Imágenes de páginas
PDF
EPUB

the sum, to the numbers on the left, which add up as in common addition.

[blocks in formation]

51. LET the fractions be prepared the same as for Addition : then the difference of the numerators set over the common denominator will give the difference of the proposed fractions.

Ex. 1. What is the difference of ¦ and 3?

The difference of the numerators 1 and 3 is 2; therefore the required difference is or 4.

2. Required the difference of 1 and 2, ?

[ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

and brought to a common denominator, are 38 and 31; therefore

[ocr errors][merged small][merged small][merged small][merged small][ocr errors]
[merged small][merged small][ocr errors][merged small][merged small][ocr errors]

52. When the difference of two mixt numbers, or a mixt number and a fraction is required, bring the fractions to a common denominator as before; then place the less number under the greater and take their difference for the answer. But if the lower fraction is greater than the upper one, subtract the numerator of the former from the sum of the terms of the latter, then set down the difference for the numerator of the remaining fraction, and carry 1 to be subtracted.

[blocks in formation]

1. And in the preceding example, 7 is taken from 18 (the sum of the terms of the fraction), which is the same thing as subtracting from

added to 14; for in either case 1 is borrowed, and evidently for the same reason that we borrow 10 in the subtraction of whole numbers when the figure to be subtracted is greater than that above it.

53. The reason why fractions must be brought to a common denominator for the purposes of addition and subtraction, will be evident, if we consider that in order to compare their several values, it is necessary to exhibit them in like parts of the integer.

Thus to compare with, if we suppose the integer 1 to be divided into

12 equal parts, will be, and will be

now the values being ex

pressed in 12ths (instead of 3ds and 4ths) it appears that is less than by also, that both together make 11.

MULTIPLICATION OF VULGAR FRACTIONS.

54. REDUCE mixt numbers to improper fractions; and whole numbers to the form of fractions, by putting 1 for the denominators. Then multiply the numerators together for the numerator, and the denominators together for the denominator of the product. This rule is the same as that for reducing a compound fraction to a simple one; for when the multiplier is a fraction, the product will be a part or parts of the multiplicand:

1 x 1
2× 2

thus of isor ; and of is or 뭏

2 x 3

3 X 4

and there

fore the fractions to be multiplied may be set down in the form of a compound fraction, aud the product found in the same manner as that is reduced to a simple one.

[ocr errors][merged small]

Then,

[blocks in formation]

3. What is the continued product of 4, 7, 3, and 1⁄2 of ?

First 44; and 7 = 1.

[blocks in formation]

product of a fraction and a whole number, multiply by the numerator, and

divide by the denominator,

VOL. I.

55. When one factor is a whole, and another a mixt number, or if one is a small fraction, and another a large mixt number, multiply the parts of the latter separately, and add the products together.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors]

72107047210704127 Ans.

56. And when both factors are mixt numbers, the product may be found by multiplying the parts separately, as in the next example.

Ex. 8. Required the product of 571 by 4851?

[merged small][merged small][ocr errors][merged small][merged small]

DIVISION OF VULGAR FRACTIONS.

57. PREPARE the fractions the same as for multiplication; then divide the terms of the dividend by the respective terms of the divisor, if they will exactly divide; but if not, then invert the divisor and procced as in multiplication.

When the terms exactly divide, the truth of the rule is manifest from the principles of common division. And the reason for inverting the divisor in the other case will be evident if we consider that division is the reverse of multiplication: thus the product of and 4 is × 42 or the half of 4; but 4 divided by will give 8, because is contained 8 times in 4, the quotient being x 4, where is the divisorinverted.

As a second example, let & be divided by ; or suppose it is required to find how often is contained in . Now if we divide 5 by }, the quotient will be × { or 15, (because is contained 15 times in 5); but when the

3 x 5

divisor is twice, or 3, the quotient will be only of 15, or 2 quotient of 5 divided by 3, consequently the 7th. of 5 (or

[blocks in formation]

the

) will give but a

divided by 3

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small]

}}=} quotient: this is called the reciprocal of the divisor 2.

9. Divide by 3 ?

« AnteriorContinuar »