NCERT Solutions Class 5 Maths
Chapter - 6. Be My Multiple, I'll be Your Factor
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1. The hungry cat is trying to catch Kunjan, the mouse. Kunjan is now on the 14th step, and it can jump 2 steps at a time. The cat is on the third step. She can jump 3 steps at a time. If the mouse reaches 28, it can hide in the hole. Find out whether the mouse can get away safely.
a) The steps on which the mouse jumps
Solution:-
The mouse jumps from the 14th step to the 16, 18, 20, 22, 24, 26, and 28th steps.
b) The steps on which the cat jumps
Solution:-
The cat jumps from the 3rd step to the 6, 9, 12, 15, 18, 21, 24, and 27th steps.
c) The steps on which both the cat and the mouse jump
Solution:-
The steps on which both the cat and the mouse jump are the 18th and 24th steps.
d) Can the mouse get away?
Solution:-
Yes, the mouse can get away.
2. Find out
If the cat starts from the 5th step and jumps five steps at a time, and the mouse starts from the 8th step and jumps four steps at a time, can the mouse get away?
Solution:-
If the cat starts from the 5th step and jumps five steps at a time, the cat jumps from the 5th step to the 10, 15, 20, and 25th steps,
Then, the mouse starts from the 8th step and jumps four steps at a time, the mouse jumps from the 8th step to 12, 16, 20, and 24th steps.
Then, the mouse cannot get away. Cat will easily catch the mouse at the 20th step.
3. Who is Monto waiting for?
Monto cat is waiting for somebody. Do you know for whom he is waiting?
There is a trick to find out.
NCERT Solutions for Class 5 Maths Chapter 6 image 1
Mark with a red dot all the numbers which can be divided by 2.
Mark a yellow dot on the numbers which can be divided by 3 and a blue dot on the numbers which can be divided by 4.
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 2
(i) Which are the boxes that have dots of all three colours?
Solution:-
The boxes with dots of all three colours are 12, 24, 36, 48, and 60.
(ii) What are the letters on top of these boxes?
Solution:-
The letters on top of these boxes are M, O, U, S, and E.
(iii) Write the letters, M, O, U, S, and E, in order.
Solution:-
MOUSE,
So, Monto cat is waiting for Mouse.
4. Meow Game: To play this game, everyone stands in a circle. One player calls out ‘one’. The next player says ‘two’ and so on. A player who has to call out 3 or a number which can be divided by 3 has to say ‘Meow’ instead of the number. One who forgets to say ‘Meow’ is out of the game. The last player left is the winner.
Which numbers did you replace with ‘Meow’?
Solution:-
The numbers which replace with ‘Meow’ and multiples of 3 are,
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45 and so on.
5. We say these numbers are multiples of 4. Find the numbers.
Play the game by changing the number to 4. Now, which numbers did you replace with ‘Meow’? These numbers are the multiples of 4.
Solution:-
The numbers which replace with ‘Meow’ and multiples of 4 are,
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, and so on.
(i) Write any ten multiples of 5.
Solution:-
Ten multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50.
6. Common Multiples
(i) Think of a number. If it is a multiple of 3, write it in the red circle. If it is a multiple of 5, write it in the blue circle.
NCERT Solutions for Class 5 Maths Chapter 6 image 3
Solution:-
6 and 36 are multiple of 3.
10 and 40 are multiple of 5.
Then,
NCERT Solutions for Class 5 Maths Chapter 6 image 4
(ii) Some numbers are multiples of both 3 and 5. So we can say that they are both 3 and 5. Think! If you write the multiples common to 3 and 5 in the purple part, then will they still be in both the red and the blue circles?
Solution:-
15 and 30 are the numbers which are multiples of both 3 and 5.
NCERT Solutions for Class 5 Maths Chapter 6 image 5
7. Repeat the game by putting the multiples of 4, 6 and 5 in the circles.
NCERT Solutions for Class 5 Maths Chapter 6 image 6
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 7
(i) What common multiples of 5 and 6 did you write in the green part?
Solution:-
30 and 60 are the common multiples of 5 and 6.
