Page images
PDF
EPUB

3. A compound fraction is the fraction of a fraction, coupled by the word, of, thus ; of, of off

4. A mixed number is composed of a whole number and a fraction joined together, thus ; 84, 162, 193, &c.

A whole number may be expressed as a fraction by drawing a line under it and putting 1 for a denominator ; thus, 6=f, and 12=1, &c.

PROBLEM I.

To reduce Fractions to their lowest terms. The numerator and denominator together are called terms of a fraction; and may often be changed without altering the value of a fraction; thus, take an orange, or any thing, and divide it into 2 equal parts, and 1 of these parts will be

of the orange: again, if we divide it into 4 equal parts, it is evident that 2 of those parts (3) will be just of the orange : and if we divide it into 8 equal parts, 4 of these parts (f) will be just equal to of the orange : and the fractions 1, 1, and , are all equal in value, but expressed in different terms. Hence the terms of fractions may be changed without altering the value of the fraction ; for if we multiply both the terms of the fraction by 2 it becomes, which is equal to 1 : again, if we divide the terms

by 2, the fraction will be }, which is expressed in its lowest terms possible.

RULE.

1. Divide the terms of the fraction by any number that will divide them both without a remainder. 2. Divide these quotients again in the same manner,

and 80 on, until no number greater than 1 will divide them:

EXAMPLES.
i. Reduce to its lowest terms.

Thus =, and 5) =}, the answer.
2. Reduce 132 to its lowest terms.

Ans. 264 3. Reduce 432 to its lowest terms.

Ans. 4. Reduce 1 47 to its lowest terms.

Ans. 5. Reduce to its lowest terms.

Ans. 343 6. Reduce 168 to its lowest terms.

Ans: 7. Reduce to its lowest terms.

168
49

[ocr errors]
[ocr errors]

Ans. It

4 1

8. Reduce 168 to its lowest terms.

252
9. Reduce to its lowest terms.

328
10. Reduce 252 to its lowest terms.
11. Reduce to its lowest terms.

Ans.. Ans. Ans. Ans.

9

PROBLEM II.

To change a Whole or Mixed Number to an Improper

Fraction.

RULE.

Multiply the whole number by the denominator of the fraction and to the product add the numerator; this sum written over the denominator will form the fraction required.

EXAMPLES.

Ans. 405.

1. In 27 dollars how many fourths of a dollar ? Operation.

$1=4 fourths of a dollar, 273

and 27 dollars=27 times 4 7.4=fourths in 1 dollar.

or 108 fourths, and 3 fourths 108=fourths in 27 dollars. added to 108 fourths make +3=fourths in

ili fourths=112 the Ans. 111 =-fourths= Ans. 111. 2. In 36 dollars, how many eighths of a dollar ?

Ans. 223 3. Reduce 45 to ninths.

4. Reduce 8á to an improper fraction, that is, reduce it to sixths.

Ans. 53 5. Reduce 33} to an improper fraction. Ans. 10.

6. Reduce 28 to a fraction having 12 for a denominator, that is, reduce it to twelfths.

Ans. 336

12. 7. Reduce 45% to fifths.

Ans.20. 8. Reduce 619,5 to an improper fraction.

Ans. 8 635

140. 9. Reduce 84 to an improper fraction.

Ans. 933

11 10. What improper fraction is equal to 5648 ?

Ans. 2250 11. What improper fraction is equal to 148%?

.

10 12. What improper fraction is equal to 2253 ?

Ans. 1693.

Ans. 1489

PROBLEM III.

To change an Improper Fraction to a Whole or Mixed

Number.

RULE.

Divide the nunterator by the denominator, and the quotient will be the value of the fraction.

EXAMPLES.

1. In 4 of a dollar, how many dollars ? Operation.

of a dollar åre equal to 1 dollar, and $1=6)45

6 is contained in 45, 7 times and of another time; therefore the answer is

7 dollars=71 dollars. 2. Find the value of 1.go of a cent.

Ans. 33 cts. 3. Find the value of 249 of a cwt.

Ans. 494cwt. 4. Reduce 5 to a mixed number.

