Students often refer to Maths Mela Class 5 Solutions Chapter 13 Animal Jumps Question Answer NCERT Solutions to verify their answers.
Class 5 Maths Chapter 13 Animal Jumps Question Answer Solutions
Animal Jumps Class 5 Maths Solutions
Class 5 Maths Chapter 13 Solutions
(Page 164)
A. Find the hidden numbers.
Numbers put in this box get multiplied by a number and come out.
(a) Can you guess the multiplier if you see the 4 numbers coming out of the box?
(b) Is there more than one possible multiplier?
(c) What numbers might have been put inside the box?
Answer:
(a) To guess the multiplier, look for numbers that divide all of 28, 36, 48 and 72 exactly. These are the common factors of the four numbers. The factors of these numbers:
- Factors of 28 include 1, 2, 4, 7, 14, 28.
- Factors of 36 include 1, 2, 3, 4, 6, 9, 12, 18, 36.
- Factors of 48 include 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
- Factors of 72 include 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
The common factors are 1, 2 and 4. So the multiplier could be 1, 2 or 4.
(b) Yes — there is more than one possible multiplier (1, 2, 4).
(c) If the multiplier was 1, the numbers put inside the box were the same: 28, 36, 48, 72.
If the multiplier was 2, the hidden numbers would be each output ÷ 2: 14, 18, 24, 36.
If the multiplier was 4, the hidden numbers would be each output ÷ 4: 7, 9, 12, 18.
B. A number, when arranged in an array, shows the factors of that number. Are there other numbers that are factors of 15? Try to make other arrays for the number 15.
Answer:
Arrays for 15: 1 × 15, 3 × 5, 5 × 3, 15 × 1.
Factors of 15 are 1, 3, 5, 15.
Let us make arrays for the number 12.
Answer:
Arrays: 1 × 12, 2 × 6, 3 × 4, 4 × 3, 6 × 2, 12 × 1. Factors of 12 are: 1, 2, 3, 4, 6, 12.
Explanation: Arrays show factor pairs.
Let Us Do (Page 165)
Make different arrays for the following numbers. Identify the factors in each case.
(a) 10
(b) 14
(c) 13
(d) 20
(e) 25
(f) 32
(g) 37
(h) 46
(i) 54
Answer:
(a) 10 Arrays: 1 × 10, 2 × 5. Factors: 1, 2, 5, 10.
(b) 14 Arrays: 1 × 14, 2 × 7. Factors: 1, 2, 7, 14.
(c) 13 Arrays: only 1 × 13. Factors: 1, 13.
Note: 13 is a prime number because it has only 1 and itself as factors.
(d) 20 Arrays: 1 × 20, 2 × 10, 4 × 5. Factors: 1, 2, 4, 5, 10, 20.
(e) 25 Arrays: 1 × 25, 5 × 5. Factors: 1, 5, 25.
(f) 32 Arrays: 1 × 32, 2 × 16, 4×8. Factors: 1, 2, 4, 8, 16, 32.
(g) 37 Arrays: only 1 × 37. Factors: 1, 37.
Note: 37 is a prime number.
(h) 46 Arrays: 1 × 46, 2 × 23. Factors: 1, 2, 23, 46.
(i) 54 Arrays: 1 × 54, 2 × 27, 3 × 18, 6 × 9. Factors: 1, 2, 3, 6, 9, 18, 27, 54.
Animal jumps (Page 165)
Common multiples of 3 and 4
A rabbit takes a jump of 4 each time. A frog takes a jump of 3 each time. Use the number line to figure out the numbers they will both touch. If the rabbit and the frog start from 0, the numbers both of them will touch are called the common multiples of 3 and 4.
12 is the first common multiple of 3 and 4. What are some other common multiples of 3 and 4? You can continue the number line or take help from the times tables of 3 and 4.
What do you notice about the common multiples of 3 and 4? Discuss in class.
Answer:
A rabbit jumps by 4 steps, a frog by 3 steps. Starting from 0, rabbits land on multiples of 4 (0, 4, 8, 12, 16,…) and frogs land on multiples of 3 (0, 3, 6, 9, 12, 15…).
Let Us Do (Pages 166-170)
Question 1.
Find 5 common multiples of the following pairs of numbers.
(a) 2 and 3
(b) 5 and 8
(c) 2 and 4
(d) 3 and 9
(e) 5 and 10
(f) 9 and 12
(g) 8 and 12
(h) 6 and 8
(i) 6 and 9
What do you notice about the common multiples of different pairs of numbers? Discuss in class.
