Students can use Class 4 Maths Solutions and Maths Mela NCERT Class 4 Maths Chapter 9 Equal Groups Question Answer Solutions to explore alternative problem-solving methods.
Class 4 Maths Chapter 9 Equal Groups Question Answer Solutions
Equal Groups Class 4 Maths Solutions
Class 4 Maths Chapter 9 Solutions
NCERT Textbook Pages 128-130 Animal Jumps
Fill in the blank spaces with the appropriate numbers. Find how many jumps the animal needs to take to reach its food.
Question 1.
The frog jumps 3 steps at a time. Which numbers will the frog touch? Will it touch 67?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 1]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 2]()
Frog will touch the numbers which are multiples of 3. That is 0, 3, 6, 9, …. But 67 is not a multiple of 3. So, frog will not touch the number 67.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
Question 2.
The squirrel jumps 4 steps at a time. Which numbers will the squirrel touch? How many times should the squirrel jump to reach 60?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 3]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 4]()
Squirrel touches the number 0, 4, 8, 12, …, which are multiples of 4.
Since squirrel jumps 4 steps at a time, and we know that 4 × 15 = 60
Thus, squirrel has to jump 15 steps to reach 60.
Question 3.
The rabbit jumps 6 steps at a time. Which numbers will the rabbit touch? What is the smallest 3-digit number on which the rabbit will land? How many times did the rabbit jump to reach this number?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 5]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 6]()
The rabbit will touch the numbers 0, 6, 12, 18, 24, …
Since 6 × 16 = 96 and 6 × 17 = 102
So, the smallest 3-digit number on which the rabbit will land is 102.
Rabbit had jumped 17 times to reach the number 102.
Question 4.
The kangaroo jumps 8 steps at a time. Which numbers will the kangaroo touch?
Are there numbers that both the rabbit and the kangaroo will touch?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 7]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 8]()
The kangaroo touches the number 0, 8, 16, 24, …, which are multiples of 8.
Rabbit touches the numbers 0, 6, 12, 18, 24, …………
So, there are numbers which both the rabbit and the kangaroo will touch, that are 24, 48, 72, …
Question 5.
To reach 48, how many times did the rabbit jump?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 9]()
How many times did the Kangaroo jump to reach the same number?
What did you observe? Share your thoughts,
Solution:
Since the rabbit jumped 6 steps at a time, 6 steps × 8 = 48. So, the rabbit jumped 8 times to reach 48.
And the kangaroo jumped 8 steps at a time, 8 steps × 6 = 48. So, the kangaroo jumped 6 times to reach the number 48.
We observe that due to size, rabbit take shorter steps than kangaroo and so reach later than kangaroo.
Question 6.
To reach 60, how many times did the frog jump? How many times did the rabbit jump to reach the same number?
What do you observe? Share your thoughts.
Solution:
Since a frog jumped 3 steps at a time and 3 steps × 20 = 60.
So, the frog jumped 20 times to reach the number 60.
And the rabbit jumped 6 steps at a time, 6 steps × 10 = 60.
So, the rabbit jumped 10 times to reach the number 60.
We observe that due to difference in jump size, frog has to take more steps to reach the number 60.
Question 7.
If the cat and the rat land on the same number, the cat will catch the rat. The cat is now on 6 and the rat on 12. When the cat jumps 3 steps forward, the rat jumps 2 steps forward. Will the cat catch the rat? If yes, at which number?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 10]()
Solution:
The cat will jump at the numbers 6, 9, 12, 15, 18, 21, 24, 27,…
And the rat will jump at the numbers 12, 14, 16, 18, 20, 22, 24, 26, 28, ….
In their 6th jump, both the cat and rat will be at 24. Hence, the cat will catch the rat at 24.
Question 8.
Find multiplication and division sentences below. Shade the sentences. How many can you find? Two examples are done for you.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 11]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 12]()
We can make 15 such sentences.
NCERT Textbook Page 130 – Common Multiples
Question 1.
Which numbers do both the frog and the squirrel touch? A few common multiples of 3 and 4 are
Solution:
The frog touches the numbers 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, ….
The squirrel touches the numbers 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ….
So the frog and squirrel both touch the numbers 12, 24, 36, 48, ….
Thus, the common multiples of 3 and 4 are 12,24, 36, 48, ….
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
Question 2.
Which numbers do both the rabbit and the kangaroo touch? A few common multiples of 6 and 8 are .
Solution:
The rabbit touches the numbers 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, ….
The kangaroo touches the numbers 8,16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ….
Both the rabbit and kangaroo touch the numbers 24, 48, 72, 96, ….
