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Exercise 5. Roman Numerals

The Romans expressed their numbers with letters instead of figures. We still use Roman numerals for certain purposes. Name several ways in which we now use Roman numerals.

In the Roman system of writing numbers the value of each of the seven capital letters that are used is as follows:

I =1; V =5; X =10; L=50; C =100; D =500; M = 1000. These letters are grouped according to certain principles:

a. Repeating a letter repeats its value. For example: III =3; XXX =30; CCC =300. b. If a letter is written before another of greater value, its

value is subtracted from the value of the greater letter. For example: IV =4; IX =9; XC =90. c. If a letter is written after another of greater value, its

value is added to the value of the greater letter. For example: VI =6; XVI = 16; CX =110. d. Placing a bar over a letter multiplies its value a thousand

times. For example, X -10,000.

Exercise 6 Read the following: 1. II. 5. XL. 9. LV.

13. MD. 2. VII. 6. XLIV. 10. DCC. 14. MDCCCC. 3. IX.

7. XC. 11. XXXII. 15. MCDXCII. 4. XLV. 8. XCIX. 12. LXXVII. 16. MDCCCCXVII. Write the following numbers in Roman numerals: 1. 4. 4. 14. 7. 21.

10. 63. 2. 8. 5. 16. 8. 34.

11. 1812. 3. 12. 6. 19. 9. 48.

12. 2000.

REVIEW OF FUNDAMENTALS

Exercise 7. Addition

Practice every day until you can say the following sums in 40 seconds or write them in 1 minute:

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73

Exercise 8. Adding by Endings A B Cut a cardboard slip inch x 5 inches. 64 89

Letter one of the slips A and the other B. 97 51 Write on them the numbers shown in the 10 87

picture. Keep the slips in your arithmetic. 83 68

1. Place card A at the edge of your paper. 59 76 92 In a column beside it write the sum of each 42 25 number and 4, as 64 and 4; 97 and 4, etc. 98 30 35 14

2. Use card B in the same way another 21 46 day.

3. Then try adding 3, 5, 6, 7, 8 and 9 to each of the numbers on these cards.

The order should be frequently changed in drilling. Means of doing this are: Flash cards; rapid dictation of the combinations by the teacher, and copied or mimeographed sheets on which the order is changed.

Exercise 9. Problems in Addition

[graphic]

1. A squad of Boy Scouts went on a hike. In the morning they

. walked 9 miles and in the afternoon 7 miles. How many miles did they walk during the hike?

2. During vacation Alexander

raised 12 bushels of onions on one piece of land and 29 bushels on another. What was his total yield of onions?

3. Martha bought a hat for $3.50 and a pair of shoes for $3.75. What did she spend for both?

4. While shopping for his mother, Albert bought a dozen oranges for 39 cents, a head of cauliflower for 15 cents and a loaf of bread for 10 cents. Find the amount of his purchases.

5. Lucile worked for a neighbor, receiving 35 cents for working in the garden and 25 cents for mowing the lawn. How much did she receive for both?

2

6. Walter and Clifton went fishing. Walter caught 19 fish

. and Clifton 27. How many did they both catch?

7. Marion entered a fly-swatting contest. Here is her record for one week: Monday 34, Tuesday 63, Wednesday 56, Thursday 40, Friday 49, and Saturday 87. Find her total for the week.

8. Hilda raises chickens to earn her spending money. She keeps them separated in three pens, containing 19, 23 and 16 each. How many has she altogether?

9. In a city school there are 4 fifth grades containing 33, 32, 36 and 29 pupils respectively. How many fifth-grade pupils are there in that school?

5. 7

5 8 4 3 7 9

13. 6

9 7 8 9 7 3 5 7

21. 2

8 6 6 9 8 9 4

Exercise 10.

Practice Exercises in Addition

Add these columns from the top downward:

3. 9

6. 8

7. 7

8. 9

5 8 3 2 6 3

2 6 3 5 7 2

9 4 2 5 3 5

4. 6

5 3 6 7 6 3

7 8 6 2 7 3

4 4 9 4 9 6

7 8 2 9 7 7

10. 9

12. 8

16. 8

9. 4

7 2 5 3 8 4 2 7

8 7 8 3 9 5 3 5

11. 7

9 5 9 6 8 6 6 9

5 3 7 9 2 9 5 6

14. 3

8 5 6 6 8 5 1 9

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16. 9

9 6 7 7 9 5 7 3

17. 2

18. 9

20. 8

22. 5

24. 6

5 8 9 9 3 6 6 7 8 9

2 3 3 5 4 9 8 7 8 3

19. 6

7 0 9 6 9 4 4 8 6 2

7 5 4 8 1 8 6 2 4 9

3 6 2 9 7 8 9 5 7 9

23. 6

5 1 6 8 3 9 9 7 9 7

7 8 5 4 8 7 4 7 0 6

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Exercise 11. Explanation for Addition

Add: 456, 372, 865 and 974. 456 Explanation: Begin adding at the units' column. The sum 372 of the units 4, 5, 2 and 6 is 17. 17 makes 7 units and 1 ten.

Write the 7 units in the units' place in the sum and add the 865

1 ten with the other tens in the second column. 1, 7, 6, 7 and 974

5 tens make 26 tens. Since 10 tens make a hundred, 26 tens 2667 make 2 hundreds, with a remainder of 6 tens. Write the 6

representing the remaining tens in the tens' place of the sum and add the 2 hundreds in with the figures in the hundreds' column. The sum of 2, 9, 8, 3 and 4 hundreds is 26 hundreds. Therefore the sum of the numbers is 2667.

Add the following examples upward and explain:
1.
2.
3.
4.
5.
6.
7.

8. 37

5 43 95 11 3 96 28 42 86 50 7 72 77 67

9 4 14 7 69

9 89 9

9 22 39 8

96
8 9

73

80 3 50

9
9 86 67 76

5 16 6 54 7 45

9

9 84 8

4 66 77 7 27 7 47 83 85 59 98 96 4 92 33 52 7 98 23 89 58 89

6

[blocks in formation]

65 878 65

7 924 476

99 38 958 749 236

82 893 823

60 207 971

9 28 607 514 533

13. 337 899

79 652 836

14.

9 70 253

6 27 947 768 39 9

998
78
46
960
805
796

38 497

79 828 65

82

5 53 739

90 367 476 89

6 82 77

38 706

68 744

77 284 939 58

6 29 497

577 647 352

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