Year 4: Roman numerals and the story of zero
Part of the Year 4 place value chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Roman numerals and the story of zero
The Romans used letters for numbers. You can still see Roman numerals on clocks, buildings and book chapters. We need five symbols to read every number from 1 to 100:
The rules. (1) Symbols that are the same add up: XX = 10 + 10 = 20. (2) A smaller symbol after a bigger one is added: XI = 10 + 1 = 11. (3) A smaller symbol before a bigger one is taken away: IX = 10 − 1 = 9. (4) You never write the same symbol more than three times in a row, so 4 is IV (not IIII) and 40 is XL (not XXXX). To write a number, do the tens first, then the ones.
| Ones | Roman | Tens | Roman |
|---|---|---|---|
| 1 | I | 10 | X |
| 2 | II | 20 | XX |
| 3 | III | 30 | XXX |
| 4 | IV | 40 | XL |
| 5 | V | 50 | L |
| 6 | VI | 60 | LX |
| 7 | VII | 70 | LXX |
| 8 | VIII | 80 | LXXX |
| 9 | IX | 90 | XC |
| 100 | C |
Why do we not use Roman numerals today? The Romans had no symbol for zero, and the position of a symbol did not matter: X always means 10, wherever it is. That makes big calculations very hard. Try adding XLVII and LXXIX without changing them into our numbers!
Our number system came about over many hundreds of years. Mathematicians in India, and then in the Middle East and Europe, developed the ten digits 0 to 9. The digit 0 became a number in its own right and also a place holder. The key idea is place value: a digit is worth more or less depending on its column. In 22, the first 2 means 20 and the second 2 means 2. In XX, both Xs mean 10. Place value and zero make it much easier to write and calculate with big numbers.
Key words. A numeral is a symbol for a number. Place value means the value of a digit depends on where it is. A place holder is a zero that keeps the other digits in the right columns.
Key ideas
- I = 1, V = 5, X = 10, L = 50, C = 100.
- Same symbols add up. A smaller symbol after adds. A smaller symbol before takes away (IV = 4, IX = 9, XL = 40, XC = 90).
- Never more than three of the same symbol in a row.
- Write the tens first, then the ones: 74 = LXX + IV = LXXIV.
- Roman numerals have no zero and no place value. Our number system has both.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.47 = 40 + 7
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).40 = XL
- Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).7 = VII
- Put the tens first, then the ones. The tens part goes on the left, the ones part on the right.XL + VII = XLVII
Check. Read it back: XL (50 − 10) + V (5) + I (1) + I (1) = 47. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. A numeral is a symbol for a number. Roman numerals use the letters I, V, X, L and C.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like IV or XL) is taken away. Otherwise just add.L = 50
X = 10
X = 10
IX = 10 − 1 = 9 (small number in front, so take it away) - Add the values. Add the bigger groups first, then the small ones.50 + 10 + 10 + 9 = 79
- Write the answer. 79
Check. Write 79 in Roman numerals: tens first, then ones: LXX + IX = LXXIX. ✓
Watch out. Read from the left. A small symbol only gets taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.94 = 90 + 4
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).90 = XC
- Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).4 = IV
- Put the tens first, then the ones. The tens part goes on the left, the ones part on the right.XC + IV = XCIV
Check. Read it back: XC (100 − 10) + IV (5 − 1) = 94. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change XVIII into a number. Split it into groups and add.XVIII = X (10) + V (5) + I (1) + I (1) + I (1) = 18
- Change XXIV into a number. Do the same.XXIV = X (10) + X (10) + IV (5 − 1) = 24
- Do the calculation. Use our normal numbers.18 + 24 = 42
- Change the answer back to Roman numerals. Tens first, then ones.42 = XL + II = XLII (42)
Check. Read XLII again: 40 + 1 + 1 = 42. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Watch out
Do not write 8 as IIX or 49 as IL. A small symbol goes in front of a bigger one to take away only in a few cases: I can go before V or X, and X can go before L or C. 49 is XL (40) + IX (9) = XLIX, not IL. And remember: the same symbol is never written more than three times in a row.Exercise 1F Roman numerals
