1. If 7 yards of cloth cost $47, what is the price per yard? 2. If a man spends $3 per day for cigars, in how many days will he spend $171? 3. If of a ton of hay costs $15, what is the cost of one ton? 4. A man has 2291 pounds of honey, which he wishes to pack in boxes containing 8 pounds each. How many boxes will he require? 5. A man owning 15 of a ship, sold of his share, and divided the remainder equally among his three sons. What part of the ship did each son own? 6. The product of two numbers is 1, and one of the numbers is 114. What is the other number? 7. What number multiplied by 18 will produce 143? 8. How many yards of cloth at $3 per yard can be bought for $317/? 9. When wheat is selling at $13 per bushel, how many bushels can be bought for $3168? 10. For $87 how many thousand feet of gas at $11 per thousand can be bought? COMPLEX FRACTIONS. A Complex Fraction has a fraction in one or both of its # # 41 % of & terms; as, 4' 7' 58' 4 ק divided by 61, we proceed according to the rule for division, and obtain §. FRACTIONAL RELATIONS. 1. In the equation, of 4 = 2, the expresses the relation of 2 to 4. If the question is asked, "What is the fractional relation of 2 to 4?" the answer simply reverses the equation, -"2 of 4." = = This equation may be derived analytically, thus: Since 1 of 4, 2, being twice 1, or of 4. 2. In like manner show the fractional relation of 3 to 9. Of 5 to 8. What part of 8 is 5? Does the answer show the relation of 5 to 8? 3. What part of $5 is $1? of $5, $1, being 1⁄2 of $1, = 1 of 1 of five dollars, or of five dollars. 4. In like manner find the fractional relation of $3 to $6. 5. What part of 7 acres is of an acre? 6. Is $5 any part of 10 acres? 7. What is the fractional relation of 7 men to 9 trees? PRINCIPLE. Only like numbers can have fractional relation to each other. EXERCISES. To find the Fractional Relation between Two Numbers. 1. Form an equation to show the fractional relation of: To find a Number from its Fractional Relation to Another 18 2. If the question arise, 3 is of what number? what is the answer? 3. The analytical answer is what? Suggestion of the number 3;, the whole of the number, =what? 7. Suggestion of the number of 14. is of what number? 8. 24 is 12 of what number? 9. 8 is 144 of what number? 10. of 3 is of what number? REVIEW. 1. The sum of two fractions is §, and their difference is 4. Required the fractions. Suggestion: Were the difference 0, the fractions would be and . Hence the greater fraction of; the less — of . 2. If a man can cut in one day of a field containing 7 acres of wheat, how many acres can he cut in of a day? 3. Reduce, and to equivalent fractions whose denominators shall be 24. 4. Add 14, 1, 4ğ, 5. Find the value of 153, and explain fully. 2114 |