NCERT Solutions for Class 4 Maths Mela Chapter 9 Equal Groups

Page 128

Animal Jumps

Fill in the blank spaces with the appropriate numbers. Find how many jumps the animal needs to take to reach its food.
1. The frog jump 3 steps at time. Which numbers will the frog touch? Will it touch 67?

Answer:
These numbers are multiples of 3: 0, 3, 6, 9, 12, 15, 21, 24, 27, 30….
To determine if 67 will be touched: 67 ÷ 3 = 22 remainder 1
Since there’s a remainder, 67 is not a multiple of 3
Therefore, the frog will not touch 67.

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?

Answer:
These numbers are multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
To reach 60: 60 ÷ 4 = 15 jumps.

3. The rabbit jumps 6 steps at a time.
Which number will the rabbit touch?
What is the smallest 3-digit number on which the rabbit will land?
How many time did the rabbit jump to reach this number?

Answer:
These numbers are multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102…
Smallest 3-digit number: 102
To reach 102: 102 ÷ 6 = 17 jumps.

4. The kangaroo jumps 8 steps at a time. Which numbers will the kangaroo touch?

Answer:
These numbers are multiples of 8: 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96…
Numbers that both rabbit and kangaroo will touch: 0, 24, 48, 72, 96…
(These are common multiples of 6 and 8, which are multiples of 24).

5. To reach 48, how many times did the rabbit jump?
Answer:
To reach 48, rabbit jumps: 48 ÷ 6 = 8 times

How many times did the Kangaroo jump to reach the same number?
Answer:
To reach 48, kangaroo jumps: 48 ÷ 8 = 6 times

What did you observe? Share your thoughts.
Answer:
I observed that the animal which jumps more steps at a time needs fewer jumps to reach the same number. Since the kangaroo jumps more than the rabbit, it reached 48 in fewer jumps.

6. To reach 60, how many times did the frog jump?
How many times did the rabbit jump to reach the same number?
Answer:
To reach 60, frog jumps: 60 ÷ 3 = 20 times
To reach 60, rabbit jumps: 60 ÷ 6 = 10 times

What do you observe? Share your thoughts
Answer:
The frog takes twice as many jumps as the rabbit because its step size is half.

Page 130

Common Multiples

1. Which numbers do both the frog and the squirrel touch? A few common multiples of 3 and 4 are ____________________________.
Answer:
The frog and the squirrel touch both touch their common multiples.
Common multiples of 3 and 4: 12, 24, 36, 48, 60, 72…

2. Which numbers do both the rabbit and the kangaroo touch?
A few common multiples of 6 and 8 are ____________________________.
Answer:
The rabbit and the kangaroo both touch their common multiples.
Common multiples of 6 and 8: 24, 48, 72, 96, 120…

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?

Answer:
Given that Cat jumps 3 steps and rat jumps 2 steps. Cat starts at 6, rat at 12.
After first jump: cat at 9, rat at 14
After second jump: cat at 12, rat at 16
After third jump: cat at 15, rat at 18
After fourth jump: cat at 18, rat at 20
After fifth jump: cat at 21, rat at 22
After sixth jump: cat at 24, rat at 24
So, the cat will catch the rat at position 24.

8. Find multiplication and division sentences below. Shade the sentences. How many can you find? Two examples are done for you.

Answer:

Page 131

Gulabo’s Garden

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.
Gulabo will have 12 × 3 petals.
Petals in 10 lilies 10 × 3 = 30 petals
Petals in 2 lilies ______________
Petals in 12 lilies ______________

Answer:
Gulabo will have 12 × 3 petals.
Petals in 10 lilies = 10 × 3 = 30 petals
Petals in 2 lilies 2 × 3 = 6 petals
Petals in 12 lilies = 30 + 6 = 36 petals

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?
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

Answer:
10 petals in 2 flowers.
20 petals in 4 flowers.
50 petals are 10 flowers.
Then, 80 petals are 2 + 4 + 10 flowers = 16 flowers.
So, there are 80 petals are 16 flowers.

