How many sevenths are there in a single thing? How many sevenths are there in two things? How many sevenths are there in three things? How many in four? How many in five? How many in six? How many in seven? How many in eight? How many in nine? How many in ten? 7. If a single thing be divided into eight equal parts, each part is called an eighth. How many eighths are there in one thing? How many in two things? How many in three? How many in four ? How many in five? How many in six? How many in seven? How many in eight? How many in nine? How many in ten? 8. If a single thing be divided into nine equal parts, each part is called a ninth. How many ninths are there in one thing? How many ninths are there in two things? How many ninths are there in three? How many in four? How many in five? How many in six? How many in seven? How many in eight? How many in nine? How many in ten? 9. If a single thing be divided into ten equal parts, each part is called a tenth. How many tenths are there in one thing? How many tenths are there in two things? How many in three things? How many in four? How many in five! How many in six? How many in seven? How many in eight? How many in nine? How many in ten? 10. How many halves make five? How many halves make nine? How many halves make fifteen? How many halves make eighteen? How many halves make twentyfive? How many halves make twenty-two? 11. How many things in three-thirds? Answer. One. How many things in four-thirds? Ans. One and onethird. How many in five-thirds? Ans. One and twothirds. How many in six-thirds? How many in seventhirds? How many in eight-thirds? How many in ninethirds? How many in ten-thirds. 12. How many things are there in four-fourths? Ans. One. How many things are there in five-fourths? Ans. One and one-fourth. How many things in six-fourths? How many in seven-fourths? How many in eight-fourths? How many in nine-fourths? How many in ten-fourths?. How many in eleven-fourths? How many in twelvefourths? 13. How many things are there in five-fifths? Ans. One. How many things are there in six-fifths? Ans. One and one-fifth. How many in seven-fifths? How many in eight-fifths? How many in nine-fifths? How many in ten-fifths? How many in eleven-fifths? How many in twelve-fifths? How many in thirteen-fifths? How many in fourteen-fifths? How many in fifteen-fifths? 14. How many things are there in six-sixths? Ans. One. How many are there in seven-sixths? Ans. One and one-sixth? How many in eight-sixths? How many in nine-sixths? How many in ten-sixths? How many in eleven-sixths? How many in twelve-sixths? 15. How many things are there in seven-sevenths? Ans. One. How many things are there in eight-sevenths? Ans. One and one-seventh. How many in nine-sevenths? How many in ten-sevenths? How many in eleven-sevenths? How many in twelve-sevenths? How many in thirteen-sevenths? How many in fourteen-sevenths? 16. How many things are there in eight-eighths. Ans. One. How many things are there in nine-eighths? Ans. One and one-eighth. How many in ten eighths? How many in eleven-eighths? How many in twelve-eighths? How many in thirteen-eighths? How many in fourteeneighths? How many in fifteen-eighths? How many in sixteen-eighths? 17. How many things are there in nine-ninths? Ans. One. How many things are there in ten-ninths? Ans. One and one-ninth. How many things are there in elevenninths? How many in twelve-ninths? How many in thirteen-ninths? How many in fourteen-ninths? many in fifteen-ninths? How many in sixteen-ninths? How many in seventeen-ninths? How many in eighteenninths? How 18. How many things are there in ten-tenths? Ans. One. How many things are there in eleven-tenths? Ans. One and one-tenth? How many in twelve-tenths? How many in thirteen-tenths? How many in fourteen-tenths? How many in fifteen-tenths? How many in sixteen-tenths? How many in seventeen-tenths? How many in eighteen tenths? How many in nineteen-tenths? How many in twenty-tenths? 19. If you pay twelve dollars for two weeks board, how much is that for one week? If you pay three dollars a week for board, how much will you pay for five weeks? If you travel four miles an hour, how far can you go in ten hours? If you travel sixty miles in four hours, how far will you travel in one hour? 20. If you pay eight dollars for a piece of cloth containing sixteen yards, how much do you pay for a yard? If you pay twenty dollars for a piece of cloth containing five yards, how much do you pay for a yard? 21. If you pay thirty cents for ten oranges, how much is that apiece? If you pay three cents apiece for twelve oranges, how much will they come to? 22. If you pay four cents for a knife, six cents for a jews-harp, and eight cents for a dozen marbles, how much do they all cost? 23. If you pay one dollar for a pair of shoes, three dollars for a hat, and six dollars for a coat, what do they all cost? If you pay twelve cents for tape, nine cents for riband, and eight cents for pins, what do they all cost? 24. If you buy a cow for eight dollars, three sheep at two dollars apiece, and a horse for one hundred dollars, what do they all come to? 25. A yoke of oxen costs seventy-five dollars, and a horse seventy-five dollars, what do they come to? 26. My coat costs me twenty-eight dollars, my pantaloons twelve dollars, and my vest five dollars, what does the whole suit cost me? ! 27. My hat costs eight dollars, my boots seven dollars, and my over-coat twenty-nine dollars, what do they all cost? 28. A man buys a pair of horses for one hundred dollars, and three more horses for sixty dollars each, what do they all cost him? Each word, one, two, three, four, five, six, &c., points out how many things are spoken of. These words are called NUMBERS. Hence, NUMBERS are the expressions for several things of the same kind. Questions. What is a single thing called? One and one? Two and one? Three and one? Four and one? Five and one? Six and one? Seven and one? &c. What are Numbers? § 2. The unit of a number is one of the equal things which the number expresses. Thus, if the number be six apples, one apple is the unit; if it be five pounds of tea, one pound of tea is the unit; if it be ten feet of length, one foot is the unit; if it be four hours of time, one hour is the unit. Q. What is the unit of a number? What is the unit of the number six apples? Of the number five pounds of tea? Of the number ten feet? Of the number four hours? § 3. ARITHMETIC treats of numbers. Numbers are expressed by certain characters, called figures. ten of these characters. They are O which is called a cipher, or Naught, 1 2 There are One, Two, Three, Four, Five, Six, Seven, Eight, Nine. Q. Of what does arithmetic treat? How are numbers expressed? How many figures are there? Name them. § 4. The character 0 is used to denote the absence of a thing. As, if we wish to express by figures that there are no apples in a basket, we write, the number of apples in the basket is 0. The nine other figures are called. significant figures, or Digits. 1 expresses a single thing, or a unit of a number. 23456789 two things of the same kind, or two units. three things four things five things nine things or three units. or four units. or five units. or six units. or seven units. or eight units. or nine units. Q. What does 0 express? What are the nine other figures called? How many things does 1 express? How many things does 2 express? How many units in 3? In 4? In 5? In 6? In 7? In 8? In 9? § 5. If we wish to express the number ten, we have no separate character for it. We must combine the characters already known. This we do by writing 0 on the right hand of the 1; thus, 10, which is read ten. This 10 is equal to ten of the units expressed by 1. It is, however, but a single ten, and in this sense may be regarded as a unit, the value of which is ten times greater |