Math Class IV PDF

# Chapter One ## Roman Numbers ### Introduction In this chapter, you will learn to read and write numbers from 1 to 1,000 in Roman numbers. These numbers range from I to M in Roman numbers. They are used in various contexts such as on the introductory pages of books and on clock faces. The competen...

# Chapter One ## Roman Numbers ### Introduction In this chapter, you will learn to read and write numbers from 1 to 1,000 in Roman numbers. These numbers range from I to M in Roman numbers. They are used in various contexts such as on the introductory pages of books and on clock faces. The competencies developed will enable you to use Roman numbers in different contexts. ### Think Life without application of numbers ### Roman Numbers from I to X Whole numbers are composed of ten digits, which are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Roman numbers are written by using some or combinations of the letters of the alphabet. | Numerals | Roman Numbers | Numbers in Words | |:---|:---|:---| | 1 | I | one | | 2 | II | two | | 3 | III | three | | 4 | IV | four | | 5 | V | five | When a smaller Roman number is written to the right of a Roman number which is equal or greater in its value, the resulting number is obtained by adding the values of those numbers. **Example 1** Write the following Roman numbers in numerals: (a) II (b) VI (c) VII (d) VIII **Solution** (a) II = 1+1 = 2 Therefore, II is 2. (b) VI = 5 + 1 = 6 Therefore, VI is 6. (c) VII = 5 + 2 = 7 Therefore, VII is 7. (d) VIII = 5 + 3 = 8 Therefore, VIII is 8. A Roman number with a smaller value written to the left of a Roman number with a greater value is obtained by subtracting the value of the smaller number from the greater number. **Example 2** Write the following Roman numbers in numerals: (a) IV (b) IX **Solution** (a) IV = 5 - 1 = 4 Therefore, IV is 4. (b) IX = 10 - 1 = 9 Therefore, IX is 9. ### Activity 1 **Identifying Roman Numbers** 1. Use various sources, such as Khan Academy, to learn items that use Roman numbers. 2. Write down the names of the items obtained from Step 1. 3. Why is it important for you to do this activity? ### Writing Roman Numbers from I to X The Roman number one (I) can be written by repeating it to form various numbers. For example: | Roman Numbers | 1 | 2 | 3 | |:---|:---|:---|:---| | Numerals | I | II | III | This number (I) cannot be repeated more than three times in one number. The Roman numbers I, V, and X are also used to create other Roman numbers. For example: | Numerals | 4 | 5 | 6 | 7 | 8 | 9 | |:---|:---|:---|:---|:---|:---|:--- | Roman Numbers | IV | V | VI | VII | VIII | IX | ### Exercise 1 1. Write IX, VI, X, IV, VII, V and VIII in ascending order. 2. Convert VII, IV, VI, V, VIII and IX into numerals. 3. Convert 3, 6, 7, 1, 8, 4, 10, 9 and 5 into Roman numbers. 4. Fill in the missing numbers in the following table: | Number in Words | Six | Seven | Nine | Four | Ten | |:---|:---|:---|:---|:---|:---| | Roman Numbers | IV | | | | | 5. A parent bought shoes with sizes X, V, I, and VII for the kids. Write the shoes sizes in numerals. ### Roman Numbers from XI to XX | Roman Numbers | Numerals | Numbers in Words | |:---|:---|:---| | XI | 11 | eleven | | XII | 12 | twelve | | XIII | 13 | thirteen | | XIV | 14 | fourteen | | XV | 15 | fifteen | | XVI | 16 | sixteen | | XVII | 17 | seventeen | | XVIII | 18 | eighteen | | XIX | 19 | nineteen | | XX | 20 | twenty | ### Example 1 Write the following numerals in Roman numbers: (a) 14 (b) 17 (c) 19 **Solution** (a) 14 = X + IV = XIV Therefore, 14 is XIV. (b) 17 = X + VII = XVII Therefore, 17 is XVII. (c) 19 = X + IX = XIX Therefore, 19 is XIX. ### Example 2 Convert the following into numerals: (a) XII (b) XV **Solution** (a) XII = 10 + 2 = 12 Therefore, 12 is XII. (b) XV = 10 + 5 = 15 Therefore, XV is 15. ### Exercise 2 1. Write the Roman number with the highest value in the following list: XII, XIII, XV, XIX, XVI, XVII, XVIII and XIV. 2. Write the following Roman numbers in words: (a) XIV (b) XVI (c) XX (d) XI (e) XV (f) XIX ### Example 1 Write the following numerals in Roman numbers: (a) 24 (b) 37 (c) 27 **Solution** (a) 24 = XX + IV = XXIV Therefore, 24 is XXIV. (b) 37 = XXX + VII = XXXVII Therefore, 37 is XXXVII. (c) 27 = XX + VII = XXVII Therefore, 27 is XXVII. ### Example 2 Write the following Roman number in numerals: (a) XXI (b) XXXIII **Solution** (a) XXI = 20 + 1 = 21 Therefore, XXI is 21. (b) XXXIII = 30 + 3 = 33 Therefore, XXXIII is 33. ### Exercise 3 1. Write the following numerals in Roman numbers: (a) 28 (b) 26 (c) 32 (d) 23 2. Write each of the following Roman number in numerals: (a) XXII (b) XXXI (c) XXX (d) XXV 3. Write the missing Roman numbers in each sequence: (a) XXI, ___, XXIII, ___, XXVI (b) XXIV, ___, XXVI, ___, XXIX, ___, XXVIII, ___, XXVI (c) XXXII, ___, XXX, ___, XXVIII, ___, XXVI (d) ___, XXV, ___, XXIII, ___, XXII, ___ ### Roman Numbers from XXI to XXXIII | Numerals | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | |:---|:---|:---|:---|:---|:---|:---|:---|:---|:---|:---|:---|:---| | Roman Numbers | XXI | XXII | XXIII | XXIV | XXV | XXVI | XXVII | XXVIII | XXIX | XXX | XXXI | XXXII | XXXIII | ### Exercise 4 1. Write the following numerals in Roman numbers : (a) 44 (b) 39 (c) 35 (d) 46 2. Write the following Roman numbers in numerals: (a) XXXVI (b) XLVIII (c) XLI (d) XXXIV 3. Write the missing Roman numbers in each sequence: (a) XXXIV, ___, XXXVI, ___, XXXIX (b) XXXVI, XXXVIII, ___, XLII, ___, XLIV, XLVI, ___, XLII, ___, XLIV, ___ , XXXVIII, ___, XXXII (c) L, ___, XLIV, ___, XL, ___, XXV (d) XXXV, XXXVII, ___, XLI, ___, XLV 4. Fill in the missing numbers in the following table: | Roman Numbers | XXXVI | XLIII | | | 46 | |---|:---|:---|:---|:---|:---| | Numerals | | | | 39 | | 5. Fill in the missing numbers in each sequence: (a) XXXII, ___, XXXVI, ___, XL ### Roman Numbers from XXXIV to L Read the following Roman numbers: XXXIV, XXXV, XXXVI, XXXVII, XXXVIII, XXXIX, XL, XLI, XLII, XLIII, XLIV, XLV, XLVI, XLVII, XLVIII, XLIX and L. ### Example 1 Write the following numbers in Roman numbers: (a) 34 (b) 41 (c) 45 **Solution** (a) 34 = XXX + IV = XXXIV Therefore, 34 is XXXIV. (b) 41 = XL + I = XLI Therefore, 41 is XLI. (c) 45 = XL + V = XLV Therefore, 45 is XLV. ### Example 2 Write the following Roman numbers in numerals: (a) XXXVII (b) XLIII (c) XLIX **Solution** (a) XXXVII = 30 + 7 = 37 Therefore, XXXVII is 37. (b) XLIII = 40 + 3 = 43 Therefore, XLIII is 43. (c) XLIX = 40 + 9 = 49 Therefore, XLIX is 49. ### Exercise 4 1. Write the following numerals in Roman numbers: (a) 44 (b) 39 (c) 35 (d) 46 2. Write the following Roman numbers in numerals: (a) XXXVI (b) XLVIII (c) XLI (d) XXXIV 3. Write the missing Roman numbers in each sequence: (a) XXXIV, ___, XXXVI, ___, XXXIX (b) XXXVI, XXXVIII, ___, XLII, ___, XLIV, XLVI, ___, XLII, ___, XLIV, ___ , XXXVIII, ___, XXXII (c) L, ___, XLIV, ___, XL, ___, XXV (d) XXXV, XXXVII, ___, XLI, ___, XLV - Fill in the missing numbers in the following table: | Roman Numbers | XXXVI | XLIII | | 39 | 46 | |---|:---|:---|:---|:---|:---| | Numerals | | | | | | 5. Fill in the missing numbers in each sequence: (a) XXXII, ___, XXXVI, ___, XL #### More Examples * X, ___, XX, XXV, ___, XL * L, ___, ___, XXX, XXV, ___, XL * XXXV, XXXVII, ___, XLI, ___, XLV #### More Examples * Arrange sticks in a shape which shows 48 in Roman numbers, then write the resulting Roman number. * Nuru saw a sign post marked with a Roman number XLIV. What number is that in numerals? * Write the following Roman numbers in words: * XLIX * XXXVI * XLV * XXXVII * Write the following in Roman numbers: * Forty-two * Thirty-nine * Forty-three * Write the following Roman numbers in words: * XLII * XXXVIII * XLIX * XXXVII ### Roman Numbers from L to C | Numerals | 50 | 60 | 70| 80 | 90 | 100 | |:---|:---|:---|:---|:---|:---|:---| | Roman Numbers | L | LX | LXX | LXXX | XC | C | | Numbers in words | fifty | sixty | seventy | eighty | ninety | one hundred | The numbers I, X, and C are the only Roman numbers that, when written to the left of a larger number, are subtracted, and when written to the right are added. These numbers cannot be repeated when written to the left of a larger number. Also, these numbers cannot be repeated more than three times when written to the right of a larger number. In numerals, these numbers correspond to 1, 10, and 100. The numbers IV and IX represent ones. Therefore, when these numbers are written after a higher value, then, the numbers are added to the larger number. | Roman Numbers | Numbers in words | Numerals | |:---|:---|:---| | LV | fifty-five | 55 | | LIX | fifty-nine | 59 | | LXXXIX | eighty - nine | 89 | | LXXII | seventy-two | 72 | | XCIX | ninety-nine | 99 | | LXIV | sixty-four | 64 | | LVIII | fifty-eight | 58 | | LXI | sixty-one | 61 | | LXXIII | seventy-three | 73 | | LXXXV | eighty-five | 85 | ### Example 1 Write the following Roman numbers in words: (a) LXV (b) LXXVI (c) XCIX (d) LIV **Solution** (a) LXV = 60 + 5 = 65 Therefore, the number LXV is sixty-five. (b) LXXVI = 70 + 6 = 76 Therefore, the number LXXVI is seventy-six. (c) XCIX = 90 + 9 = 99 Therefore, the number XCIX is ninety-nine. (d) LIV = 50 + 4 = 54 Therefore, the number LIV is fifty-four. ### Example 2 Write the following numerals in Roman numbers: (a) 53 (b) 67 (c) 57 (d) 88 **Solution** (a) 53 = L + III = LIII Therefore, 53 is LIII. (b) 67 = LX + VII = LXVII Therefore, 67 is LXVII. (c) 57 = L + VII = LVII Therefore, 57 is LVII. (d) 88 = LXXX + VIII = LXXXVIII Therefore, 88 is LXXXVIII. ### Exercise 5 1. Write the following Roman numbers in words: (a) LXVII (b) XC (c) LXXXII (d) XCVIII 2. Write the following numerals in Roman numbers: (a) 52 (b) 66 (c) 70 (d) 93 3. Write the following Roman numbers from the smallest to the largest: C, I, X, L, V, LXV, LXXXV, XCV, LV, and LXXV. 4. Write the missing Roman numbers in the following sequence: LXXX, ___, LXXXII, ___, LXXXIV, ### Roman Numbers from C to D The Roman numbers C and D are the only representations of hundreds whereas, C stand for 100, and D stands for 500. When C is written to the left of D, its value is subtracted from D; however, when C is written to the right of