INTEGERS. EACH ETH to add two or more sums together, to make one whole or total sum. RULE. There must be due regard had in placing the Figures one under the other, i. e. Units under Units, Tens under Tens, &c. then beginning with the first row of Units, add them up to the top; when done, set down the Units, and carry the Tens to the next, and so on; continuing to the last Row, at which set down the total amount. PROOF. Begin at the top of the Sum, and reckon the Figures downwards, the same as you added them up, and, if the same as the first, the Sum is supposed to be right. What is the sum of 43, 401, 9747, 3464, 2268, 314, 974 Ans. 17206. Add 246,034, 298,765, 47,321, 58,653, 64,218, 5,376, 9,821, and 640 together. Ans. 730,828. If you give A. £56, B. £104, C. £274, D. £391, E. £703, how much is given in all ? Ans. £1528. How many days are there in the twelve Calendar months. Ans. 365. (T. S.) To 424878321; add seven hundred thousand eight hundred and forty; twice 1248732; and 714217218. Add 4 times 1724321824 together. Add together twice four hundred thousand million seven hundred and forty-seven; twice 74283242; and twice 448742 To three times 47247834; add 472174. To three times four thousand million eight hundred thousand four hundred and forty-eight; add twice 9327427 493. Add 9 times 36968; to 7 times 33383. TO FROVE ADDITION. RULE 1. Add all the figures in the top row together, and having rejected as many nines as are contained in their sum, set down the remainder directly even with the rest of the figures. 2. Do theme with each of the other rows, and find the sun of all the remainders; then, if the excess of nines in this sum, be equal to the excess of nines in the total sum, the work is right. EXAMPLES. 190851 940509 1907508 44886110 22910475 44925583 79784837 81425369 12345678 20215663 56565656 23456789 8400018 54556001 43434345 55074417 45443999 18574631 87654322 81314042 80006000 76543211 28043713 111000111 TE SUBTRACTION EACHETH to take a less number from a greater, and shews the, Remainder, or Difference. RULE. This being the Reverse of Addition, you must borrow here (if it require) what you stopped at there, always remembering to pay it to the next. PROOF. Add the Remainder and less Line together, and if the same as the greater, it is right. From 271 4751 42087 452705 271508 3750215 Tuke 154 2723 34096 327616 152471 3150874 Rem. 117 Proof. 271 EXAMPLES. (T.S.) From 37284506 Take 15928734 From 104735264038 Take 67359846736 Subtract 9472863 from 140592641. From 35970462814 take 973842675. What is the difference between 35968 and 52873 ? If 372609346 be subtracted from 427350864, what will remain? The sum of two numbers is 462583 and one of them is 239468, what is the other? Subtract 304074268 from 1007306972. Take 673597046259 from 3042638974600. Tell the difference between 2565+4896+9729+9564 and five thousand five hundred and five. Take eight hundred and fifty millions; from 999,000,888. What number added to 3 times 999; will make 10 times 666 ? Take one million, one hundred thousand, one thousand and one from 1101002. From 999,888,777 take 3 times 333,000. From 123456789 take 98765432. From 3 times 8888, 4 times 1111 and 9764, take 18 times 2222 and twice 2222. A B and C have a thousand guineas, a thousand half guineas and a fifty pound note, X Y and Z want £.1200. 19. 4. from them, what sum will A B and C have left? A was born when B was 19 years of age: how old will A be when B is 74; and what will be the age of B when A is 58 ? From one thousand guineas, take one thousand pounds and two perce. From 12 times 12, take 3 times 9 and 9 times 3. TE MULTIPLICATION. EACHETH how to increase the greater of two numbers gi ven as often as there are Units in the less: and compendiously performs the office of many additions: To this Rule belong these principal Members; viz. 1, The Multiplicand, or number to be multiplied; 2, The Multiplier, or number by which you multiply; 3, The Product or Number produced by multiplying. RULE. Begin with that Figure that stands in the Unit's Place of the Multiplier, and with it multiply the first Figure of the Unit's Place of the Multiplicand. Set down the Units and carry the Tens in Mind, till you have multiplied the next Figure in the Multiplicand by the same figure in the Multiplier; to the Product of which add the Tens you kept in mind, setting down the Units, and proceed as before, till the whole Line is multiplied. PROOF. By casting out the Nines; or make the former Multiplicand the Multiplier, and the Multiplier the Multiplicand; and if the Product of this Operation be the same as before, the Work is right. B When the Multiplier is more than 12, and less than 20, mulfply by the Unit Figure in the Multiplier, adding to the Product the back Figure to that you multiplied. When the_Multiplier consists of several Figures, there must be as many Products as there are Figures in the Multiplier, observing to put the first Figure of every Product under that Figure you multiply by. Add the several Products together, and their sum will be the total Product. Multiply 271041071 by 5147. Multiply 62310047 by 1608. Multiply 1701495868567 by 4708756. When Cyphers are placed between the significant Figures in the Multiplier, they may be omitted; but great care must be taken that the next Figure must be put one place more to the left hand; i. e. under the Figure you multiply by. Multiply 571204 Multiply 7561240325 by 57002. When there are Cyphers at the end of the Multiplicand or Multiplier, they may be omitted, by only multiplying by the rest of the Figures, and setting down on the right-hand of the total Product as many Cyphers as were omitted. Multiply 1379500 |