25. The amount of money in circulation in the United States on September 1, 1908, was as follows: 2. How should numbers be written for addition? Why? What is the sum of the numbers in the first column? What 467 is the denomination of the left-hand figure in this sum? Why 985 is the 1 added to the next column? 386 the numbers in the second column? 1838 of the right-hand figure in this sum? What is the sum of 1 and What is the denomination Of the left-hand figure? Why is the 2 added to the third column? SUBTRACTION 16. Subtraction is the process of finding the difference between two numbers. The minuend is the number from which we subtract. The subtrahend is the number subtracted. The difference, or remainder, is the result obtained by the subtraction. The sign of subtraction is, and is read minus. Minuend Subtrahend Difference or Remainder. The minuend equals the sum of the subtrahend and the difference. 17. Subtraction of any number of more than one figure from any larger number. TO THE TEACHER. Before proceeding with this exercise, review Exercise 7, p. 19, and Drills 4 and 5, Exercise 10, p. 21. Adding a number to the minuend and an equal number to the subtrahend does not change the difference. 46 29 10 must be added to 6 before 9 can be subtracted. 9 from 16 leaves 7. 1 added to the next figure, 2, in the subtrahend, 17 gives 3; 3 from 4 leaves 1. Explain why adding 10 to 6 in the minuend, and 1 to the tens' figure, 2, in the subtrahend, does not make the answer wrong. 2. From 507 take 398. 507 10 added to 7 gives 17. 8 from 17 leaves 9. 1 added to 9 398 gives 10; 10 added to 0 gives 10; 10 from 10 leaves 0. 1 added to 3 gives 4; 4 from 5 leaves 1. 109 3. From 46 take 29. 46 29 17 If a number is added to the minuend, and an equal number is subtracted from it, the difference is not changed. Instead of adding 1 to the next figure of the subtrahend, after adding 10 to any figure in the minuend, 1 may be subtracted from the next figure of the minuend. 10 must be added to 6 before 9 can be subtracted. 9 from 16 leaves 7. 1 taken from 4, the next figure in the minuend, leaves 3. 2 from 3 leaves 1. Explain why adding 10 to 6, and taking 1 from 4, does not make the result wrong. 14. From 2767 take 398. 15. From 8646 take 3926. 16. Subtract 4763 from 967,608. 18. Diminish 30,406 by 5904. 19. Diminish 46,076 by 3987. 20. From seventy-seven thousand take seven thousand seventy-seven. 18. Subtraction when the numbers represent dollars and cents. Arrange the numbers for subtraction, as in former work, by placing units of the same kind in the same column. Place the decimal point in the difference below the decimal points above. Subtract, and then prefix the dollar sign to the difference. 9. What is the difference between $4976.55 and $3487.86? 11. From six thousand three hundred six dollars and sixty-seven cents take three thousand eight hundred fortyseven dollars and eighty-nine cents. PROBLEMS 19. TO THE TEACHER. See the suggestions to the teacher on page 25. 1. If a boy earns 65¢ on Monday and 50¢ on Tuesday, how much more does he earn on Monday than on Tuesday? The amount the boy earns on Monday is more than he earns on Tuesday by the difference between 65 and 50%, or 2. If I buy goods for $18 and sell them for $21, how much do I gain? and $ or $ I gain the difference between $ 3. Make a problem giving the cost and selling price of goods, showing a case in which the loss is required. Give the loss. 4. A man travels at the rate of 7 miles an hour; another starts with him and travels, in the same direction, at the rate of 5 miles an hour. How far apart are they at the end of one hour? They are as many miles apart as the difference between 5 and 7. 5. John travels direction, at the rate of miles an hour. miles an hour; Henry, in the same How far apart are they at the end of 2 hours if they start together? Fill the blanks and solve. 6. Mary buys candy for 104, a pear for 5¢, an apple for 34. How much should she pay for all? She gives the storekeeper a quarter. How much change should she get? 7. A man sells a stock buyer a cow for $25, a sheep for $7, and hogs for $8. The stock buyer gives him a $50 bill. How much has he overpaid him? Notice that two questions are to be answered in solving the seventh problem. The answer to the first forms a part of the second. First question: A man sells a stock buyer a cow for $25, sheep for $7, and hogs for $8. How much should he receive for all? Ans., $40. Second question: If a stock buyer owes a man $40 for a cow, sheep, and hogs, and gives the man a $50 bill, how much has he overpaid him? Ans., $10. 8. A man has 125 bushels of corn, wheat, and oats. He has 25 bushels of wheat and 25 bushels of corn. How many bushels of oats has he? What is the first question to be answered? Answer it. second question and answer it. HARVEY'S AR, II - 3 State the |