3. Gulabo plants some marigold saplings in a box as shown in the picture.

There are ______ saplings in each row.
Answer:
There are 5 saplings in each row.

There are ______ rows.
Answer:
There are 4 rows.

How many saplings has she planted? How did you calculate it?
Answer:
Total saplings planted: 5 × 4 = 20 saplings

Mathematical Statement_________________
Answer:
Mathematical statement:
Number of saplings in each row = 5
Number of rows = 4
So, total saplings = 4 × 5 = 20.

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.

Answer:
To find the total number of boxes, I’ll multiply the number of rows by the number of columns:
6 rows × 15 columns = 90 boxes

There are ______ columns of strawberry boxes.
Answer:
There are 15 columns of strawberry boxes.

There are _______ boxes in each column.
Answer:
There are 6 boxes in each column.

There are _______ boxes in all.
Answer:
There are 90 boxes in all.

Mathematical Statement _________________
Answer:
Number of rows = 6
Number of columns = 15
So, total number of boxes = 6 × 15 = 90.

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.

Answer:

b) She can use two such trays in her oven at a time. How many cupcakes can she make in one attempt?
Answer:
Number of cupcakes in one tray = 18
So, Number of cupcakes in 2 trays = 2 × 18 cupcakes = 36 cupcakes
Hence, she can make 36 cupcakes in one attempt.

c) Today she received a special order. She has made 108 cupcakes. How many trays has she baked?
Answer:
She has to make 108 cupcakes in total.
We know that there are 18 cupcakes in one tray.
So, the number of trays required for 108 cupcakes
= 108 cupcakes ÷ 18 = 6 trays
Hence, she has baked 6 trays of cupcakes.

d) She has another square baking tray. She can bake 36 mini cupcakes in such a tray. Complete the arrangement below.

Answer:

Number of column:_______
Answer:
Number of columns: 6

Number of cupcakes in each column: _______
Answer:
Number of cupcakes in each column: 6

Multiplication statement _______
Answer:
Number of columns = 6
Number of cupcakes in each column = 6
So, total number of cupcakes = 6 × 6 = 36

Find different ways of arranging the following numbers of cupcakes in rows and columns in your notebook. 36, 8, 12, and 24
Answer:
36 cupcakes:
6 row × 36 columns = 36 cupcakes
8 cupcakes:
2 rows × 4 columns = 8 cupcakes
4 rows × 2 columns = 8 cupcakes
12 cupcakes:
2 rows × 6 columns = 12 cupcakes
6 rows × 2 columns = 12 cupcakes
24 cupcakes:
4 rows × 6 columns = 24 cupcakes
6 rows × 4 columns = 24 cupcakes.

Page 133

The Doubling Magic

Magician Anvi came one day,
To Gulabo’s house, ready to play.
From her coat, with a grand display,
She pulled out 23 flowers, bright and gay!
She smiled and said, “Now watch and see, How many flowers will there be?”
How many flowers are there now? ______________
Answer:
There are now 46 flowers.
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

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 ______
Answer:
a) 8 × 2 = 16, ones digit: 6
b) 6 × 2 = 12, ones digit: 2
c) 5 × 2 = 10, ones digit: 0
d) 7 × 2 = 14, ones digit: 4

2. Give examples of numbers that when doubled give the following digits in the one place.
a) 0 _______
b) 2 _______
c) 4 _______
d) 6 _______
e) 8 _______
Answer:
a) 0 as ones digit: 5, 15, 25, 35, 45
b) 2 as ones digit: 1, 11, 21, 31, 41
c) 4 as ones digit: 2, 12, 22, 32, 42
d) 6 as ones digit: 3, 13, 23, 33, 43
e) 8 as ones digit: 4, 14, 24, 34, 44

What do we notice about the numbers that we get after doubling? Even or Odd?
Answer:
After doubling, we can only get even digits (0, 2, 4, 6, 8) in the ones place. We cannot get 3, 5, 7, 9 as ones digits after doubling.