D, its value can only be added up to three times. #### More Examples: * (i) CD (ii) DCC (iii) DCCC | Numerals | 100 | 200 | 300 | 400 | 500 | |:---|:---|:---|:---|:---|:---| | Roman Numbers | C | CC | CCC | CD | D | | Number in words | one hundred | two hundred | three hundred | four hundred | five hundred | #### More Examples: * Read the following numbers: * (a) 205 (b) 362 * Write the following Roman numbers in words: * (a) CXVII (b) CDXLVI * Write the following numerals in Roman numbers: * (a) 205 (b) 362 * Write the following Roman numbers in words: * (a) CXVII (b) CDXLVI ### Roman Numbers from C to D The Roman numbers C and D are the only representations of hundreds whereas, C stand for 100, and D stands for 500. When C is written to the left of D, its value is subtracted from D; however, when C is written to the right of D, its value can only be added up to three times. #### More Examples: * (i) CD (ii) DCC (iii) DCCC | Numerals | 100 | 200 | 300 | 400 | 500 | |:---|:---|:---|:---|:---|:---| | Roman Numbers | C | CC | CCC | CD | D | | Number in words | one hundred | two hundred | three hundred | four hundred | five hundred | ### Example 1 Write the following numerals in Roman numbers: (a) 205 (b) 362 **Solution** (a) 205 = CC + V = CCV Therefore, 205 is CCV. (b) 362 = CCC + LXII = CCCLXII Therefore, 362 is CCCLXII. ### Example 2 Write the following Roman numbers in words: (a) CXVII (b) CDXLVI **Solution** (a) CXVII - One hundred and seventeen. (b) CDXLVI - Four hundred and forty-six. ### CCCXLIII three hundred and forty-three 343 ### CCXXV two hundred and twenty-five 225 ### CCCXXXVIII three hundred and thirty-eight 338 ### CDXVII four hundred and seventeen 417 ### CCLIV two hundred and fifty-four 254 ### CDXXXI four hundred and thirty-one 4 31 ### Exercise 6 1. Write the following Roman numbers in words: * (a) CCCXXX (b) CCXIX (c) CDXLVII (d) CCXCII 2. Write the following in Roman numbers: * (a) Four hundred and forty-four: * (b) One hundred and fifteen: * (c) Two hundred and nine: * (d) Four hundred and fifty-four: 3. Convert the following numerals into Roman numbers: * (a) 108 (b) 374 (c) 435 (d) 442 4. The distance between City A and City B is CDLXXVIII kilometres. Write these distance in numerals. ### Roman Numbers from M to The Roman number M is 1000 in numerals. The Roman number C can only be written to the left of M, allowing it to be subtracted from M. - Read the following Roman numbers: | Roman Numbers | Number in words | |:---|:---| | DC | five hundred | | DCC | six hundred | | DCCC | seven hundred | | CM | nine hundred | | M | one thousand | ### Exercise 6 1. Write the following Roman numbers in words: * (a) CCCXXX (b) CCXIX (c) CDXLVII (d) CCXCII 2. Write the following in Roman numbers: * (a) Four hundred and forty-four * (b) One hundred and fifteen * (c) Two hundred and nine * (d) Four hundred and fifty-four 3. Convert the following numerals into Roman numbers: * (a) 108 (b) 374 (c) 435 (d) 442 4. The distance between City A and City B is CDLXXVIII kilometres. Write these distance in numerals. ### Roman Numbers from M to The Roman number M is 1000 in numerals. The Roman number C can only be written to the left of M, allowing it to be subtracted from M. * Read the following Roman numbers: | Roman Numbers | Number in words | |:---|:---| | DC | five hundred | | DCC | six hundred | | DCCC | seven hundred | | CM | nine