3. If the pieces were of a yard long, how many would there be? How does the number compare with the number when the pieces are ț of a yard long? 4. If-the pieces were of a yard long, how many would there be? How does the number of pieces compare with 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 1? What part of 8 times will it be contained in 1? 7. Since gis contained in 1 } of 8 times, or times, how many times will it be contained in 1? How many times in ? ?? 8. What is the value of 1:-1? Of 1: 4? 1:42 4:-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 % of a barrel each, can be filled from io of a barrel of flour? How many times is o contained in 1? 4 in q? o in z/? &- in 47? 11. How many pine-apples at $1 cach, can be bought for $1? 12. How many times is contained in 2? } in į? fin ? 13. How many times is { contained in 1? In 1? In ļ? 14. How many times is contained in 1? In }? In 3? WRITTEN EXERCISES. 1. Divide by PROCESS. ANALISIS.— } is contained in 1, 5 *=*= 4 X = 21 times; and is contained in 1, one- And since is contained in 1, f 4:$=3! = 3!= 1 times, in 4 it will be contained of = ? i times. Or, 4 is equal to {}, and is equal to št. 21 thirty-fifths are contained in 20 thirty-fifths zi times. Or, DIVISION. X 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. X When possible use cancellation. 14. What is the quotient of į of of 5; divided by of of 3? PROCESS. ANALYSIS.— In the soof of 1 of off lution of examples like this, all mixed numbers **$*¥*$*$x*=*=64 should be changed to in proper fractions, and all fractions that are factors of the divisor, inverted, and the product found as in previous examples. 15. Divide 4 of of 16 by of of 5). 23. How many pieces of ribbon 1 of a yard in length, can be made from ļof fr of a yard ? 24. If a man spends $; per day for cigars, in how many days will he spend $174? 25. How many yards of cloth at $3$ per yard can be bought for $317* ? Re 26. At $per bushel, how many bushels of potatoes can be bought for $171? 27. If a family uses of a barrel of flour a week, how long will 54 barrels last? 28. If a boy earns $daily, how long will it take him to earn $3? 29. A certain number multiplied by 1 is equal to . What is that number? 30. If a man can saw 11 cords of wood in one day, how lung will he require to saw 17} 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 $1} 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. 5 PROCESS. 4 ANALYSIS.— is an expression === *=of division, and is the same as 5 + 5, of Soler which is equal to in. 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? į of 1 apple? of 1 apple? ã of 1 apple? 4. What part of $5 is $2? $1?$1? $}? $3? 5. What part of $6 is $1? $1? $3? $ž? 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 number's can have relation to each other. 8. What is the relation of 5 to 9? What is the relation 9. Of 7 to 21 ? 10. Of 12 to 16? 11. Of 10 to 28? 12. Of 9 to 18? 15. Of 15 to 24? 18. What is the relation of to 2 ? What is the relation 19. Of f to 4? 20. Of 4 to 9? 21. Of to 6? 22. Of á to 8? to 15? 25. Of to 6? 1 28. What is the relation of to 4 ? ANALYSIS.--1 is off, and 1 is 7 times } of 5, or } of z; and since 1 is of , f of 1 is z of off, or 3 of 3. Hence is of 3. 192. A number and its relation to another number giveu, to find the other number. 1. 2 cents are 1 of how many cents? of how many cents ? 4 of how many cents? 2. 3 is of what number? ; of what number? t of what number? 3. 8 is of what number? of what number?. of what number? |