So, the common multiples of 6 and 8 are 24^48, 72, 96, ….
NCERT Textbook Pages 131-133 Gulabo’s Garden
Question 1.
Gulabo’s garden has lily flowers. Each lily flower has 3 petals.
How many petals are there in 12 flowers? Show how you found your answer.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 14]()
Gulabo will have 12 × 3 petals.
Petals in 10 lilies = 10 × 3 petals = 30 petals
Petals in 2 lilies = _______________________
Petals in 12 lilies = _______________________
Solution:
Gulabo will have 12 × 3 petals.
Petals in 10 lilies = 10 × 3 petals = 30 petals
Petals in 2 lilies = 2×3 petals = 6 petals
Petals in 12 lilies = 12 × 3 petals = 36 petals
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 13]()
Question 2.
In a hibiscus flower there are 5 petals. Gulabo counted all the petals and found them to be 80. How many flowers did she have?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 15]()
Gulabo has 80 ÷ 5 flowers.
5 petals is 1 flower.
10 petals are 2 flowers.
50 petals are 10 flowers.
Then, 80 petals are _______ flowers.
Solution:
Then, 80 petals are 80 ÷ 5 = 16 flowers.
Question 3.
Gulabo plants some marigold saplings in a box as shown in the picture.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 16]()
There are _______ saplings in each row.
There are _______ rows.
How many saplings has she planted? How did you calculate it?
Mathematical Statement _______
Solution:
There are 11 saplings in each row.
There are 3 rows.
Gulabo has planted a total of 33 saplings in the box.
By using multiplication, we found the number of saplings.
Mathematical statement: There are 3 rows in the box, where the saplings planted are 11 times the number of rows.
Total saplings planted = 3 × 11 = 33
Question 4.
“Dailyfresh” supermarket has kept boxes of strawberries in a big tray.
How many boxes of strawberries does the supermarket have?
Show how you found them.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 17]()
There are _______ columns of strawberry boxes.
There are _______ boxes in each column.
There are _______ boxes in all.
Mathematical Statement _______
Solution:
There are 16 columns of strawberry boxes.
There are 6 boxes in each column.
There are 96 boxes in all.
Mathematical statement: The number of boxes of strawberry = Number of columns of strawberry boxes × number of boxes in each column = 16 × 6 boxes = 96 boxes
Question 5.
Radha runs a bakery shop. She bakes 18 cupcakes in one tray of the size shown below,
(a) Complete arranging the cupcakes in the two trays given below.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 18]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 19]()
(b) She can use two such trays in her oven at a time. How many cupcakes can she make in one attempt? _______
Solution:
Number of cupcakes in a tray = 18
Number of cupcakes in two trays = 2 × 18 = 36
The number of cupcakes, she can make in one attempt = 36
(c) Today she has received a special order. She has made 108 cupcakes. How many trays has she baked?
Solution:
Number of cupcakes in two trays = 36
Number of cupcakes in 4 trays = 2 × 36 = 72
Number of cupcakes in 6 trays = 3 × 36 = 108
So, the required number of trays = 6
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
(d) She has another square baking tray. She can bake 36 mini cupcakes in such a tray. Complete the arrangement below.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 20]()
Number of columns: _______________________
Number of cup cakes in each column: _______________________
Multiplication statement _______
Find different ways for arranging the following numbers of cupcakes in rows and columns in your notebook.
36, 8, 12, and 24
Solution:
Number of columns = 6
Number of cupcakes in each column = 6
Multiplication statement: 6 × 6 = 36.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 21]()
- 36 cupcakes can also be arranged in a tray having 9 rows, and each row has 4 cupcakes.
- 8 cupcakes can be arranged in 4 columns, with 2 cupcakes in each column.
- 12 cupcakes can be arranged in 2 rows, with each row having 6 cupcakes.
- 24 cupcakes can be arranged in 6 columns, and each column has 4 cupcakes.
NCERT Textbook Pages 133-136 The Doubling Magic
Magician Anvi came one day,
To Gulabo’s house, ready to play.
From her coat, with a grand display,
How many flowers are there now? ___
Solution:
46
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 22]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 23]()
What magic did Anvi do?
a) Double of 32 =_____
b) Double of 14 =_____
c) Double of 26 =_____
d) Double of 17 =_____
e) Double of 39 =_____
f) Double of 45 =_____
Solution:
Magician Anvi makes the flowers double after her magic.
(a) Double of 32 = 64
(b) Double of 14 = 28
(c) Double of 26 = 52
(d) Double of 17 = 34
(e) Double of 39 = 78
(f) Double of 45 = 90
Question 1.
