To multiply a Fraction by a Whole Number,... To multiply a Whole Number by a Fraction,.. To multiply one Fraction by another,.. To find the Least Common Multiple of two or more Numbers,...... 119 To find the Greatest Common Divison of two or more Numbers, (reference,; 120 To reduce Fractions of Difforent Denominators to a Common Denominator, 122 Subtraction of Fractions,.......... Division of Fractions—To divide a fraction by a Whole Number,.........128 So divide a Whole Number by a Fraction,..... To divide one Fraction by another,.. To reduce Whole Numbers to the Fraction of a greater Denomination,.....131 To reduce a Fraction 10 Whole Numbers of less Denominations,..........132 To reduce Fructions of a higher Denomination to a lower,.. To reduce Fractions of a lower Denomination into a higher,... DECIMALS.-Their Table of Notation,.. To change Vulgar or Common Fractions to Decimals,. Circulating Decimals, (reference,)....: To reduce Compound Numbers to Decimuis of the highes' Denomination,.. 149 To reduce Decimals of higher Denominations to Whole Numbers of lower ....171 ..179 Concise Rule for calculating Interest in New York Statc,.. Commission, Insurance, Stock, Loss and Gain,... Time, Rate per cent., and Amount, given, to find the Principal,.. Time, Rate per cent., and Interest, being given, to find the Principal,......176 The Principal, Interest, and Time, being given, to find the Rate per cent.,. . 176 The Principal, Rate per cent., and Interest, being given, to find the Time...178 Compound Interest Compound Interest by Table,.. Ratio, or the Relation ul Numbers, Proportion arising from Ratio, or from Multiplication and Division,.... .189 Application of Ratio by Rule,.. Rule of Three in Vulgar and Decimal Fractions,.. Compound Proportion, or Double Rule of Three, hy Ratio and Analysis,...198 Questions on the foregoing...... To compute the Interest on Notes with Endorsements—three inodes......207 Practice in Compound Numbers,.... Fellowship_by Analysis—by Ratio... Compound Fellowship-by Analysis—by Ratio,.......... Mensuration-Square Measure,....... Duodccimalg Multiplication of Duodecimals,...................... To calculate Difference in Time, Tare and Trett, ez. 16, 17,... .231 | Position by Fractions, ex. 66-76. 240 Method of assessing taxes, ex. 12, 13, 215 .221 ....223 Alligation- Alligation Medial,. Extraction of the Square Root--its Application,. Extraction of the Cube Root-its Application,.. Geoinetrical Progression,..... Annuities at Simple Interest,. To find the Area of a Triangle, Tho Diameter of a Circle being given, to find the Circumference.. ..273 The Circumference of a Circle being given, to find i he Diameter,. 273 To find the Solid Contents of a Globo, To find the Solid Contents of a Cylinder, To find the Said Contents of a Pyramid,. SUGGESTIONS TO TEACHERS ON THE METHOD OF USING THIS WORK. For a course of Mental Arithmetic, adapted to the capacities of very young pupils, they may take the Mental Exercises in each: rule, as far as the first Example for the Slate. This course is not meant to include any of the exercises style.l“ Questions wil the firregoiny." This course embraces the whole of the first 27 pages, together with the Arithmetical Tables, extending to the Appendix. The necessity of impressing these Tables on the minds of pupils at an early age is sufficiently obvious. When tho pupil is perfect masier otilis course, as will, most probably, be the case attor one or two revie(13, the teacher will find no difficulty in making him understand the Operations loy Slate. lle may then take the wholo in course. In every school, it would be well to institute classes; and ns there are seldom any answers given to tre mental questions, the pupils may be allowed to real in their turns the questions from the book ; thus giving the teacher no further trouble than occasional corrections. By this, the reader will perceive, that the work may be used 10 advantage in monitorial schools, as the former editions have been In large schools, these corrections may be made by an advanced scholar, instead of the teacher. Whenever an advance scholar takes tip the book with a view of proditing from it, he should omit nothing as he progressos; but make it his practice to qualify liimself to answer any question, in the mental exercises, rules, or respecting the reason of the operations. Teachers will find it to be a useful occupation for their scholars, to assign themi il fiorning kisson, to be recited as soon as they come into school. With little exception on the part of teachers, pupils in this way may be made assiduous and ambitious, very much tu their advantage, and to the credit of their teachers. The mental questions, under the head of “ Questions on the foregoing," will, intelligently answered, furnishi lu committees un admirable test of the pupil's knowledge of this subject. The Appendix is designed for those who have time and opportunity to devoto to the study of'ilic more abstruse parts of Mathematics. Nute.-Lest some may mistake the object of the figures annexed to the ques tions, in my here be remarked, that those figures are separate answers, left without it signing ally valne to them, reserving this particular for the discretion oltines poupil, whirl he must neressarily excrrise, in order to obtain the answer which follows, Urut being the aggregate of the whole. Trichort directions are those which seem the best to the author ; but ng every intelligensie traclar has a way of his own, which, though not intrinsically the best, is, perhaps, the besi funding the subject is icspecifully submitted to lais uw choice. many have 'T I.* 1. How many little fingers have you on your right hand? How many on your left? How many on both ? 2. How many eyes have you? 3. If you have two apples in one hand, and one in the other, how many have you in both ? How many are two and one, then, put together? 4. How many do your ears and eyes make, counted together? 5. If you have two nuts in one hand, and two in the other, how you in both? How many do two and two make, put together? 6. If you have three pins in one hand, and James puts another in, how many will you have in your hand ? How many are three and one then ? 7. If you have three pins in one hand, and James puts two more in, how many will you have in your hand? How many are three and two then? 8. If you have four apples in one pocket, and two in the other, how many will you have in both ? How many are four and two then ? 9. Thomas has four cents, and William has three ; how many have they both together? How many are four and three then? 10. You have five pins in one hand, and three in the * The questions in [ I and T II are intended for very young children. Older pupils may omit these. But the two remaining sections, and the four tables, will claim an attentive perusal. other; how many have you in both ? How many are five and three then? 11. You have four nuts in one hand, and four in the other; how many have you in both ? How many are four and four then ? 12. If you count the fingers and thumb on one hand, and only the fingers on the other, how many will they make ? How many are five and four then? 13. How many fingers and thumbs have you on both hands? 14. James has five marbles, and Thomas five; how many have they both ? How many are five and five then ? 15. How many cents would it take to buy two whistles, if one cost six cents, and the other four? How many are six and four then? 16. If you have eight pins on one sleeve, and two on the other, how many will you have on both ? How many are eight and tivo then? 17. How many legs have two cats and a bird ? 18. If I should give you six cents, and you should find five, how many would you have then? How many are six and five then ? 19. If you count all your fingers, thumbs, and nose, how many will they make ? 20. If you buy a picture-book for ten cents, and a pear for two cents, how many cents will pay for both ? How many are ten and two then ? 21. How much money would you have, if your father should give you seven cents, and your brother six ? How many are seven and six then ? 22. If you have seven pins in one hand, and seven in the other, how many will you have in both ? How many are seven and seven then? 23. A man bought a chair for three dollars, and a lookingglass for twelve; how much did he give for both ? How many are three and twelve then? 24. You give thirteen cents for a spelling-book, and three for an inkstand ; how much do they come to? How many are thirteen and three? 25. Count one hundred. One .. 1 Six 6 Two.. 2 Seven 7 Three 3 Eight 8 Tour 4 Nine 9 Tivo 5 Ten. 10 |