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 fhillings.

3)40

Anf. 13 4d.

2, What is the value of of a fhilling?

8. Reduce of a lb. troy to its proper quantity.

Anf. 4d. 3 qrs. 3.

Anf. 7 oz. 4 dwt.

4.

Reduce 4 of a mile to its proper quantity.
告

Anf. 6 fur. 16 poles.

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

RULE. Reduce the given quantity to the loweft denomination mentioned for a new numerator, under which fet the integral part (reduced to the fame name) for a denominator, and it will express the fraction required.

EXAMPLES.

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

Reduce 2 quarters 33 nails to the fraction of an ell English..

Anf.

2.

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

Anf. 18

ADDITION OF VULGAR FRACTIONS.

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

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

denominator.

RULE. Add the fractions by the last cafe, and the integer as in whole numbers.

IV. To add fractions, having different denominators.

RULE. Find the least common denominator by Cafe III. in Reduc tion, in which divide each denominator, and multiply the quotient by its numerator; the fum of the products is a new numerator to the common denominator, and the fraction required,

IV. To add mixt numbers whofe fractions have different denom

RULE.

inators.

Add the fractions as in the last case, and the integers as

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

L

3. Add of a week, of a day, and of an hour together.

Ans. 2 d. 14 h.

SUBTRACTION OF VULGAR FRACTIONS.

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

RULE.

Subtract the lefs numerator from the greater, and under

the remainder put the denominator.

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

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

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

RULE. By Cafe 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.

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 fet over the common denominator, will fhew the excess or inequality.

EXAMPLE.

I

Which of the two is the greater fraction, or

48 com. denom.

IV. To fubtract a fraction or mixt number from a mixt number, when the fractional 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 fubtract the numerator of the greater fraction from the common denominator, and to the remainder add the lefs 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.