Guess what will be the ones digit of the following numbers when doubled.
Write the ones digit in the space provided,
a) 28 ______ b) 56 ______ c) 45 ______ d) 17 ______
Solution:
(a) 6
(b) 2
(c) 0
(d) 4
Question 2.
Give examples of numbers that when doubled give the following digits in the ones place,
a) 0 _______
b) 2 _______
c) 4 _______
d) 6 _______
e) 8 _______
Solution:
(a) 5
(b) 2 6
(c) 2
(d) 8
(e) 4
(Answers may vary)
What do we noticfe about the numbers that we get after doubling? Even or Odd?
Solution:
Doubling is simply an arithmetic operation, i.e., multiplication by 2. After doubling any number, we always get an even number.
Can we get 3, 5, 7, 9 as the ones digit after doubling?
Solution:
Since we only get even numbers after doubling any number. So we cannot get 3, 5, 7, or 9 as the ones digit after doubling the number.
Fill each square in the chart by multiplying the row number by the column number.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 24]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 25]()
What do you notice about the numbers shaded in green? Why is this happening?
Solution:
We notice that the numbers shaded in green, show that when we multiply any two numbers, the order does not matter. For example, 1 × 2 = 2 = 2 × 1, 2 × 3 = 6 = 3 × 2, 5 × 2 = 10 = 2 × 5 and so on.
What do you notice about the numbers shaded in green? Why is this happening?
Solution:
We notice that the numbers shaded in green, show that when we multiply any two numbers, the order does not matter. For example, 1 × 2 = 2 = 2 × 1, 2 × 3 = 6 = 3 × 2, 5 × 2 = 10 = 2 × 5 and so on.
Question 1.
Share the patterns that you notice in the table.
Solution:
We notice that each row/column is a multiple of its row/column number. Also its diagonal cells are all perfect squares.
Question 2.
Are the numbers in row 7 the same as the numbers in column 7? In general, are the numbers in a given row the same as the numbers in the corresponding column? Why does this happen?
Solution:
Yes. In multiplication two numbers can be multiplied in any order, the product remains the same for both the orders.
Question 3.
Is there a row where all answers (products) are even numbers? Which rows have this property?
Solution:
Yes, there are rows where all answers (products) are even numbers. The rows of 2, 4, 6, 8, and 10 have all the products as even numbers.
Question 4.
Is there a row having only odd numbers as products?
Solution:
No.
Question 5.
Are there rows that have both even and odd numbers? What do you notice? Why is it so?
Solution:
Yes, the rows of 1, 3, 5, 7, and 9 have both even and odd numbers. It is because when an odd number is multiplied with an even number, we get an even number, but when an odd number is multiplied with another odd number, we get an odd number.
Question 6.
Are there more even numbers in the chart or odd numbers? How do you know?
Solution:
There are more even numbers in the chart as the tables of 2, 4, 6, 8, and 10 have only even numbers.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
Question 7.
Colour the common multiples of the following numbers. Use different colours for each item.
(a) 2 and 3
(b) 4 and 8
(c) 7 and 9
Share your observations regarding the numbers that are common multiples in each case.
Solution:
(a) Common multiples of 2 and 3 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96.
The common multiples are the multiples of 6 which is the product of 2 and 3.
(b) Common multiples of 4 and 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96.
The common multiples of 4 and 8 are the multiples of 8 which itself is a multiple of 4.
(c) Common multiples of 7 and 9 are 63.
The common multiple of 7 and 9 is the multiple of 63 which is the first common multiple of 7 and 9.
Question 8.
Observe the pattern in the ones digit of the products in row 5?
Observe the ones digit of the products in other rows also. What patterns do you notice?
Solution:
We observe that the ones digits in the products of row 5 are only 0 and 5.
We also observed some other patterns in the ones digits of the products in other rows, like the ones digit in row 1 are the counting numbers from 0 to 10, the ones digits in row 2 are even numbers, the ones digit in row 10 is only 0 and so on.
Question 9.
ere is row 8 of the chart: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
The ones digit of the products are: 8, 6, 4, 2, 0, 8, 6, 4, 2,0 .
Do’ you see a repeating pattern here?
Guess the ones digit of the following products. Verify your answer by multiplying. Write the digit in the space given.
11 × 8 = _____ 12 × 8 = _____ 13 × 8 = _____
Solution:
Yes, the pattern of ones digits is 8, 6, 4, 2, 0 and is repeating.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 26]()
Since 1 × 8 = 8,
2 × 8 = 16, 3 × 8 = 24. So, the ones digits of 11 × 8, 12 × 8, and 13 × 8 are 8, 6, and 4, respectively.
