the value of the fraction in the known parts of the

integer. RULE. Multiply the numerator by the known parts of the integer and divide by the denominator.

EXAMPLES. 1. What is the value of of a £. ?

20 shillings.

2

3)40

Anf. 13 4d.
What is the value of of a shilling ?

°Anf. 4d. 3 qrs

.. 3. Reduce } of a lb. troy to its proper quantity.

Anf. 7oz. 4 dwt.
Reduce 4 of a mile to its proper quantity,

Anf. 6 fur. 16 poles.

x. To reduce any given quantity to the fraction of a greater de

nomination of the fame kind. Rule. Reduce the given quantity to the lowest denomination mentioned for a new numerator, under which set the integral part (reduced to the same name) for a denominator, and it will express the fraction required.

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

16 8

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2. Reduce a quarters 3f nails to the fraction of an ell English

Anf. §

3. Reduce 45. 6 d. to the fraction of a pound.

Anf. 109

430

ADDITION OF VULGAR FRACTIONS.

1. To add fractions that have a common denominator. RULE. Add their numerators together, and place the sum over one of the given denominators.

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II. To add mixed numbers, whose fractions have a common

denominator.

RULL. Add the fractions by the last case, and the integer as in whole numbers.

EXAMPLES. 1. Add 2 to 3tr 41 and 7ů together.

211 3r 41 711

177t Answer. 2. Add 137'5, 9i4s, and 3rs together. 3. Add it's, 22, 3i's, and 4 it together. 4. Add 91}, 711, 571, and 841 together.

Anf. 25

Ans. 12 Ans. 314

IV. To add fractions, having different denominators. Rute. Find the least common denominator by Case III. in Reduce tion, in which divide each denominator, and multiply the quotient by its numerator ; the sum of the products is a new numerator to the common denominator, and the fraction required.

EXAMPLES.

1. Add ý, t. &, , and it together.

24 com. denom.
3 8X2=16
4 6X3=18
6 4X5=20
8 3X 7=21
I 2 2 XII=22

= 47, the answer. 2. Add { }, }, }, and together. 3. Add 5, , 9, }, and is together.

Ani. 245 Anf. 37275

IV. To add mixt numbers whoje fra£tions have different denom.

inators.

Reule. Add the fractions as in the last case, and the integers as in whole numbers.

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Rule. Reduce them to their proper quantities by Case IX. in Reduction, and add as before.

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EXAMPLES 1. Add of a £. to 1' of a shilling.

15 common measure

d.
of a £ 515 63 10

is of a S.O 3} | 9

2.

Ans.

15 1045 ists
Add į of a yard, of a foot, and ] of a mile together.

Anf. 1540 yds. 2 ft. 9 inches. 3. Add of a week, of a day, and { of an hour together.

Ans. 2 d. 144h.

SUBTRACTION OF VULGAR FRACTIONS.

1. To find the difference between fimple fractions that have a

common denominator. · RULE. Subtract the less numerator from the greater, and under the remainder put the denominato:.

EXAMPLES. From &

IS Take

75

10S 200 99 200

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au long with these are a

6

Rem. }

II. To fubtract a fraktion or mixt number from a whole number.

Rule. SubtraĖt the numerator from the denominator, and under the remainder put the denominator, and carry one to be deducted from the integer.

EXAMPLES. 6

9 Take o

0 si 9918

From 3

10

100

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III. To fubtract fimple fractions that have no common denominater.

Rule. By Case IV, in Reduction, find a common denominator, in which divide each denominator, and multiply the quotient by its numerator ; the difference between the products thus found is a numerator to the common denominator, and the answer required.

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In order to distinguish the greater of two fractions, let them be reduced to a common denominator, as in case V. in Reduction, and that fraction whose numerator is greater is the greater fraction; the difference between the new numerators being set over the common denominator, will fhew the excess or inequality.

EXAMPLE.
Which of the two is the greater fraction, it or is?

48 com, denom,

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IV. To fubtract a fraction or mixt number from a mixt number,

when the fra&tional part to be fubtracted is greater than that from' which it is to be fubtracted.

RULE. Find a common denominator and a new numerator, as in the last case, and then subtract the numerator of the greater fraction from the common denominator, and to the remainder add the less numerator, and set the sum of both for a new numerator over the common denominator, and carry one to the integral part, and proceed as in whole numbers.

EXAMPLES.

27 common denominator

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