Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

16

19. What is the quotient of 16 ÷ ¦

First Solution.

divided by 1 = 1f, and by must equal 9 times

; if it contains so many times, it must contain & only as many

[blocks in formation]

Second Solution.

f divided by 1 equals, and divided by must

equal 9 times; if the quotient by equals so much, the quotient by must equal of this result.* Hence,

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

In accordance with the principle, that if a number contains another a certain number of times, it will contain 8 times that number only as many times; 12 times the number only as many times, &c. Thus, 72 ÷ 2 = 36, and 72 ÷ 6 times 2, or 12, = & of 36, or 6.

48316, and 488 times 3, or 24, = 1⁄2 of 16, or 2.

8

756, and 75 times, or §, = of 56, or 56 = 11. , and 7 times To, or To, = 4 of 5, or 58.

=

+ Reduce to an improper fraction.

==

148. Process of Division generalized.

=

(a.) Since the quotient of any number divided by † = 5 times the number; by 9 times the number; by= 13 times the number, &c.; and since the quotient of a number divided by its quotient divided by ; divided by of its quotient divided by ; divided by

g

[ocr errors]

of

its quotient divided by, &c., it follows that the quotient of a number divided by

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

of 5 times the number, = of the number;

of 9 times the number, = % of the number;
of 13 times the number, = 1 of the number;
of 100 times the number 19o of the number;

and, universally, that—

The quotient of any number divided by a fraction, is equal to the product of that number multiplied by the fraction

inverted.

Illustrations. divide by 8.

1. To divide by §, we have only to multiply by 9 and

2. To divide by, we have only to multiply by 17 and divide by 3.

3. To divide by .03, we have only to multiply by 100 and divide by 3, or, which is the same thing, to divide by 3 and remove the point 2 places towards the right.

4. To divide by .000037, we have only to multiply by 1000000, and divide by 37, or, which is the same thing, to divide by 37, and remove the point 6 places towards the right.

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

Ans.

The quotient of 520.6.011 may be obtained by dividing 520.6 by 11 and removing the point three places towards the right

[blocks in formation]

NOTE.—The second form of writing the work differs from the first only in this, that in it as many zeros are annexed to the dividend as would be necessary were the point actually changed before performing the division. Great care is necessary, by either of these forms, to insure that the point is placed correctly in the quotient; and if in any case there is a doubt as to its true position, the work should be written in full, as in the model given after example 29th, 147.

3. What is the quotient of § of 7 of & ÷ § of 12 of 2} ?

[blocks in formation]

NOTE.-The more full and analytical explanation would be the following: is the number to be operated upon. of may be expressed by making 7 a factor of the numerator, and 9 a factor of the denominator. of this may be expressed by making 4 a factor of the numerator, and 5 a factor of the denominator. The quotient of this quantity divided by 22 will be of it, and may be expressed by making 22 a factor of the numerator, and 21 a factor of the denominator. If is contained so many times, 1 of 2 must be contained

as many times, expressed by making 25 a factor of the numerator, and 12 a factor of the denominator. If this divisor (1 of 2) is contained so many times, & of it must be contained as many times, expressed by making 9 a factor of the numerator, and 8 a factor of the denominator. Hence,

[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]

tions

The equation in the parenthesis may be omitted in practical opera

What is the quotient-
4. Of 134813?
5. Of 114?

6. Of 16284?

7.

Of .00425 ?

8. Of .067.02?

9. Of 3287÷.0004?

55

10. Of of 1 of 35 ÷ 15 of 50% of 8?

11. Of of 12 of 4 of 1% of 61?

12. Ofofofofofofofofof?

13. Of of of of 7 of 13 of 11?

149. Complex Fractions.

(a.) A COMPLEX FRACTION is one having a fraction in

either numerator or denominator, or in both; as,

7 23

[ocr errors]
[ocr errors]

NOTE. Complex fractions are usually considered as expressions of unexecuted divisions, and are read accordingly. Thus,

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

(b.) To show their similarity to other fractions, we may explain them thus:

322

= 7 parts of such kind that 3 of them would equal a unit.

(c.) Complex fractions can be reduced to simple fractions by the ordinary process of division.

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

(d.) Complex fractions may often be reduced to simple ones, by reducing them to their lowest terms,

3

3

Thus Dividing both terms of by 1 gives 41 =. Dividing

[blocks in formation]

4글

13 by 13 gives 1 = 1.

Reduce each of the following in the same manner :

[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][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

(e.) Complex fractions may also be reduced to simple. ones, by multiplying both numerator and denominator by such a number as will give a whole number in place of each.

[blocks in formation]

Solution. If 4 be multiplied by 3, or some multiple of 3, and 104 be multiplied by 2, or some multiple of 2, the result will in each case be

4/ 101

a whole number. Hence, if both terms of the fraction be multiplied by some multiple of both 2 and 3, the resulting fraction will be a 4 28 4

simple one. Multiplying by 6 gives

=

101 63

In the same way reduce each of the following complex fractions to simple ones:

[blocks in formation]
« ΠροηγούμενηΣυνέχεια »