Non-calculatorKey words. A numeral is a symbol for a number. Roman numerals use the letters I, V, X, L and C.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like IV or XL) is taken away. Otherwise just add.V = 5
I = 1
I = 1 - Add the values. Add the bigger groups first, then the small ones.5 + 1 + 1 = 7
- Write the answer. 7
Check. Write 7 in Roman numerals: tens first, then ones: + VII = VII. ✓
Watch out. Read from the left. A small symbol only gets taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. A numeral is a symbol for a number. Roman numerals use the letters I, V, X, L and C.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like IV or XL) is taken away. Otherwise just add.X = 10
IV = 5 − 1 = 4 (small number in front, so take it away) - Add the values. Add the bigger groups first, then the small ones.10 + 4 = 14
- Write the answer. 14
Check. Write 14 in Roman numerals: tens first, then ones: X + IV = XIV. ✓
Watch out. Read from the left. A small symbol only gets taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. A numeral is a symbol for a number. Roman numerals use the letters I, V, X, L and C.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like IV or XL) is taken away. Otherwise just add.X = 10
X = 10
IX = 10 − 1 = 9 (small number in front, so take it away) - Add the values. Add the bigger groups first, then the small ones.10 + 10 + 9 = 29
- Write the answer. 29
Check. Write 29 in Roman numerals: tens first, then ones: XX + IX = XXIX. ✓
Watch out. Read from the left. A small symbol only gets taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. A numeral is a symbol for a number. Roman numerals use the letters I, V, X, L and C.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like IV or XL) is taken away. Otherwise just add.XL = 50 − 10 = 40 (small number in front, so take it away)
I = 1 - Add the values. Add the bigger groups first, then the small ones.40 + 1 = 41
- Write the answer. 41
Check. Write 41 in Roman numerals: tens first, then ones: XL + I = XLI. ✓
Watch out. Read from the left. A small symbol only gets taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. A numeral is a symbol for a number. Roman numerals use the letters I, V, X, L and C.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like IV or XL) is taken away. Otherwise just add.L = 50
X = 10
V = 5
I = 1
I = 1
I = 1 - Add the values. Add the bigger groups first, then the small ones.50 + 10 + 5 + 1 + 1 + 1 = 68
- Write the answer. 68
Check. Write 68 in Roman numerals: tens first, then ones: LX + VIII = LXVIII. ✓
Watch out. Read from the left. A small symbol only gets taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. A numeral is a symbol for a number. Roman numerals use the letters I, V, X, L and C.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like IV or XL) is taken away. Otherwise just add.XC = 100 − 10 = 90 (small number in front, so take it away)
IX = 10 − 1 = 9 (small number in front, so take it away) - Add the values. Add the bigger groups first, then the small ones.90 + 9 = 99
- Write the answer. 99
Check. Write 99 in Roman numerals: tens first, then ones: XC + IX = XCIX. ✓
Watch out. Read from the left. A small symbol only gets taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.9 = 9 ones (there are no tens)
- Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).9 = IX
- Write the numeral. There is only one part, so that is the whole answer.IX
Check. Read it back: IX (10 − 1) = 9. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.14 = 10 + 4
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).10 = X
- Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).4 = IV
- Put the tens first, then the ones. The tens part goes on the left, the ones part on the right.X + IV = XIV
Check. Read it back: X (10) + IV (5 − 1) = 14. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.23 = 20 + 3
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).20 = XX
- Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).3 = III
- Put the tens first, then the ones. The tens part goes on the left, the ones part on the right.XX + III = XXIII
Check. Read it back: X (10) + X (10) + I (1) + I (1) + I (1) = 23. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.38 = 30 + 8
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).30 = XXX
- Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).8 = VIII
