✅ SOLUTIONS
Class 5
Chapter 13: Animal Jumps
Math Mela · NCERT Solutions
Class 5Math Mela (NCERT)Chapter 13
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📦 Hidden Numbers Box & Arrays
Box outputs 28, 36, 48, 72 — guess the multiplier(s) and possible inputs.
Solution
(a) Since all four numbers (28,36,48,72) are divisible by 4, the multiplier could be 4.
(b) Yes — more than one multiplier works! Since all numbers are also divisible by 2 and by 1, those work too.
(c) If multiplier=4: inputs were 7, 9, 12, 18. If multiplier=2: inputs were 14, 18, 24, 36. If multiplier=1: inputs were the same numbers themselves.
1, 2, and 4 are the common factors of 28, 36, 48, and 72!
Arrays for 15 and 12 — find all factors.
Solution
15: 1×15=15, 3×5=15 → Factors of 15 = 1, 3, 5, 15
12: 1×12, 2×6, 3×4 → Factors of 12 = 1, 2, 3, 4, 6, 12
Fill blanks: 2×6=12, 3×4=12, 12×1=12, 1×12=12
Every number is always a multiple of itself and of 1!
✍️ Let Us Do — Factors of Various Numbers
Make arrays and find factors of: 10,14,13,20,25,32,37,46,54.
Solution
| Number | Arrays | Factors |
|---|---|---|
| (a) 10 | 1×10, 2×5 | 1, 2, 5, 10 |
| (b) 14 | 1×14, 2×7 | 1, 2, 7, 14 |
| (c) 13 | 1×13 only | 1, 13 (prime!) |
| (d) 20 | 1×20, 2×10, 4×5 | 1, 2, 4, 5, 10, 20 |
| (e) 25 | 1×25, 5×5 | 1, 5, 25 |
| (f) 32 | 1×32, 2×16, 4×8 | 1, 2, 4, 8, 16, 32 |
| (g) 37 | 1×37 only | 1, 37 (prime!) |
| (h) 46 | 1×46, 2×23 | 1, 2, 23, 46 |
| (i) 54 | 1×54, 2×27, 3×18, 6×9 | 1, 2, 3, 6, 9, 18, 27, 54 |
13 and 37 are prime numbers because they have EXACTLY 2 factors — just 1 and themselves. No other number divides them evenly!
🐰🐸 Common Multiples — Rabbit, Frog, Spider
Rabbit(jump 4) & Frog(jump 3): common multiples? Spider(3) & Grasshopper(6): common multiples? 4 and 6?
Solution
3 & 4: 12 is first common multiple. Others: 24, 36, 48... (all multiples of 12)
3 & 6: Common multiples: 6, 12, 18, 24... — ALL multiples of 6 are common (since 6 is itself a multiple of 3)!
4 & 6: 12 and 24 given. More: 36, 48, 60... (all multiples of 12)
✍️ Let Us Do — 5 Common Multiples
Find 5 common multiples for each pair.
Solution
| Pair | 5 Common Multiples |
|---|---|
| (a) 2, 3 | 6, 12, 18, 24, 30 |
| (b) 5, 8 | 40, 80, 120, 160, 200 |
| (c) 2, 4 | 4, 8, 12, 16, 20 |
| (d) 3, 9 | 9, 18, 27, 36, 45 |
| (e) 5, 10 | 10, 20, 30, 40, 50 |
| (f) 8, 12 | 24, 48, 72, 96, 120 |
| (g) 6, 8 | 24, 48, 72, 96, 120 |
| (h) 6, 9 | 18, 36, 54, 72, 90 |
🌟 When one number is a multiple of the other (like 3&9, or 2&4, or 5&10), the common multiples are simply the multiples of the BIGGER number!
🦌 Robby & Deeku; Mowgli's Trail
Robby(jump 4) & Deeku(jump 6) — will both reach the food?
Solution
Yes, both will reach the food — as long as the food is placed at a COMMON MULTIPLE of 4 and 6 (like 12, 24, 36...). Since 12 is the first common multiple, if the food is at position 12: Robby gets there in 3 jumps (4×3=12), Deeku gets there in 2 jumps (6×2=12) — they arrive AT THE SAME TIME, so neither is "first" — it's a tie!