Page 135

Fill each square in the chart by multiplying the row number by the column number.

What do you notice about the numbers shaded in green? Why is this happening?
Answer:
All the numbers shaded in green are even numbers. They also appear in matching pairs on both sides of the central line.
When any number is multiplied by an even number, the product is always even. The green numbers come from rows and columns with even numbers. Also, multiplication works the same way both ways (a × b = b × a), so the same number appears at the same distance on either side of the central line.
In short, the numbers are green because they are even, and they are arranged symmetrically because the order of multiplication does not change the answer.

1. Share the patterns that you notice in the table.
Answer:
Patterns in the table:
► The diagonal line from top-left to bottom-right contains square numbers (1×1, 2×2, 3×3, etc.)
► The products are symmetrical across this diagonal (e.g., 2×3 = 3×2).
► Some products appear multiple times (like 6 appears at 2×3 and 3×2).
► The shaded squares seem to highlight this symmetry pattern.

2. Are the number 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?
Answer:
Yes, the numbers in row 7 are the same as the numbers in column 7. In general, the numbers in any given row are the same as the numbers in the corresponding column. This happens because multiplication is commutative – the order of multiplication doesn’t matter (a×b = b×a).

3. Is there a row where all answers (products) are even numbers? Which rows have this property?
Answer:
Yes, there are rows where all answers are even numbers. Rows 2, 4, 6, 8 and 10 have this property because any even number multiplied by any other number always gives an even product.

4. Is there a row having only odd numbers as products?
Answer:
No, there is no row in the full multiplication table that has only odd numbers as products.

5. Are there row have both even and odd numbers? What do you notice? Why is it so?
Answer:
Yes, there are rows that have both even and odd numbers.
All the odd-numbered rows (1, 3, 5, 7, 9) contain both even and odd products.
When an odd number is multiplied by an odd number, the product is odd. When an odd number is multiplied by an even number, the product is even.

6. Are there more even numbers in the chart or odd numbers? How do you know?
Answer:
There are more even numbers in the chart than odd numbers. Out of 100 products in the chart:
► Even products occur when either factor is even.
► Odd products occur only when both factors are odd.
So odd products occur only when selecting from the 5 odd numbers (5×5 = 25 cells)
The remaining 75 cells contain even products. Therefore, 75 even numbers and 25 odd numbers in the chart.

7. Colour the common multiples of the following numbers. Use different colours for each them.
a) 2 and 3
Answer:
a) 2 and 3: 6, 12, 18, 24, 30…

b) 4 and 8
Answer:
b) 4 and 8: 8, 16, 24, 32, 40…

c) 7 an 9
Answer:
c) 7 and 9: 63, 126, 189…

Share you observations regarding the numbers that are common multiples in each case.
Answer:
For 2 and 3, the common multiples are multiples of their LCM 6. For 4 and 8, the common multiples are simply multiples of 8 since 8 is already a multiple of 4. For 7 and 9, the common multiples are multiples of their LCM 63.

8. Observe the pattern in the one digits of the products in row 5?
Observe the ones digit of the products in other rows also. What patterns do you notice?
Answer:
Pattern in the ones digits of products in row 5:
Row 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Ones digits: 5, 0, 5, 0, 5, 0, 5, 0, 5, 0
The pattern is 5, 0, 5, 0… repeating.
For other rows:
Row 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 (all digits appear)
Row 2: 2, 4, 6, 8, 0, 2, 4, 6, 8, 0 (pattern: 2, 4, 6, 8, 0 repeating)
Row 3: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 (all digits appear in cycle)
Row 4: 4, 8, 2, 6, 0, 4, 8, 2, 6, 0 (pattern: 4, 8, 2, 6, 0 repeating)

9. Here is row 8 of the chart: 8, 16, 24, 32, 30, 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 _____
Answer:
Row 8 ones digits: 8, 6, 4, 2, 0, 8, 6, 4, 2, 0
Yes, there’s a repeating pattern of 8, 6, 4, 2, 0.
For the products:
1 × 8 = 8, so ones digit in 11 is 8.
2 × 8 = 16, so ones digit in 12 is 6.
3 × 8 = 24, so ones digit in 13 is 4.