Ans. 86. 5. Reduce 405 to a whole number.

Ans. 45 6. Reduce to a whole number.

Ans. 28. 7. Find the value of 450.

Ans. 1778 8. Find the value of $835.

Ans. 61
PROBLEM IV.
To Multiply a Whole Number by a Fraction.

[ocr errors]

95

140

RULE.

1. Divide the whole number by the denominator of the fraction, (when it can be done without a remainder,) and multiply the quotient by the numerator ; or,

II. Multiply the whole number by the numerator of the fraction and divide the product by the denominator.

EXAMPLES.

1. What is the product of 48 multiplied by ? 1st mothod.

2d method. 4)48

48 12 is of 48

3 3

4) 144=3 times 48 Ans. 36=3 times of 48, 36 is of 3 times 48,

which is 1 of 48. which is the same as of 48

By this example we see, there are two ways of multiplying a whole number by a fraction, and that both methods produce the same result. Thus, by the first method, we get

of 48, and this repeated 3 times is evidently equal to ,, for 3 times of any number is equal to 1 of that number. By the second method, we repeat 48, 3 times, and then take of that product, which is the same as 3 times of 48.

2. At 25 dollars per acre, what is the cost of já of an acre of land ?

Ans. 231.dolls. 3. If a ship sail 246 miles a day, how far will she sail in z of a day?

Ans. 191] miles. 4. How much is of $1845,56 ? Ans. $1537,96%. 5. Multiply 400 by s.

Ans. 150. 6. Multiply 750 by š.

Ans. 450 7. The interest of $750 for 1 year, is $45; what is the interest on the same sun for 5 months, or is of a year ?

Ans. $18,75. Note. If the multiplier of any sum be greater than a unit or 1, the multiplicand will be increased as many times as the multiplier is greater than a unit; that is, the multiplicand will be taken as many times as the multiplier contains units. But when the multiplier is a fraction or part of a unit, the product will be only a part of the multiplicand. Hence in multiplying by, a proper fraction, the product is always less than the multiplicand, as will be seen by the preceding examples.

PROBLEM V.

To Multiply a Fraction by a Whole Number:

RULE.

Multiply the whole number and the numerator of the fraction together, and write the product over the denominator; and if it produce an improper fraction, change it to a whole or mixed number, by Prob. 3.

EXAMPLES.

1. If a man spend á of a dollar a day, how much will he spend in 11 days?

If he spend in 1 day, he will spend 11 times 5= in 11 days, and 5 of a dollar =91 dollars, the answer.

2. If 1 yard of cloth cost of a dollar, what will 15 yards cost ?

Ans. $9.

3. If a bushel of oats cost fa of a dollar, what will 23 bushels cost?

Ans. $975 4. A certain lot contains of an acre of land; how much land would 37 such lots contain ? Ans. 273 acres.

5. If a bushel of potatoes cost % of a dollar, what will 56 bushels cost?

Ans. $164 Note. The process of multiplying a fraction by a whole number,

may

be shortened, thus: Divide the denominator of the fraction by the whole number, (when it can be done without a remainder,) and over the quotient write the numerator.

6. If a pound of sugar cost do of a dollar, what will 20lb. cost.

Divide the denominator, 100, by 20, and the quotient 5, is a new denominator ; then write the numerator over it, and it becomes of a dollar=2} dollars, the answer.

7. If a pound of nails cost of a dollar, what will 11lb. cost?

Ans. $1. 8. If a pound of butter cost of a dollar, what will 5lb. cost?

Ans. $ 9. At of a dollar per pound; what will i1lb. raisins come to ?

Ans. $

PROBLEM VI.

To divide a Whole Number by a Fraction.

RULE.

Multiply the whole number by the denominator of the fraction, and divide the product by the numerator.

EXAMPLES.

[ocr errors]

1. How many times is of a dollar contained in $9? 1 dollar is 4, and 9 dollars is 9 times as many; 9x4=;

and is contained in 0 as many times as 3 is contained in 35.

Ans. 12 2. How many times is a contained in 16 ?

Thus, 16

x6=denominator. Numerator=5)96=sixths in 16

Ans. 191

« PreviousContinue »