- Put the tens first, then the ones. The tens part goes on the left, the ones part on the right.XXX + VIII = XXXVIII
Check. Read it back: X (10) + X (10) + X (10) + V (5) + I (1) + I (1) + I (1) = 38. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.44 = 40 + 4
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).40 = XL
- Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).4 = IV
- Put the tens first, then the ones. The tens part goes on the left, the ones part on the right.XL + IV = XLIV
Check. Read it back: XL (50 − 10) + IV (5 − 1) = 44. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.76 = 70 + 6
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).70 = LXX
- Write the ones in Roman numerals. Use I for 1, V for 5. For 4 we write IV (1 before 5) and for 9 we write IX (1 before 10).6 = VI
- Put the tens first, then the ones. The tens part goes on the left, the ones part on the right.LXX + VI = LXXVI
Check. Read it back: L (50) + X (10) + X (10) + V (5) + I (1) = 76. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.30 = 3 tens and no ones
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).30 = XXX
- Write the numeral. There is only one part, so that is the whole answer.XXX
Check. Read it back: X (10) + X (10) + X (10) = 30. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.50 = 5 tens and no ones
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).50 = L
- Write the numeral. There is only one part, so that is the whole answer.L
Check. Read it back: L (50) = 50. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.60 = 6 tens and no ones
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).60 = LX
- Write the numeral. There is only one part, so that is the whole answer.LX
Check. Read it back: L (50) + X (10) = 60. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.90 = 9 tens and no ones
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).90 = XC
- Write the numeral. There is only one part, so that is the whole answer.XC
Check. Read it back: XC (100 − 10) = 90. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.100 = 10 tens and no ones
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).100 = C
- Write the numeral. There is only one part, so that is the whole answer.C
Check. Read it back: C (100) = 100. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Key words. Roman numerals are the letters the Romans used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100.
Method. Split the number into tens and ones, write each part in Roman numerals, then put them side by side (tens first).
- Split the number into tens and ones. Roman numerals are built from the tens first and then the ones.40 = 4 tens and no ones
- Write the tens in Roman numerals. Use X for 10, L for 50, C for 100. For 40 we write XL (10 before 50) and for 90 we write XC (10 before 100).40 = XL
- Write the numeral. There is only one part, so that is the whole answer.XL
Check. Read it back: XL (50 − 10) = 40. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII, and 40 is XL, not XXXX.
Method. Change both Roman numerals into numbers. Then compare the numbers.
- Change XLIX into a number. Split into groups and add.XLIX = 49
- Change LI into a number. Do the same.LI = 51
- Compare the numbers. Compare from the left, as usual.49 < 51
- Write the answer with the Roman numerals. XLIX < LI
Check. XLIX is 2 less than LI. ✓
Watch out. Do not compare the number of letters. XC is short but it is 90.
Method. Change both Roman numerals into numbers. Then compare the numbers.
- Change LXIV into a number. Split into groups and add.LXIV = 64
- Change LXVI into a number. Do the same.LXVI = 66
- Compare the numbers. Compare from the left, as usual.64 < 66
- Write the answer with the Roman numerals. LXIV < LXVI
Check. LXIV is 2 less than LXVI. ✓
Watch out. Do not compare the number of letters. XC is short but it is 90.
Method. Change both Roman numerals into numbers. Then compare the numbers.
- Change XC into a number. Split into groups and add.XC = 90
- Change LXXXIX into a number. Do the same.LXXXIX = 89
- Compare the numbers. Compare from the left, as usual.90 > 89
- Write the answer with the Roman numerals. XC > LXXXIX
Check. XC is 1 more than LXXXIX. ✓
Watch out. Do not compare the number of letters. XC is short but it is 90.
Method. Change each Roman numeral into a number, order the numbers, then write the Roman numerals in that order.
