Practicing with Maths Mela Class 5 Solutions Chapter 13 Animal Jumps Question Answer NCERT Solutions improves a student’s confidence in the subject.
Class 5 Maths Chapter 13 Animal Jumps Question Answer Solutions
Animal Jumps Class 5 Maths Solutions
Class 5 Maths Chapter 13 Solutions
(NCERT Pg 164)
Question 1.
Find the Hidden Numbers.
Numbers put in this box get multiplied by a number and come out.
(i) Can you guess the multiplier if you see the 4 numbers coming out of the box?
(ii) Is there more than one possible multiplier?
(iii) What numbers might have been put inside the box?
Share your thoughts in the class.
Answer:
(i) Yes, the multiplier can be 2.
(ii) Yes, the other multipliers can be 1 and 4.
(iii) Here, if the multiplier is 1 then the numbers might be 28,36,48 and 72 itself. If the multiplier is 2 then the numbers put inside the box might be 14(28 ÷ 2), 18(36÷2), 24(48÷2) and 36(72÷2). Also, if the multiplier is 4 then the numbers put inside the box might be 7(28÷4), 9(36÷4), 12(48÷4) and 18(72÷4).
Question 2.
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:
The another possible arrays for the number 15 are
(NCERT Pg 165)
Question 3.
Do you see why 12 is a multiple of 1,2,3,4,6 and 12 ?
(i) 2 × _____ = 12
(ii) 3 × _____ = 12
(iii) 12 × _____ = 12
(iv) 1 × _____ = 12
Answer:
Yes, 12 is a multiple of 1,2,3,4,6 and 12, because
(i) 2 × 6 = 12
(ii) 3 × 4 = 12
(iii) 12 × 1 =12
(iv) 1 × 12 = 12
Let Us Do (NCERT Pg 165)
Question 4.
Make different arrays for the following numbers. Identify the factors in each case.
Numbers like 13 and 37 are called prime numbers. Why?
Answer:
(i) The arrays for number 10 are
The factors of 10 are 1,2,5 and 10.
(ii) The arrays for number 14 are
The factors of 14 are 1,2,7 and 14.
(iii) Do same as part (i).
1 × 13 = 13
Factors = 1,13
(iv) Do same as part (i).
1 × 20 = 20, 2 × 10 = 20, 4 × 5 = 20
Factors = 1,2,4,5,10,20
(v) Do same as part (i).
1 × 25 = 25,5 × 5 = 25
Factors = 1,5,25
(vi) Do same as part (i).
1 × 32 = 32,2 × 16 = 32,4 × 8 = 32
Factors = 1,2,4,8,16,32
(vii) Do same as part (i).
1 × 37 = 37
Factors = 1,37
(viii) Do same as part (i).
1 × 46=46,2 × 23 = 46
Factors = 1,2,23,46
(ix) Do same as part (i).
1 × 54 = 54,2 × 27 = 54,3 × 18 = 54,6 × 9 = 54
Factors = 1,2,3,6,9,18,27,54
We know that the prime numbers are those numbers whose factors are 1 and the number itself only. Since, 37 and 13 have only two factors 1,37 and 1,13, respectively.
So, 13 and 37 are prime numbers.
Animal Jumps (NCERT Pg 165-166)
Question 5.
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.
(i) 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.
(ii) What do you notice about the common multiples of 3 and 4 ? Discuss in class.
Answer:
(i) We know that the multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36, ……and the multiples of 4 are 4,8,12,16,20,24,28,32,36,40, ………… So, the common multiples of 3 and 4, except 12 are 24,36,48, ………… .
(ii) We notice that the common multiples of 3 and 4 are the multiples of 12 , i.e. 12,24 , 36,48, …… …….
Question 6.
A spider takes a jump of 3 every time. A grasshopper takes a jump of 6 each time. Use the number line to find the common multiples of 3 and 6.
6 and 12 are two common multiples of 3 and 6 . You can continue the pattern to find more common multiples. What do you notice about the common multiples of 3 and 6 ? Discuss.
Answer:
We know that the multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36, 39, ………..
and the multiples of 6 are 6,12,18,24, 30,36,42,48,54,60,66, ………… .
So, the common multiples of 3 and 6 are 6 , 12,18,24,30, ………… .
We notice that the common multiples of 3 and 6 are the multiples of 6 itself, i.e. 6 , 12,18,24, …………. .
Question 7.
Let us write the multiples of two numbers- 4 and 6.
Multiples of 4-4,8,12,16, ……
Multiple of 6-6,12,18, ……
12 and 24 are two of the common multiples of 4 and 6. List a few more.
Answer:
We know, multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44,48, ……
and multiples of 6 are 6,12,18,24,30,36,42,48,54,60, ………….
So, the other common multiples except 12 and 24 are 36,48,60, ……..
Let Us Do (NCERT Pg 166-170)
Question 8.
Find 5 common multiples of the following pairs of numbers.