(ii) What common multiples of 4 and 6 are written in the orange part?
Solution:-
12 and 24 are the common multiples of 4 and 6.
(iii) In which coloured part did you write the common multiples of 4, 6 and 5?
Solution:-
The common multiples of 4, 6 and 5 are written in the grey part.
(iv) What is the smallest common multiple of 4, 6 and 5?
Solution:-
The smallest common multiple of 4, 6 and 5 is 60.
8. Tamarind seeds.
(i) Sunita took some tamarind (imli) seeds. She made groups of five with them and found that one seed was left over. She tried making groups of six and groups of four. Each time one seed was left over. What is the smallest number of seeds that Sunita had?
Solution:-
From the question, it is given that,
Sunita is trying to make groups of four, five, and six every time; one seed remains.
So, now we calculate the LCM of 4, 5, and 6 and add 1 to the LCM.
LCM of 4, 5, and 6 is 60
Adding 1 to the LCM, we get 61
Therefore, the smallest number of seeds that Sunita had was 61.
9. More tamarind seeds
Ammini arranges 12 tamarind seeds in the form of different rectangles. Try to make more rectangles like this using 12 tamarind seeds. How many different rectangles can you make?
Solution:-
I got four different rectangles, as shown in the figure below,
NCERT Solutions for Class 5 Maths Chapter 6 image 8
(i) If there are 15 tamarind seeds, how many rectangles can you make?
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 9
10. Colouring the Grid
NCERT Solutions for Class 5 Maths Chapter 6 image 10
In the grid here, a rectangle made of 20 boxes is drawn.
The width of this rectangle is 2 boxes.
(i) What is its length?
Solution:-
By observing the rectangle coloured in the grid, we can say that length of the rectangle is 10 boxes.
(ii) Colour a rectangle made of 20 boxes in some other way.
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 11
(iii) What is the length and width of the rectangle you coloured?
Solution:-
The length of the rectangle is 5 boxes, and the width of the rectangle is 4 boxes.
(iv) In how many ways can you colour a rectangle of 20 boxes? Colour them all in the grid, and write the length and width of each rectangle you have coloured.
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 12
The length and width of rectangle 1 are 5 and 4, respectively.
The length and width of rectangle 2 are 4 and 5, respectively.
The length and width of rectangle 3 are 20 and 1, respectively.
11. There are 18 bangles on the rod. Meena is trying to group them. She can put them in groups of 2, 3, 6, 9 and 18 without any bangle being left.
(i) How many groups will she have if she makes groups of 1 bangle each?
Solution:-
If Meena makes groups of 1 bangle each, she will get 18 groups.
(ii) Now complete the table for different numbers of bangles. For each number, see what different groups can be made.
NCERT Solutions for Class 5 Maths Chapter 6 image 13
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 14
12. Fill the chart
Complete the multiplication chart given here.
NCERT Solutions for Class 5 Maths Chapter 6 image 15
Look at the green boxes in the chart. These show how we can get 12 by multiplying different numbers.
12 = 4 × 3, so 12 is a multiple of both 4 and 3. 12 is also a multiple of 6 and 2, as well as 12 and 1. We say 1, 2, 3, 4, 6, and 12 are factors of 12.
NCERT Solutions for Class 5 Maths Chapter 6 image 16
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 17
NCERT Solutions for Class 5 Maths Chapter 6 image 18
(i) What are the factors of 10? Can you do this from the chart?
Solution:-
From the chart, factors of 10 are 1, 2, 5 and 10.
(ii) What are the factors of 36?
Solution:-
1, 2, 3, 4, 6, 9, 12, 18 and 36 are the factors of 36.
(iii) Find out all the factors of 36 from the multiplication chart.
Solution:-
From the multiplication chart, the factors of 36 are 1, 2, 3, 4, 6, and 9.
(iv) What is the biggest number for which you can find the factors from this chart?
Solution:-
From the multiplication chart, 144 is the biggest number for which we can find the factors.
(v) What can you do for numbers bigger than that?