Answer:
(a) 2 and 3 → multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, … multiples of 3: 3, 6, 9, 12, 15, 18, …
Common multiples: 6, 12, 18, 24, 30.
(b) 5 and 8 → multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, … multiples of 8: 8, 16, 24, 32, 40, …
Common multiples: 40, 80, 120, 160, 200.
(c) 2 and 4 → multiples of 2: 2, 4, 6, 8, 10, … multiples of 4: 4, 8, 12, 16, …
Common multiples: 4, 8, 12, 16, 20.
(d) 3 and 9 → multiples of 3 are 3, 6, 9, 12, 15, 18, … and multiples of 9 are 9, 18, 27, 36, …
Common multiples: 9, 18, 27, 36, 45.
(e) 5 and 10 → multiples of 5 are 5, 10, 15, 20, 25, … and multiples of 10 are 10, 20, 30, 40, …
Common multiples: 10, 20, 30, 40, 50.
(f) 9 and 12 → multiples of 9: 9, 18, 27, 36, 45, 54,… and multiples of 12: 12, 24, 36, 48, 60,…
Common multiples: 36, 72, 108, 144, 180.
(g) 8 and 12 → multiples of 8: 8, 16, 24, 32, 40, 48, … and multiples of 12: 12, 24, 36, 48,…
Common multiples: 24, 48, 72, 96, 120.
(h) 6 and 8 → multiples of 6: 6, 12, 18, 24, 30, 36,… and multiples of 8: 8, 16, 24, 32, 40,…
Common multiples: 24, 48, 72, 96, 120.
(i) 6 and 9 → multiples of 6: 6, 12, 18, 24, 30, 36, 42, … and multiples of 9: 9, 18, 27, 36, 45, …
Common multiples: 18, 36, 54, 72, 90.
Common multiples start from the LCM and are multiples of that LCM.
Question 2.
Food is available at the end of a cobbled road. Robby, the rabbit, takes a jump of 4 each time. Deeku, the deer, takes a jump of 6 each time. They both start at 0. Will both Robby and Deeku reach the food? Who will reach first? How do you know? Explain your answer.
Answer:
Will both Robby and Deeku reach the food?
Robby’s jumps are multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64. Since 64 is a multiple of 4, Robby will reach the food.
Deeku’s jumps are multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.
Since 64 is not a multiple of 6 (64 divided by 6 is 10 with a remainder of 4), Deeku will not land exactly on 64. Therefore, only Robby will reach the food by landing exactly on the final spot.
Who will reach first?
Robby takes 64/4 = 16 jumps to reach the food.
Deeku takes 60/6 = 10 jumps to reach the 60 mark, and then his next jump would be to 66.
Since Robby lands exactly on 64 and Deeku does not, Robby effectively “reaches” the food first by landing on the exact spot.
How do you know?
A number is reached in jumps only if it is divisible by the jump size.
64 is divisible by 4 but not by 6. That is why Robby reaches and Deeku doesn’t. Robby takes 16 jumps (16 × 4 = 64).
Question 3.
Mowgli’s friends live along the trail on the marked places below. Which of his friends will he be able to visit, if he jumps by 2 steps starting from 0?
Answer:
Starting at 0 and jumping by 2 means Mowgli will land on every even number: 0, 2, 4, 6, 8, 10, 12, 14, …, up to the end of the trail shown. So, he will be able to visit friends who live at even-numbered places (2, 4, 6, 8, 10, 12, 14, …).
Part 1 — Jumping by 2 steps
Starting at 0 and jumping by 2 means Mowgli will land on every even number:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, …
Friends’ positions:
- Ant — 4 (even) → Yes
- Spider — 9 (odd) → No
- Frog — 12 (even) → Yes
- Bird’s nest — 14 (even) → Yes
- Snake — 21 (odd) → No
- Tiger — 25 (odd) → No
- Bear — 30 (even) → Yes
- Dog — 35 (odd) → No
- Deer — 39 (odd) → No
- Rabbit — 50 (even) → Yes
- Monkey — 57 (odd) → No
Mowgli will meet:
Frog (12), Bird’s nest (14), Snake (22), Bear (30), Rabbit (50).
Did Mowgli meet the ant, frog, bird and the rabbit?
