SECTION VII. RELATION OF NUMBERS. CASE I. The Relation of Whole Numbers to Whole Numbers. ORAL EXERCISE. 1. Twelve is how many times 4? 2. What is the relation of 10 to 5? Ans. 10 is 2 times 5. What is the relation— 6. If 4 pens cost 6 cents, how much will 20 pens cost? SOLUTION.-If 4 pens cost 6 cents, 20 pens, or 5 times 4 pens, will cost 5 times 6 cents, or 30 cents. Hence, if 4 pens cost 6 cents, 20 pens will cost 30 cents. 7. What will 15 slates cost if 5 slates cost 80 cents? 8. What will 48 trees cost if 4 trees cost 75 cents? 9. If 9 chickens cost $2.25, how much will 18 chickens cost? 10. If 27 oranges cost 90 cents, how much will 9 oranges cost? 11. If $24 will buy 15 turkeys, how many turkeys will $8 buy? 12. If 18 chickens cost $4.20, how much will 3 chickens cost? 13. A man can travel 33 miles in 9 hours: how far can he travel in 3 hours? 14. If 12 pairs of boots cost $40, how much will 3 pairs cost? 15. If 12 men can earn $36 in a day, how much can 4 men earn in the same time? 16. If 5 men can eat 2 loaves of bread, how many loaves can 15 men eat in the same time? WRITTEN PROBLEMS. 1. If 12 pens cost 14 cents, how much will 60 SOLUTION. 60=5×12 14×5=70 pens cost? NOTE. Let the pupil give explanations similar to solution of Problem No. 6, on preceding page. 2. If 13 horses cost $1250, how much will 39 horses cost? Ans. $3750. 3. A man bought 450 sheep for $1350: how much are 15 sheep worth? Ans. $45. 4. A farmer has 40 pigs; he sells to a butcher of his number what relation is the number remaining to the number sold? Ans. 3. 5. A boy has $100; his sister has as much, lacking $10: what part of the boy's money equals his sister's? CASE II. The Relation of Fractions to Whole Numbers. ORAL EXERCISE. 1. What part of 6 is SOLUTION 1.-1 is of 6; Ans.. 175÷7= NOTE.-The relation of one number to another is found 175× =200 by dividing the first by the second. SOLUTION.-is of; and, or 1, is 4x of, or of ; if 1 is of, is of 3 of 2, or å of §. Hence, is § of §. NOTE.-The relation of one fraction to another is found by dividing the first fraction by the second. Multiplying a number by 25 is equivalent to multiplying it by 100 and dividing by 4; hence the RULE. To multiply by 25, annex two ciphers, and divide by 4. 1. Multiply 391 by 25. To Multiply a Number by 12 Since 12 is 100, or of 100, we have the following RULE. To multiply by 121, annex two ciphers, and divide by 8. 1. Multiply 822 by 121. PROCESS. 10275 2. Multiply 984 by 121. Ans. 12300. 3. Multiply 8462 by 121. 4. Multiply 10461 by 12. Ans. 105775. Ans. 1307621. NOTE.-In multiplying any number by 125, annex three ciphers and To Multiply any Number by 331. Since 33 is 100, we have the following RULE. To multiply by 331, annex two ciphers and divide by 3. To Multiply any Number by 163. Since 16 equals 50 or 100, we have the following RULE. To multiply by 163, annex two ciphers and divide by 6. To Divide any Number by 25. Since is, we have the following RULE. To divide any number by 25, multiply by 4 and divide by 100. |