CBSE Class 8 Mathematics A Story of Numbers Practice Paper Assignment Set 01 with Answers

Practice Paper 12 for Class 8 Maths Ganita Prakash Chapter 3 A Story of Numbers is a full 40-mark paper with 20 questions across Sections A to E, and each question is followed by a clear, step-by-step solution. The questions focus on one-to-one mapping and tally marks grouped in fives, converting Roman numerals such as LXX and DLX, landmark numbers in base 7 and powers of 10, the base-60 Mesopotamian system, and adding Egyptian hieroglyphic numerals with regrouping.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. Convert the Roman numeral LXX to its equivalent in the Hindu number system.
Answer:
L = 50, X = 10, X = 10.
The symbols are in decreasing order, so we add: 50 + 10 + 10 = 70.
So LXX = 70.
In simple words: Fifty plus two tens is seventy.

Teacher's Note:
1. Add when each symbol is equal to or smaller than the one before it.
2. XX after L simply adds 20.

Question 12. What are the first three landmark numbers in a base-7 number system?
Answer:
In base 7, the landmark numbers are powers of 7.
7⁰ = 1, 7¹ = 7, 7² = 7 × 7 = 49.
So the first three landmark numbers are 1, 7 and 49.
In simple words: Start with 1 and keep multiplying by 7.

Teacher's Note:
1. The first landmark in every base is 1.
2. The next one in base 7 would be 343.

Question 13. Give the value of 10⁴ in the Hindu number system and write it in words.
Answer:
10⁴ = 10 × 10 × 10 × 10 = 10,000.
In words: ten thousand.
So 10⁴ = 10,000 (ten thousand), the place value of the fifth digit from the right.
In simple words: Write 1 followed by four zeros: 10,000, ten thousand.

Teacher's Note:
1. 10ⁿ is 1 followed by n zeros.
2. Do not confuse 10⁴ with 10 × 4 = 40.

Question 14. What is the result when you add the Roman numerals V and V? Write the answer in Roman numerals and explain the rule used.
Answer:
V + V = 5 + 5 = 10.
In Roman numerals 10 is X, so V + V = X.
Rule: by the additive principle the values add up to 10, but V is never repeated (VV is not allowed); two fives are regrouped into the next symbol, X.
In simple words: Two fives make ten, and ten is written as X, not VV.

Teacher's Note:
1. V, L and D are never written twice.
2. Regrouping in Roman numerals is like carrying in our column addition.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Explain the method of one-to-one mapping and provide a simple example of how it would have been used by Stone Age people.
Answer:
One-to-one mapping means matching each object in one collection with exactly one object (or mark) in another collection.
If every object is matched and nothing is left over on either side, the two collections have the same number of objects, even if we cannot name that number.
Example: a Stone Age shepherd could put one pebble in a bag for each sheep as it left in the morning. In the evening he takes out one pebble for each sheep that returns.
If pebbles are left in the bag, some sheep are missing; if no pebbles are left, all sheep are back.
Notches on a bone or knots on a string were used in the same way.
In simple words: Match each object with one mark or pebble; equal matches mean equal counts.

Teacher's Note:
1. One-to-one mapping is how counting began, before number names existed.
2. Tally marks are one-to-one mapping written down.

Question 16. Convert the Roman numeral DLX to the Hindu number system. Explain the logic for each component.
Answer:
D = 500, L = 50, X = 10.
D: the first and largest symbol, worth 500.
L: smaller than D and written after it, so it is added: 500 + 50 = 550.
X: smaller than L and written after it, so it is added: 550 + 10 = 560.
No smaller symbol comes before a larger one, so no subtraction is needed.
So DLX = 560.
In simple words: Symbols run from biggest to smallest, so just add: 500 + 50 + 10 = 560.

Teacher's Note:
1. Check pairs from left to right for any subtractive pair first.
2. DLX uses only the additive principle.