Answer:
Yes
Part 2 — Jumping by 3 steps
Numbers touched: 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, …
Friends at multiples of 3:
- Spider — 9 → Yes
- Frog—12 → Yes
- Snake — 21 → Yes
- Bear — 30 → Yes
- Deer — 39 → Yes
- Monkey — 57 → Yes
Mowgli will meet: Spider (9), Frog (12), Snake (21), Bear (30) Deer (39), Monkey (57).
Fill in the blank:
3 is a common factor of the numbers 9, 12, 21, 30, 39, 57.
Part 3 — Jumping by 5 steps
Numbers touched: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, …
Friends at multiples of 5:
- Tiger — 25 → Yes
- Bear — 30 → Yes
- Dog — 35 → Yes
- Rabbit — 50 → Yes
Mowgli will meet: Tiger (25), Bear (30), Dog (35), Rabbit (50).
Fill in the blank:
5 is a common factor of the numbers 25, 30, 35, 50.
Part 4 — Jumping by 10 steps
Numbers touched: 0, 10, 20, 30, 40, 50, 60, …
Friends at multiples of 10:
- Bear — 30 → Yes
- Rabbit — 50 → Yes
Mowgli will meet: Bear (30), Rabbit (50).
Fill in the blank:
10 is a common factor of the numbers 30, 50.
Question 4.
Let us find some common factors of the numbers 24 and 36. Note that all jumps in the following questions start from 0.
(a) Can we jump by 2 steps at a time to reach both 24 and 36? Yes/No.
2 is/is not a common factor of 24 and 36.
(b) Can we jump by 3 steps at a time to reach both 24 and 36? Yes/No.
3 is/is not a common factor of 24 and 36.
(c) Can we jump by 4 steps at a time to reach both 24 and 36? Yes/No.
4 is/is not a common factor of 24 and 36.
(d) What other jumps can we take to reach both 24 and 36?
(e) How many common factors can you find for 24 and 36? List them.
(f) What about jumping by 1 step each time to reach both 24 and 36?
Answer:
(a) Yes, 2 is a common factor of 24 and 36 (24 ÷ 2 = 12, 36 ÷ 2 =18).
(b) Yes, 3 is a common factor 24 and 36 (24 ÷ 3 = 8, 36 ÷ 3 = 12).
(c) Yes, 4 is a common factor 24 and 36 (24 ÷ 4 = 6, 36 ÷ 4 = 9).
(d) Other jumps: 1, 6, 12.
(e) Common factors: 1, 2, 3, 4, 6, 12 (6 factors).
(f) Yes, 1 is a common factor.
Question 5.
What are the common factors of 12 and 13?
Answer:
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 13: 1, 13 (since, the number itself and 1 are always factors of any number. 13 is prime).
The only number both sets share is 1. So common factor is 1 only.
Consecutive numbers (like 12 and 13) never share factors other than 1.
Question 6.
Find which of the following numbers can be reached by jumps of 4 steps?
4 is the common factor of the numbers.
Answer:
To be reached by jumps of 4, a number must be a multiple of 4 (i.e., divisible by 4). Check each: .
- 0 ÷ 4 = 0 → Yes (we start at 0).
- 10 ÷ 4 = 2 remainder 2 → No.
- 16 ÷ 4 = 4 → Yes.
- 27 ÷ 4 — 6 remainder 3 → No.
- 36 ÷ 4 = 9 → Yes.
- 48 ÷ 4 = 12 → Yes.
So, numbers reached by jumps of 4: 0, 16, 36, 48.
“4 is the common factor of the numbers 0, 16, 36, 48.”
Question 7.
Find the common factors of the following pairs of numbers,
(a) 12 and 16
(b) 8 and 12
(c) 4 and 16
(d) 2 and 9
(e) 3 and 5
(f) 12 and 15
(g) 20 and 5
(h) 9 and 21
(i) 6 and 27
What do you notice about the common factors of different pairs of numbers? Discuss in class.
Answer:
(a) 12 and 16
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 16: 1, 2, 4, 8, 16.
Common factors: 1, 2, 4.
(b) 8 and 12
Factors of 8: 1, 2, 4, 8.
Factors of 12: 1, 2, 3, 4, 6, 12.
Common factors: 1, 2, 4.
(c) 4 and 16
Factors of 4: 1, 2, 4.
Factors of 16: 1, 2, 4, 8, 16.
Common factors: 1, 2, 4.
(d) 2 and 9
Factors of 2: 1, 2.
Factors of 9: 1, 3, 9.
Common factor: 1 only.
(e) 3 and 5
Factors of 3: 1, 3.
Factors of 5: 1, 5.
Common factor: 1 only.
