You have studied fractions so long that you should be familiar with all the definitions and processes. Therefore explanations are omitted from this book. 1. What is a fraction? 5 7 2. Tell the meaning of 3, 8, 9, J. 3. Which term of the fraction gives the size of the parts and therefore names the fraction? 4. Which term of the fraction numbers the parts? 5. Of these fractions name the improper fractions. What is an improper fraction? 6. Apply the definition of a fraction to, and state why it might be called an incorrect fraction. 7. What is a mixed number? In the list above name the mixed numbers. 8. What do you mean by reduction of fractions? 6 9. Change to halves. What principle is illustrated when fractions are reduced to their lowest terms? 10. Change to ninths. What principle of fractions is illustrated when fractions are changed to higher terms? 11. What method did you learn in Lesson 9 for reducing a fraction to its lowest terms? 22. How do you change a mixed number to an improper fraction? 1. What are similar fractions? 2. Add, a. 45, 73, 5. b. 17, 23, 412, 5%. 3. Explain addition of fractions, and give the reasons for every step. 4. The three sides of a triangle are 53 inches, 3 inches and 6 inches. What is the perimeter? 5. From 56 take 172. 6. What number must be subtracted from 1261 to leave 377? 7. A man spent of his income for rent, & for food, and 16 for clothing. What part of his income did he spend? What part of his income was left? 8. How do you multiply an integer by a fraction? 9. At $16 a ton, how much will 93 tons of hay cost? 10. State the method of multiplying a fraction by an integer. 11. Find the perimeter of a square that measures 1512 ft. 12. What is cancelation? 13. How do you multiply a fraction by a fraction? Using cancelation find the product of: 20. Find the cost of 151⁄2 tons of hay at $183 a ton. 21. If a bird can fly 91 miles in of an hour, how far can it fly in 11⁄2 hours? 22. Find 12 of 5208. Find 3 of 444. 23. A garden is 153 yd. long and 98 yd. wide. How many square yards are there in the area of the garden? 24. A strong wind giving a pressure of 141⁄2 lb. per square foot blows squarely against the end of a building 24 ft. wide and 18 ft. high. What is the total wind pressure against the end of the building? 1. State the rule for dividing a fraction by an integer. 2. Divide: a. 32 by 9. b. 1561% by 3. 3. State a rule for dividing an integer by a fraction. 4. If 31 yd. of cloth cost $10, what will 23 yd. cost? 5. What is a complex fraction? Write one. Change it to a simple fraction. 6. Show the effect upon the value of a fraction by: a. Multiplying its numerator by 2. b. Dividing its denominator by 2. c. Multiplying both numerator and denominator by 2. d. Dividing both numerator and denominator by 2. e. Multiplying its numerator by 2 and dividing its denominator by 2. f. Dividing its numerator by 2 and multiplying its denominator by 2. 8. If 15 bbl. of flour cost $63, what will 10 bbl. cost? 9. If 13 cd. of wood cost $96, what will 51⁄2 cd. cost? 10. What part of 14 is 7? Of 360 is 144? 11. In finding what part one number is of another, which number do you place as the numerator and which one as the denominator? 12. A man starts on an automobile journey of 87 miles. What part of the distance has the automobile gone when it has traveled 171⁄2 miles? 13. In a mass of ore weighing 321 pounds, 211⁄2 pounds are pure copper. What part of the whole mass is copper? 1. Read, 300.03; 5,000.005; 7.2. 2. Read the following as a, mixed decimals. b, as thousandths: 2.007; 26.027; 250.305. 3. Name the decimal places in order from tenths to billionths. 4. How do you multiply a decimal by 10? By 100? 5. How do you divide a decimal by 10? By 1000? 6. Prefixing a cipher to a decimal has what effect upon the value of the decimal? Why? 7. How should decimals be arranged for convenience in adding or subtracting? 8. Add 2.2; 1.01; 3.21. 9. From 4.4 take 3.21. 10. How do the number of decimal places in the product compare with the number in both multiplicand and multiplier? Multiply: 11. 25 by .1 14. 15 by .01 12. 2.5 by .1 15. 1.5 by .01 13. .25 by .1 16. .15 by .01 17. In dividing a decimal by a decimal what change should you first make in the position of the decimal points? 18. Can you tell why changing the position of the points as you have indicated does not change the value of the quotient? 19. Divide 2.5 by .5. After changing the points how does this example read? Divide: 20. .12 by .4 22. 1.2 by .4 24. .012 by .4 23. .24 by .06 25. .024 by .06 State this 21. 2.4 by .6 question in another form. 27. How many thousandths make a tenth? 1. Divide 9.936 by .46. 21.6 146)9/93.6 92 73 46 276 Before dividing change the divisor to an integer by moving the decimal points in both dividend and divisor as many places as there are decimal figures in the divisor. Place the decimal point in the quotient directly above the point in the dividend. Find the specific gravity of the following substances by dividing the weight of a cubic foot as given by 62.5 lb., the weight of a cubic foot of water. Carry answer to thousandths. 8. What will 16.375 casks of wine cost, if 8.1875 casks cost $982.50? 9. Divide 234.61875 by 16. 10. If .75 of a yard of cloth cost $2.40, how many yards can be bought for $38.40? 11. The sum of two numbers is 1273, and the smaller number is 49.125. Find the greater number. 12. If a man can build .425 of a rod of fence in an hour, how many rods can 12 men build in 6.5 days, working 8.25 hours a day? 13. If .35 of a cargo of 8,000 bu. of wheat were burned, what was the value of the part left at $.875 a bushel? 14. Add: twenty-six and fifteen thousandths; eighty-one thousand nine hundred ten-thousandths; eleven and twenty thousand seven hundred four hundred-millionths; twelve hundred and twelve hundred-thousandths. |