3. If the pieces were of a yard long, how many would How does the number compare with the number there be? when the pieces are of a yard long? of a yard long, how many would number of pieces compare with the 4. If the pieces were there be? How does the number when the pieces are of a yard long? 5. How many times is contained in 1? ? ? ? ? 6. Since is contained in 1, eight times, how many times. will it be contained in? What part of 8 times will it be contained in? ?? 7. Since is contained in 1 of 8 times, or times, how many times will it be contained in? How many times in ? ? ?? 8. What is the value of 1÷? Of 1÷3? 1÷3? 3÷÷4? 9. Into how many parts of 3 eighths of a dollar each, can 6 eighths of a dollar be divided? 10. How many sacks containing filled from of a barrel of flour? contained in? in ? in ? of a barrel each, can be How many times is 3 4 in 4? 47 11. How many pine-apples at $1 each, can be bought for $1? PROCESS. Or, ANALYSIS. is contained in 1, 5 times; and is contained in 1, onethird of 5 times, or times. And since is contained in 1, § times, in it will be contained ‡ of = times. Or, is equal to 3, and is equal to 3. 21 thirty-fifths are contained in 20 thirty-fifths times. DIVISION. RULE.-Multiply the dividend by the divisor inverted.) Or, Reduce the dividend and divisor to similar fractions and divide the numerator of the dividend by the numerator of the divisor. 14. What is the quotient of 3 of 3 of 53 divided by 3 of should be changed to inproper fractions, and all fractions that are factors of the divisor, inverted, and the product found as in previous examples. 15. Divide of of 16 by & of 4 of 51. 16. Divide of 13 of 5 by 41 times of 16. 17. Divide of of 4 by 4 of 4. of by 5 times 3 of §. of 15 by 3 of 5 of 6. off of 22 by of 1⁄2 of 16. 18. Divide of 19. Divide of 20. Divide 21. Divide 22. Divide 8 of 33 of 6 by 3 of 6 times 13. times of 7 by & of 3 of 5. 23. How many pieces of ribbon can be made from of of a yard? of a yard in length, 24. If a man spends $3 per day for cigars, in how many days will he spend $171⁄2? 25. How many yards of cloth at $3 per yard can be bought for $317?? 26. At $3 per bushel, how many bushels of potatoes can be bought for $174? 27. If a family uses of a barrel of flour a week, how long will 5 barrels last? 28. If a boy earns $ daily, how long will it take him to earn $33? 29. A certain number multiplied by is equal to . What is that number? 30. If a man can saw 1 long will he require to saw 17 cords of wood in one day, how cords? 31. If a horse eats 12 bushels of oats in 5 weeks, how much does he eat in a day? 32. When wheat is selling at $13 per bushel, how many bushels can be bought for $3168? FRACTIONAL FORMS. 189. Expressions of unexecuted division are often written in the form of a fraction. 190. A fractional form having an integral denominator and a fractional numerator is called a Complex Fraction. Thus, and are complex fractions. Expressions which have a fraction in the denominator can not properly be regarded as Complex Fractions, though they are commonly classified as such. 1. Find the value of the fractional form PROCESS. x= 3 4 21 ANALYSIS.- a is an expression X=2of division, and is the same as §÷3, which is equal to . 191. To find the relation of one number to another. 1. What part of 5 cents is 1 cent? 2 cents? 3 cents? 4 cents? 2. What part of 9 acres is 5 acres? 7 acres? 3 acres? 4 acres? 3. What part of 4 apples is 1 apple? of 1 apple? of 1 apple? of 1 apple? 4. What part of $5 is $2? $1? $1? $1? $3? 5. What part of $6 is $1? $1? $1? $? 6. Henry had $5 and gave his brother $3. What part of his money did he give his brother? 7. James earned $7, and his brother $2. What part of the whole did each earn? PRINCIPLE.-Only like numbers can have relation to each other. 8. What is the relation of 5 to 9? ANALYSIS.-1 is of 9, and 5 is 5 times of 9, or, . ANALYSIS.-is of, and 1 is 7 times of, or of; and since 192. A number and its relation to another number given, to find the other number. 1. 2 cents are of how many cents? of how many cents? of how many cents? 2. 3 is of what number? of what number? of what number? 3. 8 is of what number? of what number?. of what number? |