10. In row 8 of the chart, there is no number whose one digit is 1. What other digits do not appear as the ones digit?
Answer:
In row 8, the digits that don’t appear as ones digits are: 1, 3, 5, 7, 9
(Only 0, 2, 4, 6, 8 appear as ones digits in row 8).

11. Is there a row in which all the digits from 0 to 9 appear as the ones digit? Which row in which all the digits from 0 to 9 appear as the ones digit? Which rows have this property?
Answer:
Yes, row 9 has all digits from 0-9 appearing as ones digits:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90
Ones digits: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
Row 1 also has this property: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Ones digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0

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.
Answer:
In row 8, 0 appears as ones digit when 8 × 5 = 40 and 8 × 10 = 80.
Numbers that when multiplied by 8 give 0 as ones digit: 5, 10, 15, 20, 25
(Any multiple of 5 will work because 5 × 8 = 40, which ends in 0).

13. Is there a row in which 0 appears as the ones digit only once? Which rows have this property?
Answer:
Rows where 0 appears as ones digit only once:
Row 1: Only 1 × 10 = 10 ends in 0
Row 3: Only 3 × 10 = 30 ends in 0
Row 7: Only 7 × 10 = 70 ends in 0
Row 9: Only 9 × 10 = 90 ends in 0
In general, rows with odd numbers have this property.

14. What do you notice about the answers for Questions 11 and 13? Share in the grade .
Answer:
For Question 11 and 13: The rows that have all digits 0-9 as ones digits (Question 11) are rows 1 and 9.
The rows where 0 appears only once (Question 13) include rows 1, 3, 7 and 9.
The connection is that rows 1 and 9 appear in both answers. This happens because rows with numbers that are relatively prime to 10 (like 1, 3, 7, 9) produce all possible digits as remainders when their multiples are divided by 10.

Page 137

Multiples of Tens

1. Let us count the number of wheels in tricycles.

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 = _____
Answer:
Number of wheels in 10 tricycles with 3 wheels each is 10 × 3 wheels = 30 wheels.
Number of wheels in 10 more tricycles with 3 wheels each is 10 × 3 wheels = 30 wheels.
Number of wheels in 20 tricycles with 3 wheels each is 20 × 3 wheels = 60 wheels. (Can also be calculated as 30 + 30 = 60 wheels)
10 × 3 = 30
20 × 3 = 60.

2. Let us count the number of wheels in cars.

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.
10 × 4 = _____
30 × 4 = _____
Answer:
Let us count the number of wheels in cars:
Number of wheels in 10 cars with 4 wheels each is 10 × 4 wheels = 40 wheels.
Number of wheels in 30 cars with 4 wheels each is 30 × 4 wheels = 120 wheels.
(Can be calculated as 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) a) 10 × 6 = ____
b) 40 × 6 = ____
c) 10 × 8 = ____
d) 60 × 8 = ____
e) 6 × 8 = ____
f) 60 × 8 = ____
g) 4 × 6 = ____
h) 40 × 8 = ____
Answer:
a) 10 × 6 = 60
b) 40 × 6 = 240
c) 10 × 8 = 80
d) 60 × 8 = 480
e) 6 × 8 = 48
f) 60 × 8 = 480
g) 4 × 6 = 24
h) 40 × 8 = 320.

Page 138

Multiplying Using 10s

1. Radha is packing  cupcakes in boxes of 4. She has packed 18 boxes. How many cupcakes are there in the packed boxes?
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.
Answer:
18 boxes have 4 cupcakes in each, so there are 18 × 4 = 72 cupcakes.
10 boxes with 4 cupcakes in each contain 10 × 4 = 40 cupcakes.
8 boxes with 4 cupcakes in each contain 8 × 4 = 32 cupcakes.
18 boxes with 4 cupcakes in each contain 40 + 32 = 72 cupcakes.

