596

472

267

79

138

54

877

815

48

45

28

3298

Exercise 12. Civil Service Method of Adding

Our state and the United States have many men and women employed to carry on the business affairs of our government who are called civil service employees. These workers are often interrupted when they are adding. In order to prevent the necessity of adding several columns over again, they put down the sum of each column separately and then add those sums together to get the total sum.

In the example at the left, the sum of the units' column is written as 4 tens and 8 units; the sum of the tens' column is 4 hundreds and 5 tens; the sum of the hundreds' column is 2 thousands and 8 hundreds. Adding the three sums, the

result is 3298.

Care must be taken to write the right hand figure of the tens' sum in the tens' column, the right hand figure of the hundreds' sum in the hundreds' column, etc. There is no carrying from one column to another except in adding the three sums to get the final result.

Practice until you can say all the remainders to the following subtraction facts in 50 seconds or write them in 70 seconds.

9

Exercise 14. Subtraction Drill 2

Use the same time limits for this exercise as for Exercise 13.

It is a good plan to try out pupils individually on these facts while the remainder of the class is doing written work. Keep a record for each pupil of the facts which cause him difficulty so that he may concentrate his attention on those facts. Speed and accuracy in longer subtraction problems depend upon a thorough mastery of these two drills.

Exercise 15. Subtraction by Endings

The cards which were used for addition on page 6 should also be used for subtracting by endings. Have the pupils exchange papers and check them as the correct answers are read. These drills should be used at the beginning of each recitation while the class is reviewing subtraction.

1. Practice subtracting 1, 2, 3, 4, 5, 6, 7, 8 and 9 from each of the numbers on drill cards A and B.

2. Begin with 100 and subtract by 4's until you reach 0, saying only the remainders: 100, 96, 92, 88, 84, etc.

3. Subtract by 2's from 50 to 0; by 3's from 60 to 0; by 5's from 100 to 0.

4. Begin with 108 and subtract by 9's to 0.

5. Subtract by 8's from 99 to 3; by 7's from 97 to 6; by 6's from 100 to 4.

=

Explanation1: We can not take 7 units from 5 units, so we change 1 of the 3 tens to 10 units. 10 units + 5 units = 15 units. 7 units from 15 units leaves 8 units. Write the 8 in units' place in the remainder. We can not take 8 tens from the 2 tens that were

=

1 hundred.

= 4148.

left in the minuend, so we change 1 of the 4 hundreds to 10 tens. 10 tens + 2 tens 12 tens. 8 tens from 12 tens leaves 4 tens. Write the 4 in tens' place in the remainder. 2 hundreds from 3 hundreds 5 thousands from 9 thousands = 4 thousands. The remainder 1The Additive method may be substituted by teachers who prefer it: 7 and 8 give a 5 ending. Write the 8 in units' place in the remainder. 7 and 8 15. Carry the 1 ten of the 15 to the next figure 8 of the subtrahend. 8 tens + 1 ten 9 tens. 9 and 4 are 13. Write the 4 in tens' place in the remainder. Carry the 1 to hundreds' column. 2 and 1 are 3. 3 and 1 are 4. Write the 1 in hundreds' place. 5 and 4 are 9. Write the 4 in thousands' place. Remainder = 4148.

=

In order that we may have common names to use in speaking of the numbers of a subtraction problem, mathematicians have agreed on naming the number subtracted the subtrahend, the number from which another number is subtracted the minuend, and the result that is left after subtracting, the remainder.

Exercise 18. Problems in Subtraction

1. Kenneth counted the marbles in his marble bag. He had 237. He gave his cousin 65 of them for helping him with some work. How many had he left?

2. Robert weighs 68 pounds and Jane weighs 59 pounds. How much more does Robert weigh than Jane?

3. Walter took 75 cents to the butcher shop to buy meat. He bought 53 cents worth of sirloin steak. How much money did he have left?

4. Edwin has 169 stamps in his collection and Philip has 153. How many more stamps does Edwin have than Philip?

5. Arthur raised 38 bushels of popcorn. He sold 13 bushels to a grocer. After keeping 1 bushel for his own use he shipped the remainder to the city. How many bushels did he ship to the city?

6. Jane was given $2.25 by her mother for buying refreshments for a party. She spent only $1.79. How much did she have left to return to her mother?

7. Helen and Alexander were to choose sides for a spelling match. To decide which was to have first choice, they were to guess the number on the page in a book where a marker had been placed. Helen guessed 125 and Alexander guessed 165. The page was 139. Which was the better guess?

8. A fifth-grade class gave an entertainment. They received $28.75 for admissions, and their expenses were $12.29. What were their profits on the entertainment?

9. In a recent year there were 5,468,190 inhabitants in the city of New York and 2,447,045 in Chicago. How much did the population of New York exceed that of Chicago?