1. Compare the quotients of 24 ÷ 2 and 24+ 6. 2. Compare 380 ÷ 10 and 380 ÷ 5. 3. If 38 is the quotient of some number divided by 10, 2 x 38 is the quotient of the same number divided by what? 4. Explain: 320 ÷ 5 = 2 x 320 ÷ 10 = 64. 7. Compare 375 ÷ 25 with 4 × 375 ÷ 100. 8. Explain: 925 ÷ 25 = 4 × 925 ÷ 100 = 3700 ÷ 100 = 37. In the same way divide the following by 25:· : 18. 96 ÷ 163 =? × 96 ÷ 100. 19. Make a rule for dividing by 163. 20. Make a rule for dividing by 331. Use these rules in finding quotients in the following: 33. How many will $3 buy at $0.25 each? 34. How many yards will $5 buy at 163 cents a yard? 35. I paid $8 for tea at 331 cents a pound. How many pounds did I buy? 36. My milk bill was $8.75 at 25 cents per gallon. How many gallons did I buy? as in 3+4 × 5=35, shows that () as in (3+4) x 5 = 35, or the numbers inclosed or beneath are to be treated as one number. 1. (96) x (8-5)=x; 3+7 × 10 − 5 = x. - 2. 3 × 52+7= x; 4 × 102+50=x; 27÷3-√4 = x. 3. 52-5×2=x; 18-3÷√25=x; (10-4)+6-3=x. Observe the following and tell which process is performed first when x or is on one side of a number and + or 4. 3+4x5=3+20=23. 5. 4+16÷8 = 4+2 = 6. on the other: 6. 6 x 12-8÷2-72-4 = 68. 7.5 x 15+24÷6 = 75+4=79. 8. Compare in value 13 – 5 x 2 + 8 and (13—5) × (2 +8). 9. 364-45 ÷ 9=x. 11. of (7+14) — 4 of (37 — 9) = x. 10. 2+5x6+8+2=x. 12. of (41-16) + of (19-7)=x. } 13. What expressions are here marked to be treated as one number? 8 × 16÷8+8 × (16 − 9) = √3 × 9 × 3 × 108 ÷ 12 − 10 + 1. (6 × 5+ 4 × 9) ÷ 11 = [(6 +5) × (10 − 4)]÷ 11. 22. Show why it was better to use brackets [ ] than curves ( ). 26. [(17+39)2 + ÷√64=x. 27. (12 × 4+6 × 12) ÷ √100 · =x. x=12+25 means that x stands for some number which is equal to the sum of 12 + 25, hence x=37. Find the value of x in the following: 16. I am x years old; in 8 years my age will be 36 years. 17. After taking $ 14, $ 16, and $12 out of a sum of money $3.75 remained. There were $x at first. х $14 — $16 – $12 = $3.75. 18. A prize cup contains 23 oz. of gold, 10 oz. of silver, and x oz. of alloy. The cup weighs 42 oz. (Make an equation.) 19. 25 gallons run into a tank, were closed, 80 gallons remained. There were a gallons in the tank when the faucets were opened. (Equations.) 20. Make a problem about the weather in March to suit this equation: 31 da. = 12 da. + x da. +10 da. 3x means 3×x. 3x=15 means that 3 times some number equals 15. Find the value of x in the following and explain your method :· 1. If 16 cords of wood cost $120, 24 cords will cost what? In solving such a problem, which of these suggestions seem most important? I. What is to be found out? (Cost of 24 cords.) II. What facts will help to find this? (16 cords cost $120.) III. Comparison of what is given to what is wanted. (24 cords will cost 1 times as much as 16 cords.) IV. Process, briefly set down. (1 × $120 cost of 24 cords.) V. Work performed. (1 x $120 $120+ $60 = $180.) VI. Does the result seem reasonable? = 2. Bought 12 lb. tea at 754, and 20 lb. coffee at 40%. How much butter at 30% would cost the same? 3. Exchanged a 60-acre farm worth $2400 for 200 acres of woodland valued at $13.75 an acre. Find the gain. STATEMENT. 200 x $13.75 - $2400 = x. 4. Gave 3000 sq. ft. of 20 land for a span of horses and $75. What were the horses valued at? STATEMENT. 3000 x $0.20 - $75 = x. 5. A man purchased 130 bbl. of flour at $4.50 per barrel, and a number of barrels at $4. He paid $665. How many barrels of the cheaper flour did he buy? 6. Sixty-four men are employed 25 days in digging a sewer. The contract price was $1200. Nothing was gained or lost. What were the men paid each per day? 7. If 14 lb. cost $2.94, what will 10 lb. cost? 8. If 17 tons of coal cost $134, what will 51 tons cost? Applying the suggestions on the preceding page, state the following and explain orally: 1. I bought a field of 10 acres for $1000. I sold 7 acres of it at $125 an acre, and the remainder at $85 an acre. How much did I gain? 2. I sold 50 acres of land for $5000. This was a loss of $15 per acre. What did the land cost me? 3. A boat goes 10 miles an hour downstream and 6 miles an hour upstream. How long does it take to go 30 miles and return? 4. If 15 men can do a piece of work in 90 days, how long will it take 6 men? 5. If 14 bbl. of apples are worth $35, what are 21 bbl. worth? 6. A train runs 280 miles in 11 hours. Seven 3-minute stops are made, and a hot axle makes a detention of 39 minutes. The rate per hour was a miles. 7. Six men buy 640 acres at $125, and sell for $95,000. Each man gains of ($95,000 - 640 × $125) = each man's gain. In the statement what represents the cost of the land? The proceeds of the sale? The whole gain? 8. Bought 39 bbl. of flour at $4.75; sold 15 bbl. at $5, and the remainder at $5.25. Required, my gain. 9. Three 1-pound packages will go by mail each for 1¢ an ounce plus registration; by express, for 25 each. Which way is cheaper? 10. A peck, 2 bushels, and 5 quarts are to be divided equally among 7 persons. Any two receive a quarts. 11. I spent $4485 for cattle and horses, buying the same number of each. If I paid $75 apiece for the horses, and $40 each for the cows, how many of each did I buy? SUGGESTION. What did 1 horse and 1 cow cost? Then how many times can I buy a horse and a cow with $4485? |