- Change each to a number. Split into groups and add.XXXIV = 34
XLIII = 43
XXIV = 24
XL = 40
LX = 60 - Order the numbers. Compare from the left (tens first).24, 34, 40, 43, 60
- Write the Roman numerals in that order. XXIV, XXXIV, XL, XLIII, LX
Check. Count: 5 numerals in the question and 5 in the answer. ✓
Watch out. Write the answer in Roman numerals, because that is what the question asks for.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change IX into a number. Split it into groups and add.IX = IX (10 − 1) = 9
- Change XI into a number. Do the same.XI = X (10) + I (1) = 11
- Do the calculation. Use our normal numbers.9 + 11 = 20
- Change the answer back to Roman numerals. Tens first, then ones.20 = XX + = XX (20)
Check. Read XX again: 10 + 10 = 20. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change XV into a number. Split it into groups and add.XV = X (10) + V (5) = 15
- Change XXV into a number. Do the same.XXV = X (10) + X (10) + V (5) = 25
- Do the calculation. Use our normal numbers.15 + 25 = 40
- Change the answer back to Roman numerals. Tens first, then ones.40 = XL + = XL (40)
Check. Read XL again: 40 = 40. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change LXII into a number. Split it into groups and add.LXII = L (50) + X (10) + I (1) + I (1) = 62
- Change XVII into a number. Do the same.XVII = X (10) + V (5) + I (1) + I (1) = 17
- Do the calculation. Use our normal numbers.62 + 17 = 79
- Change the answer back to Roman numerals. Tens first, then ones.79 = LXX + IX = LXXIX (79)
Check. Read LXXIX again: 50 + 10 + 10 + 9 = 79. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change C into a number. Split it into groups and add.C = C (100) = 100
- Change XXV into a number. Do the same.XXV = X (10) + X (10) + V (5) = 25
- Do the calculation. Use our normal numbers.100 − 25 = 75
- Change the answer back to Roman numerals. Tens first, then ones.75 = LXX + V = LXXV (75)
Check. Read LXXV again: 50 + 10 + 10 + 5 = 75. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change L into a number. Split it into groups and add.L = L (50) = 50
- Change XIV into a number. Do the same.XIV = X (10) + IV (5 − 1) = 14
- Do the calculation. Use our normal numbers.50 − 14 = 36
- Change the answer back to Roman numerals. Tens first, then ones.36 = XXX + VI = XXXVI (36)
Check. Read XXXVI again: 10 + 10 + 10 + 5 + 1 = 36. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change XC into a number. Split it into groups and add.XC = XC (100 − 10) = 90
- Change XLII into a number. Do the same.XLII = XL (50 − 10) + I (1) + I (1) = 42
- Do the calculation. Use our normal numbers.90 − 42 = 48
- Change the answer back to Roman numerals. Tens first, then ones.48 = XL + VIII = XLVIII (48)
Check. Read XLVIII again: 40 + 5 + 1 + 1 + 1 = 48. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Method. Look at the short hour hand first, then the long minute hand.
- Read the hour hand. The short hand is just past IV, so the hour is 4.IV = 4
- Read the minute hand. The long hand points to III. III is the 3rd mark. Each mark is 5 minutes.3 × 5 = 15 minutes
- Write the time. 4 hours and 15 minutes (quarter past 4).4:15
Check. IV is 4 and III is 3: 4 o’clock and 3 × 5 minutes. ✓
Watch out. The short hand shows the hour and the long hand shows the minutes.
Method. Work out each number properly using the rules. Do the tens first, then the ones.
- Write 8. 8 is 5 + 3, so write V and then three Is after it.8 = V + III = VIII
- Write 49. 49 is 40 + 9. Write the tens first, then the ones.40 = XL and 9 = IX, so 49 = XLIX
- Say what went wrong. IIX has two Is in front of the X, but a small symbol can only be taken away once. For 49, Noah put I in front of L, but I can only go in front of V or X.The correct numerals are VIII and XLIX.
Check. VIII = 5 + 1 + 1 + 1 = 8. XLIX = 40 + 9 = 49. ✓
Watch out. Break the number into tens and ones, then write each part.