2. 8 bamboo rods are needed to make a bullock cart. How many bamboo rods are needed for 23 carts?
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.
Answer:
For 23 carts, we need 23 × 8 = 184 bamboo rods.
23 carts need 23 × 8 rods = 184 rods.
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.
Total: 160 + 24 = 184 rods.

Page 139

Let Us Solve

1. A flock of 25 gees and 12 sheep have gathered around a pond. Chippi the lizard sees many legs. How many legs does it see?
Answer:
Geese have 2 legs each, so total legs of Geese = 25 × 2 = 50 legs
Sheep have 4 legs each, so total legs of Sheep = 12 × 4 = 48 legs
Total number of legs = 50 + 48 = 98.

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?
Answer:
In an auditorium:
Number of rows = 15
Children in each row = 8
So, total children in auditorium = 8 × 15 = 120.

3. A book shop has kept 9 books in each row. There are 14 such piles. How many books does the shop have?
Answer:
Number of rows = 14
Books in each row = 9
Therefore, total number of books = 9 × 14 = 126.

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?

Answer:
Surya has arranged the beads in equal groups forming a rectangular patchwork.
The patchwork has 6 rows and 8 columns of small squares.
Each small square contains 4 beads (2 golden and 2 white).
Total number of small squares = 6 × 8 = 48
Total beads used = 48 × 4 = 192
Golden beads = 48 × 2 = 96
White beads = 48 × 2 = 96
So, Surya has used 192 beads in total. He used 96 golden beads and 96 white beads.

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
Answer:
a) 34 × 3
Story: There are 34 boxes. Each box has 3 pencils. How many pencils are there in all?
Calculation: 34 × 3 = 102
So, There are 102 pencils.
b) 75 × 5
Story: A teacher gives 5 chocolates to each of the 75 students. How many chocolates are given in total?
Calculation: 75 × 5 = 375
So, 375 chocolates are given.
c) 46 × 6
Story: A shopkeeper has 46 packets. Each packet contains 6 biscuits. How many biscuits are there altogether?
Calculation: 46 × 6 = 276
So, there are 276 biscuits.
d) 50 × 9
Story: There are 50 rows of chairs. Each row has 9 chairs. How many chairs are there in total?
Calculation: 50 × 9 = 450
So, there are 450 chairs.

Page 140

Division

1. A factory has ordered 58 wheels for the small tempos that they make Each tempo has 3 wheel? In how many tempos can they fix the wheels?
Discuss you 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.
Can we make another tempo?
How many total tempos can the factory make using the 58 wheels?

Answer:
Out of 58 wheels:
30 wheels make 10 tempos, 28 wheels left.
Out of 28 wheels:
15 wheels make 5 tempos, 13 wheels left.
Out of 13 wheels:
9 wheels make 3 tempos, 4 wheels left.
Out of 4 wheels:
3 wheels make 1 tempo, 1 wheel left.
So, there are total 19 tempos with 1 wheel left over.

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.
Number of legs of a cow: ________
Number of cows is 88 ÷ ________

Answer:
Total number of legs = 88.
So, 88 legs ÷ 4 = 22 cows.
We can do it as follows:
40 legs make 10 cows, 48 legs left.
40 legs make 10 cows, 8 legs left.
8 legs make 2 cows, 0 legs left.
So, total number of cows = 22.

Page 141

Let Us Solve

1. In a big aquarium, Jolly fish see 73 legs of octopuses. How many octopuses are there in the aquarium?
Answer:
Number of legs in each octopuses = 8
Total number of legs = 72
Therefore, the number of octopuses = 72 ÷ 8 = 9.

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?
Answer:
Number of shuttlecocks packed in a box = 4
Number of total shuttlecocks = 50
So, number of boxes = 50 ÷ 4 = 12 remainder 2.
Therefore 12 full boxes with 2 shuttlecocks left over.

3. Rakul Chachi uses a part of her 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?
Answer:
Total number of saplings = 75
Number of saplings in each row = 5
Therefore, the number of rows = 75 ÷ 5 = 15.

