4 Practical ARITHMETIC. CHAP. I. The fundamental RULES in Common ARITHMETIC. § I. Of NUMERATION. NUMERATION teacheth to write any number named, and to read any number written. Obferve therefore the places, names, and value of the figures in the Table. NUMERATION TABLE &c. Hundred Thousands of Millions w Ten Thousands of Millions ~ Thousands of Millions 2 3 w Hundreds of Millions **Tens of Millions 7 3 94 7 5 5 5 1. The value of any number does not depend on the figure or figures alone, but upon the figure or figures where they ftand jointly. The order of places is backward from the right hand to the left: therefore any character is increased, in its value in a tenfold proportion as it is removed to the left of the other figures with which it is connected: as in the figures 555, the firft 5 is five ones but the fecond is 5 tens, or fifty, and the third is 5 five hundreds and fo on. Therefore the numbers in the Table are read as follows. Seven hundred and thirty two thoufands, three hundred and eighty nine millions, four hundred and fixty seven thousands, five hundred and fifty five.. 2. A cypher of itself is nothing; yet when put on the right hand of other figures, it increases their value in the fame tenfold proportion as above defcribed. Thus 47 fignifies 4 ones, but 40 fignifies four tens or forty, 400 fignifies 4 hundred, and 4coo four thousand, &e. Alfo I fignifies one, 10 ten, 100 a hundred, 1000 a thousand, and fo on; and in general ten units make one ten, ten tens make one, hundred, ten hundreds make 1 thousand, &c. 3. To be able to read twelve figures is as much as any common bufinefs requires, but you may read as many as you please by the following Rule RULE. Begin at the units place and diftinguish your figures into periods of fix figures each, and half periods of three figures each. The first period to the right is units, the 2d millions, the 3d bi-millions, the 4th tri-millions, the 5th quadri-millions, the 6th, 7th, &c. quinti-millions, fexti-millions, fepti-millions, octi-millions, noni-millions, deci-millions, &c. The first half of any period is fo many ones of it, but the last half is so many thousands of it. Example 1. Let it be required to read the following numbers, Sexti-mil, quinti-mil. quadri-mil. tri-mil, bi-mil. Millions units. th. un. th. un. th. un, the un. the un. th. un. cxtcxu 673,874. 231,043 756,131. 736;730 567;311. 726,734. 967,361. Six hundred feventy three thoufand, eight hundred feventy four fexti-millions; Two hundred thirty one thoufand, forty three quinti-mil. Seven hundred fifty fix thousand, one hundred and thirty one quadri-millions; Seven hundred thirty fix thousand, feven hundred and thirty tri-millions; Five Five hundred fixty feven thoufand, three hundred and eleven bi-millions; Seven hundred twenty fix thoufand, feven hundred thirty four millions; Nine hundred fixty feven thoufand, three hundred and fixty one. 2. It is required to exprefs in words, 3700474. 3. Write down in words 720 103467467013. 4. Write down in figures, thirty feven thousand bi-millions, three hundred forty thoufand, nine hundred and thirty four millions, two hundred five thousand, five hundred twenty four. ນ § II. SIMPLE ADDITION. IMPLE ADDITION is a rule by which feveral Snumbers of the, fame dénomination are collected ro gether. The number arifing from thofe collections is called their Sum. RULE. . 1. Place the feveral numbers under each other fo, that units may ftand under units, tens under tens, hundreds under hundreds, &c. and draw a line underneath. 100% 2. Begin at the place of units, add up all the figures in that row, and if their fum be less than ten, fet down that fum strait below; if their fum be even ten or tens, fet down a cypher; if above ten or tens, fet down the overplus, and for every ten carry an unit to the next row. 3. Add up in like manner all the figures in the tens place together with the units you carried; fet down the overplus above the even tens as before, carry the tens to the next row; and fo on to the last ; and the figures below the line will be the whole Sum. To prove addition, begin at the top, add all the figures downwards, by the fame rule as you added them upwards; if the fum is the fame the work is right. Example Example 1. Let the numbers, 8967, 890, 103, and 76, be added together. When placed down according as the rule directs, they will ftand thus ; 8967 10 3 Sum 1 0 0 36 Beginning at 6, fay 6 and 3 is 9 and 7 is 16, fet down 6 and carry 1. Then fay 1 and 7 is 8 and 9 is 17 and 6 is 23, fet down 3, and carry 2. Then 2 and 1 is 3 and 8 is II and 9 is zo, fet down o, and carry 2, laftly, 2 and 8 is 10, which being the last, fet down. It is very easy to conceive the reafon of carrying the tens to the next place; for the fum of 6, 3 and 7 being 16, the 6 belongs to the units, and the r to the tens. Again, the fum of 1, 7, 9 and 6 being 23, which are tens, the three belongs to the tens, and the 2 to the hundreds. Then the fum of 2, 1, 8, and 9 being 20, which are 20 hundreds, the 。 belongs to that place, and the 2 to the next place which is thousands. Laftly the fum of 2 and 8 is 10 i. e. 10 thousand, that is o is in the place of thou fands, and I in the place of ten thousands. Or in short, thus. The fum of the row of units 16 220 1.800 800 1 0 0 3 6 by axm 9 4:0.7.4 6 1 407.3 4907 20 Ex. 4. 26. 4 37 4 188 7610 1 0 1 37 22398 5. A perfon dying left to his Widow 5000 pounds. He bequeathed to a Charity 864 pounds; to each of his five. Nephews nephews 1765 pounds: to each of his feven nieces 1053 pounds to 10 poor Houfe-keepers 6 pounds each, and 563 pounds to his Executor; how much did he die poffeffed of Anfwer 22683 pounds. 6. From the Creation to the Flood was 1656 years; thence to the building of Solomon's Temple 1336 years; thence to the birth of Chrift 1008 years; in what year of the world was Chrift born? Answer Anno M. 4000. § III. Of Simple SUBTRACTION. the called the fubducend, from a greater, called the minuend, in order to find a third number, called the remainder, or difference. RULE. ift. Place the minuend uppermost, and the subducend under, fo as units may ftand under units, tens under tens, &c. and under them draw a line. 2. Begin at the place of units, and take each lower figure from that which stands over it, fetting the remainder ftrait under them below the line, and all those remainders together will be the required difference. 3. When the lower figure is greater than that which ftands over it, conceive ten to be added to the upper, and take the lower from the fum, fet down the remainder, carrying to be added to the next lower figure, take the fum from the upper, fet down the remainder; and fo proceed from one row to another. To prove fubtraction, add the remainder to the fubducend, and if the fum be equal to the minuend, the work is right. 1. From Take EXAMPLE 3 S. 8 0 4 2 6 7 8 the Minuend. Rem. 3 2 9 1 5 2 4 3. or difference. |