11 × 8 = 88 12 × 8 = 96 13 × 8 = 104
Question 10.
In row 8 of the chart, there is no number whose ones digit is 1. What other digits do not appear as the ones digit?
Solution:
The digits 3, 5, 7, and 9 do not appear as the ones digit in the row 8 of the chart.
Question 11.
Is there a row in which all the digits from 0 to 9 appear as the ones digit? Which rows have this property?
Solution:
Yes, rows 1, 3, 7, and 9 have this property.
Question 12.
It can be seen in row 8 that 0 appears as the ones digit two times.
___ × 8 gives 0 as the ones digit.
What numbers can go in the box? Give 5 examples of such numbers.
Solution:
5 × 8 = 40 or 10 × 8 = 80, gives 0 as the ones digit.
15 × 8 = 120, 20 × 8 = 160, 25 × 8 = 200, 30 × 8 = 240, 35 × 8 = 280.
Question 13.
Is there a row in which 0 appears as the ones digit only once?
Which rows have this property?
Solution:
Yes, the rows of 1, 3, 7, and 9 have this property.
Question 14.
What do you notice about the answers for Questions 11 and 13? Share in the grade.
Solution:
Do it yourself.
NCERT Textbook Page 137 Multiples of Tens
Question 1.
Let us count the number of wheels in tricycles.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 27]()
Number of wheels in 10 tricycles with 3 wheels in each is 10 × 3 wheels = ______ wheels.
Number of wheels in 10 more tricycles with 3 wheels in each is 10 × 3 wheels = _______ wheels.
Number of wheels in 20 tricycles with 3 wheels in each is 20 × 3 wheels = ______ + _____ = ______ wheels.
10 × 3 = _____
20 × 3 = _____
Solution:
Number of wheels in 10 tricycles with 3 wheels in each is 10 × 3 wheels = 30 wheels.
Number of wheels in 10 more tricycles with 3 wheels in each is 10 × 3 wheels = 30 wheels.
Number of wheels in 20 tricycles with 3 wheels in each is 20 × 3 wheels = 30 + 30 = 60 wheels.
10 × 3 = 30
20 × 3 = 60
Question 2.
Let us count the number of wheels in cars.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 28]()
Number of wheels in 10 cars with 4 wheels in each is 10 × 4 wheels = _______ wheels.
Number of wheels in 30 cars with 4 wheels in each is 30 × 4 wheels = _____ + _____ + _____ = _____ wheels.
Solution:
Number of wheels in 10 cars with 4 wheels in each is 10 × 4 wheels = 40 wheels.
Number of wheels in 30 cars with 4 wheels in each is 30 × 4 wheels = 40 + 40 + 40 = 120 wheels.
10 × 4 = 40
30 × 4 = 120
Solve the following in a similar way. Share how you found the answers.
a) 10 × 6 = ____
b) 40 × 6 = ____
c) 10 × 8 = ____
d) 60 × 8 = ____
e) 6 × 8 = ____
g) 4 × 6 = ____
f) 60 × 8 = ____
h) 40 × 8 = ____
Solution:
(a) 10 × 6 = = 60
(b) 40 × 6 = = 60 + 60 + 60 + 60 = 240
(c) 10 × 8 = 80
(d) 60 × 8 = 80 + 80 + -80 + 80 + 80 + 80 = 480
(e) 6 × 8 = 48
(f) 60 × 8 = = 10 × 48 = 480
(g) 4 × 6 = 24
(h) 40 × 8 = 40 + 40 + 40 + 40 + 40 + 40 + 40 + 40 = 320
What happens when the number of groups is a multiple of 10?
Solution:
If a number of groups is a multiple of 10, then it always ends with 0 as ones digit.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
NCERT Textbook Page 138-139 Multiplying Using 10s
Question 1.
Radha is packing cupcakes in boxes of 4. She has packed 18 boxes. How many cupcakes are there in the packed boxes?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 29]()
18 boxes have 4 cupcakes in each.
So, there are 18 × 4 cupcakes.
10 boxes with 4 cupcakes in each contain
10 × 4 cupcakes = ______ cupcakes.
8 boxes with 4 cupcakes in each contain
8 × 4 cupcakes = _________ cupcakes.
18 boxes with 4 cupcakes in each contain
____ + ____ cupcakes
= _________ cupcakes.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 30]()
Solution:
18 boxes have 4 cupcakes in each.
So, there are 18 × 4 cupcakes.