4. Make stories for the following problems and solve them:
a) 70 ÷ 5
b) 84 ÷ 7
c) 69 ÷ 3
d) 93 ÷ 6
Answer:
a) 70 ÷ 5 = 14
Story: A baker has 70 cupcakes to pack in boxes of 5. How many boxes can be filled?
b) 84 ÷ 7 = 12
Story: 84 students need to be divided into teams of 7. How many teams can be formed?
c) 69 ÷ 3 = 23
Story: A teacher has 69 pencils to distribute equally among 3 classes. How many pencils will each class receive?
d) 93 ÷ 6 = 15 remainder 3
Story: 93 marbles need to be placed in jars, with 6 marbles in each jar. How many jars will be filled and how many marbles will be left over?

Page 142

Multiples of 100

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?
Answer:
100 bikes with 2 people each: total 100 × 2 = 200 people
200 bikes with 2 people each: total 200 × 2 = 400 people
100 cars with 4 people each: total 100 × 4 = 400 people
500 cars with 4 people each: total 500 × 4 = 2000 people.

Page 142

500 × 4 = _____
100 × 4 = _____
5 × 4 = _____
50 × 4 =_____
Answer:
500 × 4 = 2000
100 × 4 = 400
5 × 4 = 20
50 × 4 = 200.

Page 143

Observe the pattern and complete the answer.

Answer:

Page 143

More Multiplication

1. Big electric autorickhaws run in small towns of India and can carry 8 passengers. How many people can travel in 125 such autos in a single round?
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.
Answer:
The total number of passengers 125 × 8.
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.

2. Kuhlu 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?
The total number of kulhads is ________.
Answer:
Number of boxes = 174
Kulhads per box = 6
100 boxes: 100 × 6 = 600 kulhads
70 boxes: 70 × 6 = 420 kulhads
4 boxes: 4 × 6 = 24 kulhads
So, 174 boxes = 600 + 420 + 24 = 1044 kulhads.

Page 144

Let Us Solve

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?
Answer:
Number of students = 465
Number of pencils per student = 2
Therefore, the total number of pencils needed = 465 × 2 = 930.

2. 234 children of a school have decide to organise a school mela. Each child contributes ₹5 for the organisation of the mela. How much money do they collect?
Answer:
Number of students = 234
Contribution from each student = ₹5
Total money collected = 234 × 5 = ₹1170.

3. Make stories for the following problems and solve them.
a) 439 × 4
b) 514 × 8
c) 356 × 5
d) 623 × 7
Answer:
a) 439 × 4 = 1756
Story: Tiwari Academy teaches 439 students per day. How many students will be taught in 4 days?
b) 514 × 8 = 4112
Story: A printer prints 514 pages per hour. How many pages will it print in 8 hours?
c) 356 × 5 = 1780
Story: A school needs 5 notebooks for each of its 356 students. How many notebooks are needed in total?
d) 623 × 7 = 4361
Story: A charity donates 7 meals to families for each donation received. If they received 623 donations, how many meals can they provide?

Page 146

Patterns in Division

How much money will each get? Draw arrows linking the money and the children to answer the questions.

Answer:

Using the above way of thinking, solve the following problems, Observe and explain the patterns that you noticed below.

Answer:

1. A load carrying truck has 6 tyres. Chippi the lizard sees 60 tyres. How many trucks are there?
Answer:
Number of tyres = 60
Number of tyres in one truck = 6
Therefore, the total number of trucks = 60 ÷ 6 = 10.

2. Chippi sees 80 wheels in a car parking space. How many cars are standing in the parking space?
Answer:
Number of wheels = 80
Number of wheels in one car = 6
Therefore, the total number of cars = 80 ÷ 4 = 20.

3. Chippi sees 600 legs of ants walking towards the anthill. How many ants are there?
Answer:
Number of legs = 600
Number of legs in an ant = 6
Therefore, the total number of ants = 600 ÷ 6 = 100.

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?
Answer:
Number of rubber bands = 800
Number of rubber bands in one packet = 4
Therefore, the total number of packets = 800 ÷ 4 = 200.