Mowgli's trail — friends at 4,12,14,50 (jump 2); 9,21,39,57 (jump 3); jump 5 and jump 10?
Solution
Jump by 5: touches 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 — 5 is a common factor of all these numbers.
Jump by 10: touches 10, 20, 30, 40, 50 — 10 is a common factor of all these numbers.
🎯 Common Factors of 24 and 36
Which jump sizes reach both 24 and 36? List all common factors.
Solution
| Jump | Reaches 24? | Reaches 36? | Common factor? |
|---|---|---|---|
| (a) 2 | Yes (12 jumps) | Yes (18 jumps) | Yes |
| (b) 3 | Yes (8 jumps) | Yes (12 jumps) | Yes |
| (c) 4 | Yes (6 jumps) | Yes (9 jumps) | Yes |
(d) Other jumps that work: 6 and 12
(e) ALL common factors of 24 and 36: 1, 2, 3, 4, 6, 12
(f) Jump of 1 step: ALWAYS works — 1 is a factor of every number!
Q5. Common factors of 12 and 13?
Solution
Since 13 is prime (factors only 1 and 13, and 13 doesn't divide 12), the ONLY common factor of 12 and 13 is 1.
🔍 More Common Factors & True/False
Q6. Which numbers (0,10,16,27,36,48) can be reached by jumps of 4?
Solution
4 is a common factor of 16, 36, and 48 (10 and 27 are NOT multiples of 4).
Q7. Find common factors of each pair.
Solution
| Pair | Common Factors |
|---|---|
| (a) 12, 16 | 1, 2, 4 |
| (b) 8, 12 | 1, 2, 4 |
| (c) 4, 16 | 1, 2, 4 |
| (d) 2, 9 | 1 |
| (e) 3, 5 | 1 |
| (f) 12, 15 | 1, 3 |
| (g) 9, 21 | 1, 3 |
| (h) 6, 27 | 1, 3 |
🌟 When two numbers share NO factors besides 1 (like 2&9, or 3&5), they're called co-prime!
Q8. True or False?
Solution
| Statement | Answer | Why |
|---|---|---|
| (a) Factors of even numbers must be even | False | 12 is even but has odd factors 1 and 3 |
| (b) Multiples of odd numbers cannot be even | False | 3 is odd, but 3×2=6 is even |
| (c) Factors of odd numbers cannot be even | True | An even factor would force the result to be even |
| (d) A common multiple of two consecutive numbers is their product | True | Consecutive numbers share no common factor besides 1, so their LCM = product |
| (e) The only common factor of two consecutive numbers is 1 | True | Consecutive numbers are always "co-prime" |
| (f) 0 cannot be a factor of any number | True | Dividing by 0 is undefined |
🐯 Sher Khan, Bagheera & Jungle Puzzles
Q9. Sher Khan hunts every 3rd day, Bagheera every 5th day. When do they hunt together?
Solution
Common multiples of 3 and 5: 15, 30, 45...
They hunt together on Day 15, then again every 15 days after (Day 30, Day 45...)!
Q10. (a) Reach Baloo(30) but avoid Sher Khan(25) — jump sizes? (b) Meet Kaa(21) AND Akela(35)?
Solution
(a) Need a factor of 30 that does NOT divide 25 evenly. Factors of 30: {1,2,3,5,6,10,15,30}. Factors of 25: {1,5,25}. Excluding 1 and 5 (which are common to both): valid jump sizes = 2, 3, 6, 10, 15, or 30 steps
(b) Need a common factor of 21 and 35. Factors of 21: {1,3,7,21}. Factors of 35: {1,5,7,35}. Common: 1 or 7 steps
🔟 Sorting by Divisibility
Q11. Sort: 90,22,38,30,75,45,66,78,62,40,84,56,25,95,55 by divisibility.
Solution
| Category | Numbers |
|---|---|
| Divisible by 2 ONLY | 22, 38, 66, 78, 62, 84, 56 |
| Divisible by 5 ONLY | 75, 45, 25, 95, 55 |
| Divisible by 2, 5, AND 10 (all three) | 90, 30, 40 |
💡 A number "divisible by 10 only" is IMPOSSIBLE as a separate category — any number divisible by 10 is AUTOMATICALLY divisible by both 2 and 5 too! So "divisible by 10" and "divisible by 2, 5, and 10" are actually the SAME group: 90, 30, 40.