10 boxes with 4 cupcakes in each contain 10 × 4 cupcakes = 40 cupcakes
8 boxes with 4 cupcakes in each contain 8 × 4 cupcakes = 32 cupcakes
18 boxes with 4 cupcakes in each contain 40 + 32 cupcakes = 72 cupcakes
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 31]()
Question 2.
8 bamboo rods are needed to make a bullock cart. How many bamboo rods are needed for 23 carts?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 32]()
One cart needs 8 bamboo rods. 23 carts need 23 × 8 rods.
20 carts with 8 rods in each need 20 × 8 rods = ________ rods.
3 carts with 8 rods in each need 3 × 8 rods = _________ rods
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 33]()
Solution:
20 carts with 8 rods in each need 20 × 8 rods = 160 rods.
3 carts with 8 rods in each need 3 × 8 rods = 24 rods.
So, 23 carts need = 160 rods + 24 rods = 184 rods.
NCERT Textbook Page 139 – Let Us Solve
Question 1.
A flock of 25 geese and 12 sheep have gathered around a pond. Chippi the lizard sees many legs. How many legs does it see?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 34]()
Solution:
Each goose has 2 legs, and each sheep has 4 legs.
25 geese have, 25 × 2 legs = 50 legs
12 sheep have, 12 × 4 legs = 48 legs
Total legs seen by Chippi = 25 geese’s legs + 12 sheep’s legs = 50 legs + 48 legs = 98 legs.
Question 2.
In an auditorium, 8 children are sitting in each row. There are 15 such rows in the school auditorium. How many children are in the auditorium?
Solution:
Children sitting in 1 row = 8
Children sitting in 15 rows = 15 × 8 = 120
So, 120 children are in the auditorium.
Question 3.
A book shop has kept 9 books in each pile. There are 14 such piles. How many books does the shop have?
Solution:
1 pile has 9 books.
14 piles have, 14 × 9 books = 126 books
So, the shop has a total of 126 books.
Question 4.
Surya is making a patch work with beads of two colours as shown in the picture. How many beads has he used? How many each of golden colour beads and white colour beads has he used in making this patch work?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 35]()
Solution:
Number of columns in the patch = 8
Number of beads in 1 column = 4 × 5 = 20
Total number of beads used by Surya = 20 × 8 = 160
Number of white beads in each consecutive 2 columns = 20,
so total number of white beads in the patch = 20 × 4 = 80
Also, Number of golden beads in each consecutive 2 columns = 20,
so total number of golden beads in the patch = 20 × 4 = 80
Question 5.
For each of the following multiplication problems, make your own stories as above. Then find out the product.
(a) 34 × 3
(b) 75 × 5
(c) 46 × 6
(d) 50 × 9
Solution:
(a) In a park, 3 people can sit on 1 bench. There are 34 such benches in the park. How many people can sit on the benches in the park?
34 × 3 = 102 people.
(b) A library has 5 books in 1 shelf. There are 75 such shelves. How many books are there in the library?
75 × 5 = 375 books.
(c) 6 flowers are required to make a bouquet. How many flowers are required to make 46 such bouquets?
46 × 6 = 276 flowers.
(d) Aman is packing 9 cups in a box. He has packed 50 boxes. How many cups are there in the packed boxes?
50 × 9 = 450 cups. (Stories may vary)
NCERT Textbook Pages 140-141 Division
Question 1.
A factory has ordered 58 wheels for the small tempos that they make. Each tempo has 3 wheels.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 36]()
In how many tempos can they fix the wheels? Discuss your thinking in each step.
Number of tempos is 58 ÷ 3
30 wheels are needed for 10 tempos. _______wheels are left.
15 wheels are needed for _______ tempos. _______wheels are left.
9 wheels are needed for_______ tempos. _______ wheels are left.
_______ wheels are needed for_______ tempos.
_______ wheels are left
Solution:
Number of tempos is 58 ÷ 3
30 wheels are needed for 10 tempos. 28 wheels are. left.
15 wheels are needed for 5 tempos. 13 wheels are left.
9 wheels are needed for 3 tempos. 4 wheels are left.
3 wheels are needed for 1 tempos. 1 wheel is left.
Can we make another tempo?
Solution:
No, as only 1 wheel is left.
Question 2.
A dairy farm has many cows. Chippi the lizard is surprised to see 88 legs.
How many cows are there in the farm? Write appropriate sentences as above to show your thinking.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 37]()
Number of legs of a cow: ________
Number of cows is 88 ÷ ________
Show your work using the table below.
