8. What part of 1 year is 3 months? 9. What part of 1 gallon is 3 quarts? 10. 2 feet is what part of 1 yard? 97. To find what fractional part one number is of another: Take the number which denotes the part for the numerator and the number which denotes the whole for the denominator. Exercises in finding Fractional Parts 98. 1. A football team played 12 games and lost 3. What part of their games did they lose? What part did they win? 2. A man had $50 and spent $8 What part of his money did he spend? did he have left? for a coat. What part 3. From a barrel containing 31 gallons of oil 6 gallons are taken. What part of the whole remained? 4. A man had 1250 acres of land and sold 350 What part of his land had he left? acres. 5. A man had 750 sheep and sold 240 of them. What part of his flock did he sell? 6. 350 is what part of 900? 7. What part of 750 is 200? 8. 165 is what part of 660? 9. What part of 10000 is 875? 10. 125 is what part of 2000? FINDING THE WHOLE FROM A FRACTIONAL PART 99. 1. If of an acre of land is worth $36, what is 1 acre worth? acres are worth $36. 1 acre is worth $36 or $96. Ans. Note. The "old line" analysis and solution for this class of examples may be used if it be preferred. It was as follows: If acres are worth $36, acre is worth of $36, or $12. or 1 acre is worth 8 times $ 12 or $96. 66 This form is often confusing to the child, especially in oral analysis, if he give it in full and states that “} is worth },” etc., as a part of the analysis. 39 If the fraction is considered as an entire expression of quantity, as 12, 15, or 18 would be considered if used in its place, the analysis becomes very simple, establishes a type form for general application, and the child is less likely to make errors in its application. If 3 acres cost $36, what will 1 acre cost? If acres cost $36, what will 1 acre cost? If 2 acres cost $36, what will 1 acre cost? If .25 acres cost $36, what will 1 acre cost? Exercises like those just given may all be placed under the general type of " dividing the given cost by the given quantity to find the cost of 1." yard of cloth. 2. Paid 60 for 3 yards cost at that rate? What would 3. Paid 75 for 6 yards of cloth. What will 31 yards cost at that rate? 4. If 31 acres of land cost $252, what will 51 acres cost? 5. If of a farm is worth $1500, what is the value of the whole farm? G After losing a part of the money, a man had $60 or of it left. How much did he lose? 7. If a train runs 36 miles in of an hour, how far will it run in 24 hours at the same rate? 8. After spending of his money, a man has $50 left. How much had he at first? 9. In a school of the pupils are girls and there are 360 boys. How many pupils in the school? 10. If yard of cloth cost 15, what will 5 yards cost at the same rate? 11. A farmer had of his sheep in one pasture, in another, and the remainder, which was 77, in the third pasture. How many sheep had he? + 1 = 9 2 part in the first and second pastures. 28-21 in the third pasture. = of the entire number of sheep = 77. Entire number of sheep=77+11=140. Ans. 12. A man lost of his money, then earned $18, when he had as much as he had at first. How much had he at first? 13. A man spends $1500 a year, which is of his income. How much is his income? 14. At the rate of 3 for 54, what will 18 oranges cost? 15. There are 1200 girls in a school and they are of the entire number of pupils. How many pupils in the school? 16. If of the cost of a farm is $1500, what is the value of the entire farm at the same rate? of 17. At the rate of 8 for 25, what will 1 dozen eggs cost? 18. Henry spilled of his berries and had 8 quarts left. How many quarts of berries had he at first? 19. If of a ton of hay cost $7.50, what part of a ton can be bought for $15? 20. If of a cord of wood costs $4, what will 21 cords cost at the same rate? CHANGING FRACTIONS TO DECIMALS AND DECIMALS TO FRACTIONS Changing Decimals to Common Fractions 100. 1. Change .5 to a common fraction. 2. Change .05 to a common fraction. .05=150-20 Ans. 3. Change .005 to a common fraction. .005=1000=200 Ans. 4. Change .075 to a common fraction. 3 .075=1750-40 Ans. 5. Change 8.075 to fractional form. Reduce the following to their simplest fractional forms: 6. 28125. 10. 4.025. 14. .9375. 18. 5.0008. 7. .0625. 11. 6.875. 15. 4.125. 19. 6.0075. 8. 65.625. 16. .0325. 20. 15.0015. 9. .6875. 12. .0875. 13. .16. 17. 4.1575. Changing Common Fractions to Decimal Form Introduction 101. 1. Reduce to a decimal. .5 Ans. 2)1.0 2. Reduce to a decimal. .25 Ans. 4)1.00 3. Reduce to a decimal. .375 Ans. 8)3.000 102. To change a fraction to a decimal divide the numerator by the denominator. 103. Change the following fractions to decimal |