(i) 2 and 3
(ii) 5 and 8
(iii) 2 and 4
(iv) 3 and 9
(v) 5 and 10
(vi) 9 and 12
(vii) 8 and 12
(viii) 6 and 8
(ix) 6 and 9
What do you notice about the common multiples of different pairs of numbers? Discuss in class.
Answer:
(i) We know, the multiples of 2 and 3 are 2,4,6,8,10,12,14,16,18,20,22,24, 26, 28, 30, …… and 3,6,9,12,15,18,21,24,27,30,33, ………. respectively.
Then, the five common multiples are 6, 12, 18, 24, 30.
(ii) Do it same as part (i).
40,80,120,160,200
(iii) Do it same as part (i).
4,8,12,16,20
(iv) Do it same as part (i).
9,18,27,36,45
(v) Do it same as part (i).
10,20,30,40,50
(vi) Do it same as part (i).
36,72,108,144,180
(vii) Do it same as part (i).
24,48,72,96,120
(viii) Do it same as part (i).
24,48,72,96,120
(ix) Do it same as part (i).
18,36,54,72,90
We Observe that
(i) The common multiples of two numbers are always multiples of their least common multiple.
(ii) If one number is a multiple of the other then the common multiples are simply the multiples of the larger number.
Question 9.
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:
Given, Robby, the rabbit takes a jump of 4 steps and Deeku, the deer takes a jump of 6 steps, each time.
The food is kept at 64.
So, the rabbit will land at the multiples of 4 i.e. 4,8,12,16,20,24,28,32,36,40,44, 48,52,56,60,64,68,72, …………. and the deer will land at the multiples of 6 i.e. 6,12,18,24,30,36,42,48,54,60, 66, 72, ……
Clearly, Deeku will not reach the food but Robby will reach the food.
Also, Robby will reach the food first by directly landing on 64 in 16th step. It is because Deeku will jump past 64, i.e. he will pass the food.
Question 10.
(i) 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 ?
(ii) Did Mowgh meet the ant, frog, bird and the rabbit? Notice their positions- 4, 12,14, and 50.2 is a common factor of these numbers.
(iii) Which of his friends will he be able to meet if he jumps by 3 steps? 3 is a common factor of the numbers 9,21,39, and 57.
(iv) Which numbers will he touch if he jumps by 5 steps? _____.
5 is a common factor of the numbers ______.
(v) Which numbers will he touch if he jumps by 10 steps? ______.
10 is a common factor of the numbers
Answer:
(i) Since, Mowgh jumps by 2 steps starting from 0.
So, he will land on the multiples of 2 along the trail, i.e. 2,4,6,8,10,12,14,16,18, 20,22,24,26,28,30,32,34,36,38,40, 42,44,46,48,50,52,54,56,58,60, ______.
As his friends ant, frog, bird, bear and rabbit live at the positions 4, 12, 14, 30 and 50, respectively, that is at the multiples of 2.
So, Mowgli will be able to visit ant, frog, bird, bear and rabbit.
(ii) Yes, Mowgli meet the ant, frog, bird and the rabbit.
(iii) Given, 3 is a common factor of the numbers 9, 21, 39 and 57, at which spider, snake, deer and monkey live, respectively.
So, Mowgli will be able to meet spider, snake, deer and monkey, if he jumps by 3 steps.
(iv) Since, 5 is a common factor of the number 5,10,15,20,25,30,35,40,45,50,55, ……
So, he will touch the multiples of 5, if he jumps by 5 steps.
5 is a common factor of the numbers 25,30,35,50.
(v) Since, 10 is a common factor of the numbers 10,20,30,40,50,60, …………
So, he will touch the multiples of 10 , if he jumps by 10 steps.
10 is a common factors of the numbers 30, 50.
Question 11.
Let us find some common factors of the numbers 24 and 36. Note that all jumps in the following questions start from 0.
(i) 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.
(ii) 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.
(iii) 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.
(iv) What other jumps can we take to reach both 24 and 36?
(v) How many common factors can you find for 24 and 36 ? List them.
(vi) What about jumping by 1 step each time to reach both 24 and 36?
Answer:
We know that the factors of 24 are
1,2,3,4,6,8,12,24
and the factors of 36 are
1,2,3,4,6,12,18,36
So, the common factors of 24 and 36 are 1,2,3,4,6,12
(i) Yes; 2 is a common factor of 24 and 36.
(ii) Yes; 3 is a common factor of 24 and 36.
(iii) Yes; 4 is a common factor of 24 and 36.
(iv) We can take jumps of 1, 6 and 12 as these two numbers are the common factors except 2,3 and 4.
(v) Since, 1, 2, 3, 4, 6 and 12 are the common factors of 24 and 36.
So, there are 6 common factors for 24 and 36.
(vi) Yes, we can reach both 24 and 36 jumping by 1 step. It is because 1 is a factor of every number.
Question 12.
What are the common factors of 12 and 13?
Answer:
We know that factors of 12 and 13 are 1,2,3,4,6, 12 and 1,13, respectively.
Clearly, the common factor of 12 and 13 is only 1.
Alternatively, we know that 13 is a prime number.
So, the common factor of any number and a prime number is always 1, unless the other number is not a multiple of that prime number.