Hint: Taking out groups of 10s is easy.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 38]()
Total number of cows = ______
Solution:
Number of legs of a cow: 4
Number of cows is 88 ÷ 4
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 39]()
Total number of cows = 10 + 7 + 5 = 22
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
NCERT Textbook Page 141 – Let Us Solve
Question 1.
In a big aquarium, Jolly fish sees 72 legs of octopuses. How many octopuses are there in the aquarium?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 40]()
Solution:
Number of legs of an octopus = 8
Number of octopuses in the aquarium = 72 ÷ 8
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 41]()
Total number of octopuses = 5 + 3 + 1 = 9.
Question 2.
A sports store packs 4 shuttlecocks in a bigger box. They have 50 shuttlecocks. How many boxes will they need to pack all of them? Can they pack all the shuttlecocks in the boxes? How many are left?
Solution:
Number of shuttlecocks in a bigger box = 4
Total shuttlecocks = 50;
Number of required boxes to pack all the shuttlecocks = 50 ÷ 4
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 42]()
Total number of bigger }oxes needed to pack
the shuttlecocks = 10 + 2 = 12
But 12 boxes only pack 48 shuttlecocks.
Left shuttlecocks = 50 – 48 = 2
Question 3.
Rakul Chachi uses a part other farm to grow flowering plants for the upcoming festive season. She has planted 75 saplings of roses. Each row has 5 saplings. How many rows of saplings has she planted?
Solution:
Number of saplings in a row = 5
Number of rows of saplings planted = 75 ÷ 5
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 43]()
Total number of rows of saplings = 10 + 4 + 1 = 15
Question 4.
Make stories for the following problems and solve them:
(a) 70 ÷ 5
Solution:
Reema packs 5 balls in a box. She has a total of 70 balls. How many boxes will she need to pack all of them?
So, 70 ÷ 5 = 10 + 4 = 14
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 44]()
(b) 84 ÷ 7
Solution:
Rakul made cupcakes for ?70(10+2 the children. She arranged 7 cupcakes in one row on a cT tray. She made a total of 84 cupcakes. How many rows of cupcakes has she arranged?
So, 84 ÷ 7 = 10 + 2 = 12
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 45]()
(c) 69 ÷ 3
Solution:
Mohan fixes 69 wheels for autorickshaws. How many rickshaws can he fix the wheels of, if he fixes all the – 9 wheels of each rickshaw?
Number of auto rickshaws = 69 ÷ 3 = 10 + 10 + 3 = 23
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 46]()
(d) 93 ÷ 6
Solution:
A group of 93 students is going to a field trip. Six mini buses are available for the trip. If all 30 buses carry an equal number of 3 students, how many do not go on trip?
93 ÷ 6 = (10 + 5) = 15, 3 students will not go on the trip. (Stories may vary)
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 47]()
NCERT Textbook Pages 142-143 – Multiples of 100
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 48]()
100 bikes with 2 people on each have
100 × 2 people = _____ people.
200 bikes with 2 people on each have ______people. How did you find it?
100 cars with 4 people in each have 100 × 4 people = _______ people.
500 cars with 4 people in each have ______people.
How did you find it?
Solution:
100 bikes with 2 people on each have
= 100 × 2 people
= 200 people.
200 bikes with 2 people on each have
= 200 × 2 people
= 100 × 2 people + 100 × 2 people
= 200 people + 200 people
= 400 people
100 cars with 4 people in each have
= 100 × 4 people
= 400 people.
500 cars with 4 people in each have
= 500 × 4 people
= (100 × 4 + 100 × 4 + 100 × 4 + 100 × 4 + 100 × 4)
= (400 + 400 + 400 + 400 + 400) people
= 2000 people
How did you find it?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 49]()
500 × 4 = _____
100 × 4 = _____
5 × 4 = _____
50 × 4 = _____
Solution:
We multiplied the number of bikes by the number of people on each bike.
500 × 4 = 2000
5 × 4 = 20
100 × 4 = 400
50 × 4 = 200
What do you notice about multiplying by multiples of 100s.
Solution:
When multiplying a number by multiples of 100s, we get the product of non-zero numbers with the number of zeros that present in multiples of 100s.
Observe the pattern and complete the answers.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 50]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 51]()
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
NCERT Textbook Pages 143-144 More Multiplication
Question 1.
Big electric autorickshaws run in small towns of India and can carry 8 passengers.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 52]()
How many people can travel in 125 such autos in a single round?
i![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 53]()
The total number of passengers 125 × 8.
100 autorickshaws with 8 passengers in each have 100 × 8 passengers = ______ passengers.
20 autorickshaws with 8 passengers in each have 20 × 8 passengers = _______ passengers.