Question 17. How does the use of the symbol V (5) and L (50) make the Roman number system more efficient than a simple tally system?
Answer:
In a simple tally each object needs one mark, so 5 needs 5 marks and 50 needs 50 marks.
Roman numerals replace a whole group with one symbol: V stands for five I's, and L stands for five X's (fifty).
Example: 57 needs 57 tally marks, but in Roman numerals it is LVII, only 4 symbols.
Fewer symbols means numbers are quicker to write, shorter to read and easier to compare, and mistakes in counting marks are avoided.
In simple words: One V or L does the job of 5 or 50 marks, so numbers become much shorter.

Teacher's Note:
1. V and L are “halfway” landmarks between I, X and C.
2. Grouping is the key idea that makes any number system better than tallies.

Section D: Long Answer Question (5 Marks)

Question 18. A tailor has C meters of fabric. He sells LXX meters. How many meters of fabric does he have left? Write your final answer in both Roman and Hindu numerals.
Answer:
Fabric left = C − LXX.
Step 1: Convert to Hindu numerals. C = 100; LXX = 50 + 10 + 10 = 70.
Step 2: Subtract. 100 − 70 = 30.
Step 3: Convert back. 30 = 10 + 10 + 10 = XXX.
Check: 70 + 30 = 100, so LXX + XXX = C.
The tailor has 30 metres (XXX metres) of fabric left.
In simple words: 100 metres minus 70 metres leaves 30 metres, which is XXX.

Teacher's Note:
1. Converting to Hindu numerals makes the subtraction easy.
2. Always check a subtraction by adding the answer back.
3. Remember 30 is XXX, since X can be repeated up to three times.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study-1: The Tally Counter
An ancient shepherd uses a tally system to count his flock of 15 goats. He makes a single mark on a stick for each goat. To make counting easier, he uses a simple five-grouping method.
(i) How many total marks (symbols) will the shepherd use to count his 15 goats? (1)
(ii) Draw or describe how the marks would look using the shepherd's five-grouping method. (1)
(iii) If the shepherd saw 5 more goats, how many total marks would he have? (1)
(iv) The shepherd's method demonstrates which fundamental counting principle? (1)
Answer:
(i) One mark for each goat, so 15 marks.
(ii) In each group, 4 upright marks are drawn and the 5th mark is drawn across them. 15 goats give 3 such groups of five:

(iii) 15 + 5 = 20 marks (4 groups of five).
(iv) One-to-one mapping (one mark for each goat), with grouping in fives to make counting easier.
In simple words: Each goat gets one mark, and marks are bundled in fives so they can be counted quickly.

Teacher's Note:
1. Grouping in fives lets you count 5, 10, 15 instead of one by one.
2. Grouping does not change the number of marks, only how easy they are to read.

Question 20. Case Study-2: The Egyptian Accountant
An Egyptian scribe, using the additive base-10 system, needs to add the values of two piles of symbols.
Pile A: 4 symbols for 100, and 7 symbols for 10.
Pile B: 3 symbols for 100, and 5 symbols for 10.
(i) What is the value of Pile A in the Hindu number system? (1)
(ii) What is the value of Pile B in the Hindu number system? (1)
(iii) What is the total sum of the two piles in the Hindu number system? (1)
(iv) How many 100 symbols and how many 10 symbols would the final sum have in the Egyptian system? (1)
Answer:
(i) Pile A = 4 × 100 + 7 × 10 = 400 + 70 = 470.
(ii) Pile B = 3 × 100 + 5 × 10 = 300 + 50 = 350.
(iii) Total = 470 + 350 = 820.
(iv) Putting the piles together gives 7 hundred-symbols and 12 ten-symbols. Ten of the 10-symbols are exchanged for one more 100-symbol, leaving 2 ten-symbols. So the sum has 8 symbols for 100 and 2 symbols for 10 (800 + 20 = 820).
In simple words: 470 + 350 = 820, written as eight 100-symbols and two 10-symbols.

Teacher's Note:
1. In the Egyptian system ten of any symbol are replaced by one of the next symbol.
2. This exchange is the same as carrying in column addition.