So, the common factor of 12 and 13 is 1.
Question 13
Find which of the following numbers can be reached by jumps of 4 steps?
4 is the common factor of the numbers ……… .
Answer:
The numbers that can be reached by jumps of 4 steps will be given by multiples of 4.
We know, the multiples of 4 are 4,8,12, 16,20,24,28,32,36,40,44,48.
So, 16,36 and 48 are three numbers out of given numbers that can be reached by jumps of 4 steps, starting from zero.
Also, 4 is the common factor of 16, 36 and 48.
Question 14.
Find the common factors of the following pairs of numbers.
(i) 12 and 16
(ii) 8 and 12
(iii) 4 and 16
(iv) 2 and 9
(v) 3 and 5
(vi) 12 and 15
(vii) 20 and 5
(viii) 9 and 21
(ix) 6 and 27
What do you notice about the common factors of different pairs of numbers.
Discuss in class.
Answer:
(i) We know that the factors of 12 are 1,2,3,4,6 and 12 and the factors of 16 are 1,2,4,8 and 16.
Then, the common factors of 12 and 16 are 1, 2 and 4.
(ii) Do same as part (i).
Answer: 1, 2, 4
(iii) Do same as part (i).
Answer: 1, 2, 4
(iv) Do same as part (i).
Answer: 1
(v) Do same as part (i).
Answer: 1
(vi) Do same as part (i).
Answer: 1, 3
(vii) Do same as part (i).
Answer: 1, 5
(viii) Do same as part (i).
Answer: 1, 3
(ix) Do same as part (i).
Answer: 1, 3
We observe that
(i) Some pairs of numbers have only 1 as their common factor (such numbers are called coprime numbers).
(ii) If one number is a factor of another number then the smaller number will be the greatest common factor.
(iii) 1 is always a common factor.
(iv) The common factors are less than or equal to the smaller number.
Question 15.
State whether the following statements are true or false.
(i) Factors of even numbers must be even.
(ii) Multiples of odd numbers cannot be even.
(iii) Factors of odd numbers cannot be even.
(iv) One of the common multiples of two consecutive numbers is their product.
(v) The only common factor of any two consecutive numbers is 1.
(vi) 0 cannot be a factor of any number.
Answer:
(i) False
∵ The factors of even numbers need not to be even.
e.g. The factors of 6 are 1,2,3 and 6 , where 3 is an odd number.
(ii) False
∵ The multiples of odd numbers can be even.
e.g. 6, 12 etc. are even multiples of 3.
(iii) True
∵ The factors of odd numbers cannot be even.
(iv) True
∵ The product of two consecutive numbers is one of their common multiples.
(v) True
∵ Two consecutive numbers share no common factor other than 1 .
(vi) True
∵ No number can be divided by 0 . So, 0 cannot be a factor of any number.
Question 16.
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:
Given, the tiger, Sher Khan goes hunting every 3rd day.
So, Sher Khan goes hunting on days which are multiples of 3 i.e. 3,6,9,12,15,18, 21,24,27,30, …….
Also given, the panther, Bagheera goes hunting every 5th day. So, Bagheera goes hunting on days which are multiples of 5 i.e. 5,10,15,20,25,30, …….
Now, if both of them start on the same day then they will be hunting together on days which are multiples of their common multiple i.e 15,30,45, …….
So, they will be hunting together on 15th, 30th, 45th, … days.
Question 17.
(i) In the trail shown carter, 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?
(ii) 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:
(i) Given, Sher khan’s house number =25 and Baloo’s house number = 30
We know, the factors of 25 are 1,5,25 and the factors of 30 are 1,2,3,5,6,10, 15,30.
Then, the common factors are 1 and 5 . Since, Mowgli wants to meet Baloo but wants to avoid Sher Khan.
So, he cannot jump in the steps of 1 or 5 , as by jumping 1 and 5, Mowgli, will land on Sher Khan’s and Baloo’s houses.
Therefore, he could jump in steps of 2, 3, 6,10,15 and 30.
(ii) Given, the snake’s house number = 21 and the wolf’s house number = 35
We know, the factors of 21 are 1,3,7,21 and the factors of 35 are 1, 5, 7, 35.
Then, the common factors of 21 and 35 are 1 and 7.
Since, Mowgli wants to meet both Kaa and Akela, he could jump in steps of either 1 or 7.
Question 18 Sort the following numbers into those that are
(i) divisible by 2 only
(ii) divisible by 5 only
(iii) divisible by 10 only
(iv) divisible by 2,5 and 10
Answer:
Given numbers gre 90,22,38,30,75,45, 66,78,62,40,84,56,25,95, and 55.
(i) Here, the numbers that are divisible by 2 only are 22,38,66,78,62,84 and 56.
(ii) Here, the numbers that are divisible by 5 only are 75,45,25,95 and 55.
(iii) There are no numbers in the list that are divisible by 10 only.
(iv) Here, the numbers that are divisible by 2, 5 and 10 are 90, 30 and 40.
The given below is the required diagram.