5 autorickshaws with 8 passengers in each have 5 × 8 passengers = __________ passengers.
125 autorickshaws with 8 passengers in each have ____ + ____ + ______= _________ passengers.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 54]()
Solution:
The total passengers are 125 100 autorickshaws with 8 passengers in each have
= 100 × 8 passengers
= 800 passengers
20 autorickshaws with 8 passengers in each have = 20 × 8 passengers = 160 passengers
5 autorickshaws with 8 passengers in each have = 5 × 8 passengers = 40 passengers
125 autorickshaws with 8 passengers in each have = 800 + 160 + 40 = 1000 passengers
Question 2.
Kahlu and Rabia are potters and make earthen pots (kulhad) for trains.
They pack 6 kulhads in a box and have packed 174 boxes for delivery. How many kulhads have they made?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 55]()
Solution:
The total number of kulhads is 174 × 6 = 600 + 420 + 24 = 1044
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 56]()
NCERT Textbook Pages 144-145 Let Us Solve
Question 1.
BP Girl’s school has decided to give all its students two pencils on the first day of school. It has 465 students.
How many pencils does the school need to buy?
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 57]()
Number of pencils given to each student = 2
Total number of students = 465
Total pencils school need to buy = 465 × 2 = 800 + 120 + 10 = 930
Question 2.
234 children of a school have decided to organise a school mela. Each child contributes ?5 for the organisation of the mela. How much money do they collect?
Solution:
Money contributed by each child = ₹ 5
Total children in school mela = 234
Money collected for school mela = 234 × ₹ 5
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 58]()
The total money collected from 234 children, with each contributing ₹ 5 = ₹ 1000 + ₹ 150 + ₹ 20 = ₹ 1170
Question 3.
Make stories for the following problems and solve them.
(a) 439 × 4
(b) 514 × 8
(c) 356 × 5
(d) 623 × 7
Solution:
(a) An NGO organise a game show for children in which they provide tickets of 4 games to each child. There are 439 children. How many tickets are distributed to children?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 59]()
Total tickets distributed = 439 × 4
= 1600 + 120 + 36 = 1756
(b) Raman and Ishita are toymakers and make toys for children. They packed 8 toys in a box and delivered 514 boxes to a company. How many toys have they made?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 60]()
Total number of toys made = 514 × 8 = 4000 + 80 + 32
= 4112
(c) A machine packets 5 notebooks in 1 one bundle.
If the machine packed 356 bundles, how many books were packed?
Total number of books packed = 356 × 5 = 1500 + 250 + 30
= 1780
(d) A factory has ordered 623 packets of bottles, containing 7 bottles in each packet. How many bottles are ordered by the factory?
Total number of bottles ordered = 623 × 7 = 4200 + 140 + 21
= 4361
(Stories may vary)
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
NCERT Textbook Page 146 – Patterns in Division
How much money will each get? Draw arrows linking the money and the children to answer the questions.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 61]()
1. ₹ 30 shared equally among 3 children ______________
2. ₹ 900 shared equally among 3 children ______________
Solution:
1. ₹ 30 shared equally among 3 children = ₹ 30 + ₹ 3 = ₹ 10
2. ₹ 900 shared equally among f 3 children = ₹ 900 + ₹ 3 = ₹ 300
Using the above way of thinking, solve the following problems. Observe and explain the patterns that you notice below.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 62]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 63]()
Question 1.
A load carrying truck has 6 tyres. Chippi the lizard sees 60 tyres. How many trucks are there?
Solution:
Number of tyres in a truck = 6
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 64]()
Total tyres = 60
Number of trucks = 60 + 6 = 10 (i.e., 60 tyres are divided by 6 as each truck has 6 tyres.)
Question 2.
Chippi sees 80 wheels in a car parking space. How many cars are standing in the parking space?
Solution:
Number of wheels in a car = 4
Total wheels of cars in parking space
= 80
Number of cars = 80 + 4 = 20 (i.e., 80 wheels are divided by 4 as there are 4 wheels in one car)
Question 3.
Chippi sees 600 legs of ants walking towards the anthill. How many ants are there?
Solution:
Number of legs of an ant = 6
Total legs of ants walking towards the anthill = 600
So, Ants walking towards the anthill = 600 + 6 = 100 (i.e., 600 legs are divided by 6 as there are 6 legs of an ant)
Question 4.
A fancy shop has packed 800 rubber bands in several packets. Each packet has 4 rubber bands. How many packets of rubber bands does the shop have?
