SUBTRACTION ORAL EXERCISE 1. What number added to the lower of these numbers 2. If you hand a merchant $1, how much change should you get if you owe him 75 ct.? 60 ct.? 25 ct.? 88 ct.? Throughout the course there should be much oral drill on such problems as the above. It is expeditious, in the case of 75-48, to think: "48 and 2 are 50, and 25 more are 75; 2 + 25 = 27.” 75 48 27 15. Difference. The number which added to one number makes another is called the difference between them. That is, the difference between 75 and 48 is 27, because 48 +27 75. = 16. Subtraction. The operation of finding the difference between two numbers is called subtraction. Subtraction may also be defined as the operation of taking one number from another, and the result may be defined as the remainder or difference. But since a great deal of subtraction is "making change," where the work is based on addition, the definitions first given are better. 17. Subtrahend. The number to which the difference is added, or the number which is subtracted, is called the subtrahend. 563 minuend 127 subtrahend 436 difference or remainder 18. Minuend. The sum of the difference and subtrahend, or the number from which we now used 10 of the 30, leaving 20. We cannot subtract We have now used 100 of 50 from 20, but 120-50 the 1600, and 1500 – 700 : = 70. = The above is one of the most common methods of subtracting, but the class should follow the method learned in the earlier grades. It is confusing to learn new methods that are little better than the old ones. The teacher is advised to give but little time to asking for such definitions as those on page 10, for the terms are rarely used in business. The business man says, "Deduct $10 and pay me the balance," instead of "Subtract $10 and pay me the remainder.” 20. Making change. If you owe 70 cents and give the merchant $1, he says: "70 and 5 are 75, and 25 more makes a dollar," at the same time laying down 5 cents and 25 cents. He thus sees that $1 $0.70 = $0.30. ORAL EXERCISE 1. Make change for $1, when you owe 55 ct.; 37 ct. 2. Also for $2, when you owe $1.49; $1.62; $1.16. 3. Also for $5, when you owe $2.75; $3.10; $1.48. INTERESTING FACTS IN OUR HISTORY A few important dates 1492. Columbus discovered America. 1620. Landing of the Pilgrims at Plymouth. 1664. New York City captured from the Dutch. WRITTEN EXERCISE 1. How many years since Columbus discovered America? 2. How long after that was the Hudson explored? Landing of the Pilgrims 3. How many years since Washington was inaugurated? 4. How long ago did the Mayflower reach Plymouth? 5. How many years after that did the English capture New York from the Dutch? 6. How many years from the Declaration of Independence to the next Fourth of July after to-day? 7. How long after Columbus discovered America was the landing of the Pilgrims? 8. It lacked only 2 years of being a century and a quarter from the battle of Lexington to that of Manila, 1898. ORAL EXERCISE 1. The subtrahend is 7, the minuend 21; what is the difference? How much is 21 minus 7? 2. The difference is 11, the minuend 16; what is the subtrahend? What number minus 16 equals 11? 3. The subtrahend is 27, the remainder 14; what is the minuend? 27 minus what number equals 14? 4. The minuend is 25 more than the subtrahend; what is the difference? 5. The subtrahend is 47 less than the minuend; what is the difference? 6. The subtrahend and difference together equal 39; what is the minuend? 7. Mr. Roberts owed Mr. Lambert $75 yesterday. To-day he has paid him $25. What balance is due? WRITTEN EXERCISE Perform these subtractions, and check every answer by adding the remainder and subtrahend. See how many you can perform in five minutes. 15. $62,341.75-$12,986.50. 16. $42,350.50 - $19,625.08. MULTIPLICATION ORAL EXERCISE 1. Read the products by 2: 4, 7, 1, 9, 6, 2, 8, 3, 11, 5, 10. This or a similar set of numbers should be written on the board. 2. In the same way, read rapidly the products by the various numbers from 3 to 10. Also by 20, 30, 100. 3. Count by 2's from 2 to 20, and give the multiplication. table of 2's. Give the multiplication tables from 3 to 10. 4. How much is 4+4 +4 +4 +4? 5 times 4? Multiplication is a short form of what other process? 21. Abstract numbers. A number that does not refer to any particular kind of object or measure is called an abstract number. For example, 10, 42, 31, are abstract numbers. 22. Concrete numbers. A number that refers to some particular kind of object or measure is called a concrete number. For example, $10, 32 ft., 6 mo., are concrete numbers. 23. Multiplication. The process of taking one number as many times as there are units in another is called multiplication. This means multiplication by an abstract integer. Thus, to multiply $3 by 2 means that $3 is taken 2 times. 24. Multiplicand. The number mul tiplied is called the multiplicand. 25. Multiplier. The number by which we multiply is called the multiplier. $325 multiplicand 3 multiplier $975 product 26. Product. The result of multiplying is called the |