« ΠροηγούμενηΣυνέχεια »
20 quills at 3 farthings each. 2 farthings, are half a penny, 220 1 farthing is half a halfpenny, 110
Page 303. 1d./s. 8612 at 1d.19. 10. s.14121 at 1d.29. 19.d. 717 8d
29. d. 343 5 179 5
171 8 2 20 | 897 1 20 515 1 2 Ans. £.44 17s. 1d. Ans. £25 15 1 2
Page 304. 2d. s. 6181at2d. 19. 20.8. 1218 at 2d.29 1030 2
29.1 | 203 128 9 1
50 9 20 1158 11 1 20
253 g Ans. £.57 18 11 1 |Ans. £. 12 13 9
“EVERY MAN HIS OWN TEACHER."
RULE IN MULTIPLICATION.
Point off so many decimals in the product, as there are in the two face tors counted together.
RULE IN DIVISION. The decimals in the divisor and quotient, counted together, must be equal in number to the decimals in the dividend.
EXAMPLES. 1. Multiply 486.5
Proof by division. by 3.25
REMARKS. 1st. In Division, begin by counting the Decimals in the dividend; then begin again and count the Decimals in the divisor, turn from that to the right of the quotient and continue counting towards the left, till you have a number equal to the Decimals in the dividend; there place the point.
2d. If, after Division is performed, there is not a sufficient number of Decimals in the divisor and quotient, counted together, then prefix cyphers to the quotient, till the deficiency in number is made good.
3d. When the dividend is 100 small to admit the divisor, annex cyphers to the dividend ; five in number for a general rule, but sometimes less, and sometimes more, according to the nature of the case under consideration.
EXAMPLES 1. Divide 2.08080 by 4624. Make it .00045
DIRECT PROPORTION; or, THE SINGLE RULE OF THREE MADE DIRECT IN ALL CASES.
RULE. Compare objects with objects of the same name and kind; as, prices with prices, or dollars with dollars, shillings with shillings, bushels with bushels, gallons with gallons, ounces with ounces, &c. for the two first terms; then place that which is of the same name of the answer, in the third term.
EXAMPLE 1. If 2 gallons cost 8s. what will 4 Proportional Statement. gallons cost?
When the nature of the question
shows that the answer must be great2 : 4 :: 8 to a fourth number.
er than the sum in the demand, then 4
take the lesser term in the supposition
for the first ; but if it appear that the 2)32(16s. answer.
answer must be less than the demand, then take the greater term in the sup
position for the first.
EXAMPLE 2. If 4 men can do a piece of work in 10 days, how many men will be stifficient to do the same in 20 days?
D. D. M.
Although this question is of the 20 : 10 :: 4
inverse kind, yet the method of stal4
ing affords a direct operation, and
will hold good in all cases. 20)40(2 men, for answer.
EXAMPLE 3. If 6 men can do a piece of work in 5 days, how many men can do the same in 15 days?
Answer, 2 men. In this example we perceive, that the answer in men will require a less number than 6 mentioned in the supposition; therefore take the greatest number of days, in the supposition and demand, for the first term, and the other for the second.
OPERATION D. D. M.
Say, as 15 days are to 5 days, so 15 : 5 :: 6 to a fourth number, are 6 men to a fourth number, or the 6
number of men required.
PROOF OF EXAMPLE 3. If 2 men can do a piece of work in 15 days, how many men can do the same in 5 days?
Answer, 6 men. Here the nature of the question shows, that the answer must be greater than the number of men in the supposition; thus,
D. D. M.
5)30(6 answer. N. B. In Compound Proportion, or Double Rule of Three, make two statements.
on, THE DIFFERENT CASES IN PRACTICE WROUGHT UNDER ONE CASE.
RULE. Find the price of unity, or one, in the denomination next above the highest denomination in the given price ; this will immediately give the price of the given number of intigers; then take parts in the usual manner.
LESSON 1. 1817 at 1q. Say, 1817 at 1d. the next higher denomination; then divide by 12 and by 20, which operation will inake £7 11s. 5d.; then divide that sum by 4, and the quotient will be the answer; because 19. is the fourth of a penny.
For example, if 1817 apples, at 1d., will amount to £7 11s. 5d., they will amount io one fourth of this sum at a farthing, viz. £1 178. 10d. 19. OPERATION.
19. # 10.1817 at 19. 201 1518. 5d.
121 454 19. 4 7 11s. 5d.
37 10d. Ans. £1 176. 10d. 19.
Ans. £1 178. 10d. 19.