Page 147

Let Us Solve

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?
Answer:
Number of children = 245
Number of busses = 7
Therefore, the number of children in one bus = 245 ÷ 7 = 35.

2. The Darjeeling Himalayan Railway is fondly called 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?
Answer:
Distance travelled in one day = 88 km
Therefore, the distance travelled in 7 days = 88 × 7 = 616 km.
So, it travels 616 km in a week.

3. The 16 Km river rafting from Shivpuri to Rishikesh in the Ganga provides the most interesting rafting opportunity. In the summer months, Venture Out company took 259 people for rafting. Each raft can take 7 people. How many rafts did it take?
Answer:
Number of people in one raft = 7
Number of people = 259
Therefore, number of raft required = 259 ÷ 7 = 37.

4. Anu saves ₹45 every month by putting it in her piggy bank.
a) How much money will Anu save in 6 months?
b) She distributes the total money saved after 6 months among 6 of her friends. How much does each friend get?
c) If she decides to distribute the saved money among 3 friends after 6 months, how much money will each get?
Answer:
Anu’s saving per month = ₹45
a) Savings in 6 months = 45 × 6 = ₹270
b) Money received by each of 6 friends = 270 ÷ 6 = ₹45
c) Money received by each of 3 friends = 270 ÷ 3 = ₹90.

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?
Answer:
We cannot calculate a) and c) without additional information.
b) Number of trips in 7 days = 8 × 7 = 56.
d) Number of trips in 4 weeks = 8 × 7 × 4 = 224.

6. Solve
a) 45 × 9
b) 507 × 7
c) 94 ÷ 4
d) 778 ÷ 6
c) 94 ÷ 4
d) 778 ÷ 6
e) 94 × 5
g) 83 ÷ 3
h) 635 ÷ 5
Answer:
a) 45 × 9 = 405
b) 507 × 7 = 3549
c) 94 ÷ 4 = 23 remainder 2
d) 778 ÷ 6 = 129 remainder 4
e) 94 × 5 = 470
f) 396 × 4 = 1584
g) 83 ÷ 3 = 27 remainder 2
h) 635 ÷ 5 = 127

7. In mathematics, some statement are always true, some are sometimes true, and some are never true.
Tick in the appropriate column.

Answer:

We have already learned and understood the way the divide method works for the higher numbers but do you know? The dividing method actually works for dividing any shape into equal halves. This is why the divide method is useful. To prove this method is useful you will see the story in the chapter.

In this Chapter two cats are being tricked by a monkey but let me say this while Cats are cute and independent you will see in every story the clever animal is a monkey maybe this is the reason we love it so much. Isn’t it? So, if it had done the wrong thing by tricking the cats it taught them a valuable lesson and that is not to be tricked.

If you want to know how the cats are being tricked check in the chapter. With saying, do you have any of such stories in your mind where monkey actually tricked the other animals or maybe other animals tried to harm the monkey but its clever mind and funny habits actually saved him? If yes, discuss it with your parents and friends. Apart from this funny story, you will actually find an easy way to divide any shapes.

Since you might have read the chapter so you know how to do it? Even if you haven’t read the chapter yet then also this activity is for you because in this chapter you will find the solution of this activity so it is a must if you want to know the answer. So, the activity is to cut different papers.

The papers that you’re going to cut should be in different shapes and every shape should be different and cut equally so that when you try to join it can come into equal halves. Since you have studied this so far you must have understood that this chapter is going to be more creative work than you had studied in previous ones.

Question:
Ravi wants a pencil. It costs Rs 2. He gives a one-rupee coin, one half-rupee coin and one quarter-rupee coin. Is it enough?

Answer:
Ravi has different value coin a one-rupee coin, one half-rupee coin and one quarter-rupee coin
Total value of these coins = 1 + 0.50 + 0.25 = Rs. 1.75
Cost of pencil is Rs. 2 but Ravi has only Rs. 1.75 which short than 0.25. So Ravi could not buy a pencil.