Solution:-
First, we will extend the multiplication chart and then complete the chart.
13. Common Factors
(i) Write the factors of 25 in the red circle and the factors of 35 in the blue circle.
NCERT Solutions for Class 5 Maths Chapter 6 image 19
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 20
(ii) Which are the factors of 25 and 35 you have written in the common part (purple) of both circles?
Solution:-
5 and 1 are the common factors of 25 and 35 written in the common part (purple).
(iii) Now write the factors of 40 in the red circle and 60 in the blue circle.
NCERT Solutions for Class 5 Maths Chapter 6 image 21
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 22
(iv) What are the factors written in the common (purple) part of the circle? Which is the biggest common factor of 40 and 60?
Solution:-
The factors written in the common (purple) part of the circle are 1, 2, 4, 5, 10 and 20.
20 is the biggest common factor of 40 and 60.
14. Factor Tree
(i) Look at the factor tree. Now can you make another tree like this?
NCERT Solutions for Class 5 Maths Chapter 6 image 23
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 24
(ii) In how many ways can you draw a factor tree for 24? Draw three of them below.
NCERT Solutions for Class 5 Maths Chapter 6 image 25
Solution:-
NCERT Solutions for Class 5 Maths Chapter 6 image 26
15. Tiling Problems
(i) There is a garden in Anu’s house. In the middle of the garden, there is a path. They decided to tile the path using tiles of lengths 2 feet, 3 feet and 5 feet.
The mason tiled the first row with 2 feet tiles, the second row with 3 feet tiles and the third row with 5 feet tiles. The mason has not cut any of the tiles. Then, what is the shortest length of the path?
Solution:-
From the question, it is given that the mason tiled the first row with 2 feet tiles, the second row with 3 feet tiles and the third row with 5 feet tiles.
So, now we have to find the LCM of 2, 3 and 5.
The LCM of 2, 3, and 5 is 30.
Therefore, the shortest length of the path is 30 m.
(ii) Manoj has a new house. He has to lay tiles on the floor. The size of the room is 9 feet × 12 feet. In the market, there are three kinds of square tiles: 1 foot × 1 foot, 2 feet × 2 feet and 3 feet × 3 feet. Which size of tile should he buy for his room so that he can lay it without cutting?
Solution:-
From the question, it is given that the size of the room is 9 feet × 12 feet.
Size of the tiles available in the market are: 1 foot × 1 foot, 2 feet × 2 feet and 3 feet × 3 feet.
Here, 2 is not a factor of the width of the room, i.e. 9 feet, so Manoj cannot lay 2 feet × 2 feet tiles.
1 and 3 are the factors of 3 and 9.
Therefore, Monoj can buy 1 foot × 1 foot and 3 feet × 3 feet so that he can lay it without cutting.
(iii)
NCERT Solutions for Class 5 Maths Chapter 6 image 27
Rani, Geetha and Naseema live near each other. The distance from their house to the road is 90 feet. They decided to tile the path to the road. They all bought tiles of different designs and lengths. Rani bought the shortest tile, Geetha bought the middle-sized one, and Naseema bought the longest one. If they could tile the path without cutting any of the tiles, what is the size of the tiles each has bought? Suggest 3 different solutions. Explain how you get this answer.
Solution:-
From the question, the distance from their house to the road is 90 feet.
Factors of 90 are 1, 2, 3, 5, 6, 9 etc.
Then, possible sizes of tiles are 1 foot × 1 foot, 2 feet × 2 feet, 3 feet × 3 feet, 5 feet × 5 feet, 6 feet × 6 feet and 9 feet × 9 feet etc.
Then the size of the tiles each has bought are,
(i) Rani 1 foot × 1 foot
Geetha 2 feet × 2 feet
Naseema 3 feet × 3 feet
(ii) Rani 2 feet × 2 feet
Geetha 3 feet × 3 feet
Naseema 5 feet × 5 feet
(iii) Rani 3 feet × 3 feet
Geetha 5 feet × 5 feet
Naseema 6 feet × 6 feet
Either way the teacher or student will get the solution to the problem within 24 hours.