Method. Look at what the zero is doing in 3,040.
- Write 3,040 in a place-value table. There are 3 thousands, 0 hundreds, 4 tens and 0 ones.
Th H T O 3 0 4 0 - What does the zero in the hundreds column do? It shows that there are no hundreds. It keeps the 3 in the thousands column.3 thousands + 0 hundreds + 4 tens + 0 ones
- What would happen without it? Without the zeros we would write 34, which is a much smaller number.The zeros hold the places so that 3 stays in the thousands column and 4 stays in the tens column.
Check. 3,040 is three thousand and forty. If you leave out the zeros you get 34, which is thirty-four. ✓
Watch out. A zero is a place holder. It is the digit that says “nothing in this column”.
Method. Find the value of each symbol in both numbers.
- Look at 22 in a place-value table. The first 2 is in the tens column and the second 2 is in the ones column.
T O 2 2 - Work out the values. Digit times the value of its column.2 × 10 = 20 and 2 × 1 = 2
- Look at XX. Each X is 10, wherever it is. Roman numerals do not use place value.X + X = 10 + 10 = 20
- Write the answer. In 22 the 2s are worth 20 and 2 (place value). In XX each X is worth 10.
Check. 20 + 2 = 22 and 10 + 10 = 20. ✓
Watch out. Place value is the big idea in our number system: the same digit can be worth different amounts.
Method. Think about what you have learnt about Roman numerals and place value.
- Decide. Compare the sentence with what you know.The sentence is false.
- Give a reason. Roman numerals have no zero. The symbols are I, V, X, L and C, and there is nothing for “nothing”.
Check. Use what you know about the symbols and our number system. ✓
Watch out. Read the sentence carefully before you decide.
Method. Think about what you have learnt about Roman numerals and place value.
- Decide. Compare the sentence with what you know.The sentence is true.
- Give a reason. In 3,456 the 3 is worth 3,000, but in 345 it is worth 300. The position decides.
Check. Use what you know about the symbols and our number system. ✓
Watch out. Read the sentence carefully before you decide.
Method. Think about what you have learnt about Roman numerals and place value.
- Decide. Compare the sentence with what you know.The sentence is true.
- Give a reason. Mathematicians in India developed the ten digits and the idea of zero. They then spread through the Middle East to Europe over many hundreds of years.
Check. Use what you know about the symbols and our number system. ✓
Watch out. Read the sentence carefully before you decide.
Method. Change both numerals to numbers, find how far apart they are, then add 1 because the first and last books both count.
- Change XL to a number. XL is 10 before 50, so take away.XL = 50 − 10 = 40
- Change LV to a number. L is 50 and V is 5.LV = 50 + 5 = 55
- Find the difference. From 40 to 55.55 − 40 = 15
- Add 1. The first book (40) also counts, so the books are 40, 41, …, 55.15 + 1 = 16 books
Check. Count them: 40, 41, 42, …, 55. That is 16 numbers. ✓
Watch out. Counting from 40 to 55 gives 15 steps but 16 numbers. Add 1 to include both ends.
Method. The tens part and the ones part both use the most letters when they have the most repeated symbols. Think about which tens and ones use the most letters.
- Find the tens that use the most letters. Use the table: LXXX (80) uses 4 letters, and XXX (30) uses 3. Any other tens use 2 letters or fewer.LXXX = 4 letters
- Find the ones that use the most letters. Look at the ones: VIII (8) uses 4 letters, VII uses 3.VIII = 4 letters
- Put them together. The tens and the ones with the most letters give the longest numeral.80 + 8 = 88 → LXXXVIII
- Count the letters. L X X X V I I I = 8 letters. Only 88 needs this many.
Check. The next longest are 78, 87 and 38 with 7 letters, so 88 is the longest. ✓
Watch out. Roman numerals with a four (IV) or a nine (IX) are short. The ones with the most repeats are long.