(f) 12 and 15
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 15: 1, 3, 5, 15.
Common factors: 1, 3.
(g) 20 and 5
Factors of 20: 1, 2, 4, 5, 10, 20.
Factors of 5: 1, 5.
Common factors: 1, 5.
(h) 9 and 21
Factors of 9: 1, 3, 9.
Factors of 21: 1, 3, 7, 21.
Common factors: 1, 3.
(i) 6 and 27
Factors of 6: 1, 2, 3, 6.
Factors of 27: 1, 3, 9, 27.
Common factors: 1, 3.
(Note for students: To find common factors, list the factors of each number and pick the ones that appear in both lists.)
Question 8.
State whether the following statements are true (T) or false (F).
(a) Factors of even numbers must be even.
(b) Multiples of odd numbers cannot be even.
(c) Factors of odd numbers cannot be even.
(d) One of the common multiples of two consecutive numbers is their product.
(e) The only common factor of any two consecutive numbers is 1.
(f) 0 cannot be a factor of any number.
Answer:
(a) False, Example: 6 is even. One factor of 6 is 3 (odd). So, factors of even numbers can be odd or even.
(b) False, Example: 3 is odd. A multiple of 3 is 6, and 6 is even. So, multiples of odd numbers can be even.
(c) True, If a number is odd, none of its factors can be even. Odd numbers have only odd factors. Example: Factors of 15 are 1, 3, 5, 15 — all odd.
(d) True, If two numbers are consecutive (like 4 and 5), their product (4×5 = 20) is a multiple of both 4 and 5, so it is a common multiple.
(e) True, Two consecutive numbers have no common factor other than 1 (they are co-prime). Example: 8 and 9 have only 1 in common.
(f) True, We cannot divide by 0, so 0 is not called a factor of a number. (Saying “0 is a factor” would mean dividing by 0, which is not allowed.)
Question 9.
Sher Khan, the tiger, goes hunting every 3rd day. Bagheera, the panther, goes hunting every 5th day. If both of them start on the same day, on which days will they be hunting together?
Answer:
Together every 15th day (LCM of 3 and 5): Day 15, 30, 45, 60, etc.
We want common multiples of 3 and 5.
Multiples of 3: 3, 6, 9, 12, 15,…
Multiples of 5: 5, 10, 15, 20, …
The first common multiple is 15. So, they hunt together every 15th day (on day 15, 30, 45, …).
Reason: 15 is the smallest number both can reach, so after every 15
Question 10.
(a) In the trail shown earlier, Sher Khan’s house is on number 25 and that of Baloo the bear is on number 30. Mowgli wants to meet his friend Baloo the bear but wants to avoid Sher Khan’s house. How long (in steps) could each jump be?
(b) What number of jumps (in steps) he could choose so that he can meet both Kaa, the snake, at 21 and Akela, the wolf, at 35?
Answer:
(a) A jump length that reaches 30 must divide 30 exactly (so after a certain number of jumps we get to 30).
Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
To avoid 25, the jump length must not reach 25 (i.e., it must NOT divide 25).
Factors of 25: 1, 5, 25. So step sizes 1 and 5 would land on 25 — these must be avoided.
So acceptable jumps (that reach 30 but avoid 25) are: 2, 3, 6,10,15, 30.
(b) Step size must land on both 21 and 35 from 0, so it must divide both 21 and 35.
Common factors of 21 and 35 are found by listing factors:
Factors of 21: 1, 3, 7, 21 Factors of 35: 1, 5, 7, 35
Common factors of 21 and 35: 1 and 7.
So, Mowgli can choose step length 7 (or 1 — but 1 is boring because it visits everything). 7 is the useful jump length to meet both at those places.
Question 11.
Sort the following numbers into those that are—
(a) divisible by 2 only
(b) divisible by 5 only
(c) divisible by 10 only
(d) divisible by 2, 5 and 10.
Answer:
(a) Divisible by 2 only (even numbers not divisible by 5):
34, 22, 66, 56, 38, 78, 62
Check: Each is even (divisible by 2) and not a multiple of 5.
(b) Divisible by 5 only (end with 5, not even):
45, 25, 95, 75, 55
Check: Each ends with 5 (so divisible by 5) and is not even, so not divisible by 2.
(c) Divisible by 10 (divisible by 2 and 5):
90, 30, 40
Check: These end with 0 so they are multiples of 10 (thus divisible by 2 and 5).
(d) Divisible by 2, 5, 10: 90, 30, 40.