Solution:
Rubber bands in 1 packet = 4
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 65]()
Total rubber bands = 800
Number of packets of rubber bands = 800 + 4 = 200 (i.e., 800 rubber bands have been packed, with 4 rubber bands in each packet)
NCERT Textbook Pages 147-148 Let Us Solve
Question 1.
A school bus hires 7 buses to take 245 children to the transport museum. Each bus carry the same number of children. How many children are traveling in each bus?
Solution:
Number of children travelling museum = 245
Number of buses hired by school = 7
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 66]()
Number of children in each bus = 245 ÷ 7 = 10 + 10 + 10 + 5 = 35
Question 2.
The Darjeeling Himalayan Railway is fondly called as the “Toy Train”. This toy train ride is also a UNESCO World Heritage Site.
This amazing train runs between New Jalpaiguri and Darjeeling and it also passes through one of the highest stations in the world, namely, Ghum. It runs 88 km daily. How much distance does it travel in a week?
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 67]()
Solution:
Distance travelled by “Toy Train” daily = 88 km
Number of days in a week = 7
Distance travelled by “Toy Train” in a week = 88 km × 7 = 560 km + 56 km = 616 km
Question 3.
The 16 km river rafting from Shivpuri to Rishikesh in the Ganga provides the most interesting rafting opportunity. In the summer months, VentureOut company took 259 people for rafting. Each raft can take 7 people. How many rafts did it take?
Solution:
Number of people for rafting = 259
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 68]()
Each raft takes 7 people.
Number of rafts required = 259 ÷ 7
= 10 + 10 + 10 + 7 = 37
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
Question 4.
Anu saves ₹ 45 every month by putting it in her piggy bank.
(a) How much money will Anu save in 6 months?
Solution:
Money saved by Anu in 6 months = ₹ 45 × 6 = ₹ 40 × 6 + ₹ 5 × 6 = ₹ 240 + ₹ 30 = ₹ 270
(b) She distributes the total money saved after 6 months among 6 of her friends. How much does each friend get?
Solution:
Total money distributed equally 210 among 6 friends.
So, money got by each 90- friend = ₹ 270 ÷ 3
= ₹(10 + 10 + 10 + 10 + 5)
= ₹ 45
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 69]()
(c) If she decides to distribute the saved money among 3 friends after 6 months, how much money will each get?
Solution:
Money saved by Anu in 6 months = ₹ 270
Money got by each of 3 friends = ₹ 270 – 3
= ₹ (10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10) = ₹ 90
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 70]()
Question 5.
Raju drives an auto in his village and takes people to the bus stand.
He makes 8 trips in a day. Which of the following questions can be exactly calculated with the above statement?
(a) How much money does he make in a day?
(b) How many trips does he make in 7 days?
(c) How much time does one trip take? *
(d) How many trips does he make in 4 weeks?
Solution:
(a) We cannot say how much money he makes in a day as the price of each trip is not given.
(b) Number of trips made in 7 days = 8 trips × 7 = 56 trips
(c) We cannot say how much time he takes for a trip, as time is not mentioned.
(d) Number of trips in a week (7 days) = 8 × 7 = 56
Number of trips in 4 weeks = 56 × 4 = 50 × 4 + 6 × 4 = 200 + 24 = 224
Question 6.
Solve
(a) 45 × 9
Solution:
45 × 9
So, 45 × 9 = 360 + 45
= 405
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 71]()
(b) 507 × 7
Solution:
507 × 7
So, 507 × 7
= 500 × 7 + 7 × 7
= 3549
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 72]()
(c) 94 ÷ 4
Solution:
When 94 is divided by 4, we get(10 + 10 + 3) = 23, with remainder 2.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 73]()
(d) 778 ÷ 6
Solution:
When 778 is divided by 6, we get (100 + 10 + 10 + 5 + 4) = 129, with remainder 4.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 74]()
(e) 94 × 5
Solution:
94 × 5
So, 94 × 5
= 90 × 5 + 4 × 5
= 450 + 20
= 470
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 75]()
(f) 396 × 4
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 76]()
396 × 4
So, 396 × 4
= 300 × 4 + 90 × 4 + 6 × 4
= 1200 + 360 + 24
= 1584
(g) 83 ÷ 3
Solution:
When 83 is divided by 3, we get (10 + 10 + 5 + 2) = 27, with remainder 2.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 77]()
(h) 635 ÷ 5
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 78]()
When 635 is divided by 5, we get 100 + 10 + 10 + 7 = 127.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9]()
Question 7.
In mathematics, some statements are always true, some are sometimes true, and some are never true. Tick (√) in the appropriate column.
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 79]()
Solution:
![Equal Groups Class 4 Solutions Question Answer Maths Chapter 9 80]()
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