Mental Exercises combined with Exercises for the Slate. COMPOUND NUMBERS. Federal Money, different Denominations,.... Subtraction of Federal Money,.. Multiplication of Federal Money,.. Questions on the foregoing—Bills of goods sold, 105 Fractions arise from Division,..........................................108 To change a Mixed Number to an Improper Fraction,.... To reduce a Fraction to its lowest Terms, ........108 ..........18 To multiply a Fraction by a Whole Number,.. ...................113 To multiply a Whole Number by a Fraction,........................ To multiply one Fraction by another,............ To find the Least Common Multiple of iwo or more Numbers,.... ....119 To find the G-eatest Common Divisor of two or more Numbers, (reference,) 120 To reduce Fractions of Different Denominators to a Common Denominator, 122 Division of Fractions—To divide a Fraction by a Whole Number,.........128 To divide a Whole Num)ser by a Fraction,.. To divide one Fraction by another, To reduce Whole Numbers to the Fraction of a greater Denomination,.....13) To reduce a Fraction to Whole Numbers of less Denominations,.. .132 To reduce Fractions of a higher Denomination to a lower,.. To reduce Fractions of a lower Denomination into a higher,.. 135 DECIMALS.-Their Table of Notation,..... Multiplication of Decimals,.... To change Vulgar or Common Fractions to Decimals,. Circulating Decimals, (reference,)... To reduce Compound Numbers to Decimals of the highest Denomination,.,149 To reduce Decimals of higher Denominations to Whole Numbers of lower ....144 .......163 .......171 ..188 ...189 Concise Rule for calculating Interest in New York State,. Commission, Insurance, Stock, Loss and Gain,.... Time, Rate per cent., and Amount, given, to find the Principal,... .173 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, Rase per cent., and Interest, being given, to find the Time,...178 Compound Interest-Compound Interest by Table, Rule of Tlıree, by Analysis,.. Ratio, or the Relation of Numbers,. J.92 Rule of Thrce in Vulgar and Decimal Fractions, Compound Proportion, cr Double Rule of Three, by Ratio and Analysis,...198 To compute the Interest on Notes with Endorsements--three modes,.. Practice in. Con poun' Numbers,.. Fellowship-by Analysis by Patio,.. Solid, or Cubi • 1 easu ,..... .221 Duodecimals Mu'tiplic ition of Duodecimals,...................., .225, 227 ex.55-64,........... .231 | Position by I 'ractions, ex. 66–76. 240 Barter, er. V-3), ..234 | Discourt, .. .174 Method of assessin, tax 's ex. 12,13, 215 ..196 Alligation-Alligation Medial,.. Extraction of the Square Root-its Application,.. Extraction of the Cube Root-its Application,... Arithinetical Progression,.... The Diameter of a Circle beirg given, to find the Circumference,.. The Circumference of a Circie being given, to find the Diameter,. To find the Area of a Circle,... To find the Solid Contents of a Globe,.. To find the Solid Contents of a Cylinder, To find the Solid Contents of a Pyramid, SUGGESTIONS TO TEACHERS ON THE METHOD OF USING THIS WORK. t'or 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 an of the exercises otyled“ Questions on the foregoing." This course embraces the whole of the first 27 pages, together with tn, Arith metical Tables, extending to the Appendix. The necessity of impressing these Tables on the minds of pupils at an early age is sufficiently obvious. When the nupil is perfect master of this course, as will, most probably, be the case after one or two reviews, the teacher will' find no difficulty in making him understand the Operations by Slate. He may then take the whole in course. In every school, it would be well to institute classes; and as there are seldom any answers given to the mental questions, the pupils may be allowed to read 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 to advantage in monitorial schools, as the former editions have heen. In Jarge schools, these corrections may be made by an advanced scholar, instead of the teacher. Whenever an advanced scholar takes up the book with a view of profiting from it, he should omit nothing as he progresses, but make it his practice to qualify himself 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 them a morning lesson, to be recited as soon as they come into school. With little exertion on the part of teachers, pupils in this way may be made assiduous al ambitious, very much to their advantage, and to the credit of their teachers. The mental questions, under the head of “ Questions on the foregoing," will, intelligently answered, furnish to committees an admirable test of the pupil's knowledge of this subject. The Appendix is designed for those who have time and opportunity to devota in the study of the more abstruse parts of Mathematics. Note.-Lest some may mistake the object of the figures annexed to the ques. sous, it may here be remarked, that these figures are separate answers, left without assigning any value to them, reserving this particuiar for the discretion of the papil, which he must necessarily exercise, in order to obtain the answer which follows, that being the aggregate of the whole. The above directions are those which scem the best to the author; but as every intelligent teacher has a way of his own, which, though not intrinsically the best, is, perhaps, the best for him, tho subject is respectfully submitted to his own choice. ARITHMETIC. ADDITION. 9 1.* 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 to gether? 5. If you have two nuts in one hand, and two in the other, how many have 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 I and IT II are intended for very young children. Older pupils may omit these. But the two remaining sections, and the four tablos. will claim an attentive perusa). 1 |