hundred | | M | one thousand | - Read the following Roman numbers: | Number in words | Roman Numbers | |:---|:---| | five hundred and eleven | DXI | | seven hundred and ninety-nine | DCCXCIX| | six hundred and seventy-four | DCLXXIV| | nine hundred and eighty-four | CMLXXX | | five hundred and fifty | DLV | | seven hundred and twenty-eight | DCCXXVIII | ### Example 1 Write the following Roman numbers in numerals: (a) CMIX (b) DCCLXXIV **Solution** (a) CMIX = 900 + 9 = 909 Therefore, CMIX is 909. (b) DCCLXXIV = 700 + 74 = 774 Therefore, DCCLXXIV is 774. ### Example 2 Write the following numerals in Roman numbers: (a) 576 (b) 688 (c) 842 (d) 964 **Solution** (a) 576 = D + LXXVI = DLXXVI Therefore, 576 is DLXXVI. (b) 688 = DC + LXXXVIII = DCLXXXVIII Therefore, 688 is DCLXXXVIII. (c) 842 = DCCC + XLII = DCCCXLII Therefore, 842 is DCCCXLII. (d) 964 = CM + LXIV = CMLXIV Therefore, 964 is CMLXIV. ### Activity 2 **Learning Roman Numbers** - Description: Use various reliable internet sources such as Khan Academy to learn more about Roman numbers. ### Exercise 7 1. Write the following Roman numbers in words: * (a) CMLXXIX (b) DLXXVIII (c) CMXCIV (d) DCCCVI 2. Write the following in Roman numbers: * (a) Five hundred fifty-nine (b) Seven hundred sixty-four (c) Nine hundred eighty-two (d) Six hundred sixty-seven 3. Convert the following numerals into Roman numbers: * (a) 572 (b) 698 (c) 755 (d) 916 4. Karol was given a card marked with the number DLVII. Anna was given a card marked with the number DXLVII. * (a) Who was given a card with high value? * (b) Write the number on each card in numerals. ### Summary: 1. Numerals are composed of ten digits which are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. 2. There is no Roman number representing 0. 3. The basic Roman numbers I, V, X, L, C, D, and M, are used to create other Roman numbers. 4. In Roman numbers, letters are not repeated more than three times consecutively in one number. ### Revision Exercise 1. Write the following Roman numbers in words: * (a) CMXC (b) DLXIV (c) CMLXXI (d) DCXCVII 2. Write the following in Roman numbers: * (a) Six hundred and twenty-one (b) Eight hundred and fifty-five (c) Eight hundred and eighteen (d) Nine hundred and fifty 3. Write the following Roman numbers in words: * (a) XCI (b) CCXCII (c) DCCCLXXI (d) CMXCIX 4. The length of the road is CMXCVI kilometres. Write this length in numerals. ### Revision Exercise 1. Write the following Roman numbers in words: * (a) CMXC (b) DLXIV (c) CMLXXI (d) DCXCVII 2. Write the following in Roman numbers: * (a) Six hundred and twenty-one (b) Eight hundred and fifty-five (c) Eight hundred and eighteen (d) Nine hundred and fifty 3. Write the following Roman numbers in words: * (a) XCI (b) CCXCII (c) DCCCLXXI (d) CMXCIX 4. The length of the road is CMXCVI kilometres. Write this length in numerals. ### More Examples 1. Two cards were marked with the following numbers; DCVI and CMXI. * (a) Which card had the higher value? * (b) Write the number of the card with the smaller value in numerals. 2. Write the missing Roman numbers in each sequence: * (a) CXV, CCXXX, ___, DLXXV, ___ * (b) DCXIX, DCXCIX, ___, DCCLXXXIX, ___ 3. Arrange the following numbers from the smallest to the largest: XCV, XLVII, CCIX, CLI, LXXIII, CMV, CMXCII, III, XV, XCII. 4. The distance between two towns E and F is CMXLIX kilometres. Write this distance in numerals.