Practicing with Maths Mela Class 4 Solutions Chapter 9 Equal Groups Question Answer NCERT Solutions improves a student’s confidence in the subject.
Class 4 Maths Chapter 9 Equal Groups Question Answer Solutions
Equal Groups Class 4 Maths Solutions
Class 4 Maths Chapter 9 Solutions
Animal Jumps (NCERT Pg 128-130)
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 ?
Answer:
The frog will touch the numbers that are
0,3,6,9,12,15,18,21,24,27,30,33
36,39,42,45,48,51,54 ……………
No, frog will not touch 67 because 67 is not a multiple of 3.
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?
Answer:
The squirrel will touch the numbers that are
0,4,8,12,16,20,24,28,32,36,40,44,
48,52,56,60,64,68 …………….
Jumps needed to reach 60=60 ÷ 4
=15 times
The squirrel needs to jump 15 times 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?
Answer:
The rabbit will touch numbers that are 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102 and 108.
The first 3-digit number touched by rabbit is 102.
Now, jumps needed to reach 102 = 102 = 6 = 17 times
So, the rabbit jumped 17 times to reach 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?
Answer:
The kangaroo will touch the numbers that are 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144 and and 152.
Common numbers are the common multiples of 6 and 8.
24, 48, 72, 96, 120 are common multiples of 6 and 8.
So yes, the numbers like 24, 48, 72, 96, 120 are touched by both.
Question 5.
(a) To reach 48, how many times did the rabbit jump?
Answer:
(a) To reach 48
For rabbit
Rabbit jumps 6 steps at a time So, rabbit needs to jump to reach 48 = 48 + 6 = 8 times
(b) For kangaroo
Since, the kangaroo jumps 8 steps at a time.
So, kangaroo needs to jump to reach 48 = 48 + 8 = 6
(c) We observe that the number 48 is a common multiple of both 6 and 8.
Question 6.
(a) To reach 60, how many times did the frog jump?
(b) How many times did the rabbit jump to reach the same number?
(c) What do you observe? Share your thoughts.
Answer:
(a) To reach 60,
For Frog
Since, the frog jumps 3 steps at a time.
So, frog needs to jump to reach 60 = 60 + 3 = 20 times
(b) For Rabbit
Since, the rabbit jumps 6 steps at a time. So, rabbit needs to jump to reach 60 = 60 + 6 = 10 times
(c) We observe that the number 60 is a common multiple of both 3 and 6.
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?
Answer:
Cat starts at 6, jumps 3 steps forward every time and rat starts at 12, jumps 2 steps forward every time. We can list their jumps
Cat’s jumps
6→9→12→15→18→21→24
Rat’s jumps
12→14→16→18→20→22→ 24 Both cat and rat land on the same number at 24.
Yes, 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.
Common Multiple (NCERT Pg 130)
Question 1.
Which numbers do both the frog and the squirrel touch? A few common multiples of 3 and 4 are …..
Answer:
Frog touches multiples of (3)
0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33,
36, 39, 42, 45, 48, 51 and 54.
Squirrel touches multiples of (4)
0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40,
44, 48, 52, 56, 60, 64, 68 and 72.
Both the frog and the squirrel touch the numbers 0, 12, 24, 36, 48.
A few common multiples of 3 and 4 are 0, 12, 24, 36, 48, 60, 72, 84 and 96.
Question 2.
Which numbers do both the rabbit and the kangaroo touch? A few common multiples of 6 and 8 are
Answer:
Rabbit multiples (6)
0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90 and 96.
Kangaroo multiples (8)
0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104 and 112.
Both the rabbit and the kangaroo touch the numbers 0, 24, 48, 72, 96.
A few common multiples of 6 and 8 are 0, 24, 48, 72, 96 and 120.
Gulabo’s Garden (NCERT Pg 131-133)
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.
Gulabo will have 12><3 petals.
Petals in 10 lilies 10×3 petals = 30 petals
Petals in 2 lilies
Petals in 12 lilies
Answer:
Petals in 2 lilies 2×3 petals = 6 petals
Petals in 12 lilies 12×3 petals = 36 petals
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?
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:
v 80 +5 = 16
So, 80 petals are 16 flowers.
Question 3.
Gulabo plants some marigold saplings in a box as shown in the picture.
(i) There are ………….. saplings in each row.
(ii) There are ………….. rows.
(iii) How many saplings has she planted?
(iv) How did you calculate it?
(v) Mathematical Statement …………..
Answer:
(i) 11
(ii) 3
(iii) She has planted 11 x 3 = 33 saplings.
(iv) We calculated saplings by using multiplication because we have equal groups (i.e. rows) and each group contains the same number of item (i.e. saplings).
So, 11 x 3 = 33 saplings
(v) Mathematical statement :
The total number of saplings
= Number of saplings in one row x Number of rows
= 11×3
= 33 saplings
Question 4.
‘Dailyfresh’ super market has kept boxes of strawberries in a big tray.
(i) How many boxes of strawberries does the supermarket have? Show how you found them.
(ii) There are ———-columns of strawberry boxes.
(iii) There are ———-boxes in each column.
(iv) There are ———-boxes in all.
(v) Mathematical Statement———-
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 two trays given below.
(b) She can use two such trays in her oven at a time. How many cupcakes can she make in one attempt?
(c) Today she has received a special order. She has made 108 cupcakes. How many trays has she baked?
(d) She has another square baking tray. She can bake 36 mini cupcakes in such a tray. Complete the arrangement below.
(i) Number of columns
(ii) Number of cupcakes in each column
(iii) Multiplication statement
(e) Find different ways of arranging the following numbers of cupcakes in rows and columns in your notebook. 36,8, 12 and 24.
Answer:
(a) Do yourself
(b) Number of cupcakes in 1 tray
= Number of cupcakes in 1 row
x Number of cupcakes in 1 column = 6x 3= 18
Number of cupcakes in 2 trays = 2 x 18 = 36 cupcakes So, she makes 36 cupcakes in one attempt.
(c) Each tray has 18 cupcakes.
So, number of trays = Total cupcakes + Cupcakes per tray = 108 -5-18 = 6 trays
(d) (i) 6
(ii) 6
(iii) Total number of cupcakes
= Total number of columns x number of cupcakes in each column = 6x 6 = 36
(e) Given numbers are 36, 8, 12 and 24. Different ways of arrangements in rows and columns.
- 36 → 6×6 or 9×4 or 4×9 or 3×12 or 12 x 3
- 8 → 4 x 2 or 2×4
- 12 → 3×4 or 4×3 or 2×6 or 6×2
- 24 → 6×4 or 4×6 or 3×8 or 8×3 or 2 x 12 or 12 x 2
The Doubling Magic (NCERT Pg 133-134)
Question 6.
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
(i) How many flowers will there be?”
(ii) How many flowers are there now?
(iii) What magic did Anvi do?
(iv)
(v) (a) Double of 32 = …………..
(b) Double of 14 = …………..
(c) Double of 26 = …………..
(d) Double of 17 = …………..
(e) Double of 39 = …………..
(f) Double of 45 = …………..
Answer:
(i) 23
(ii) 46
(iii) Anvi doubled the flowers by magic.
(iv)
| Flowers before magic | 23 | 10 | 51 | 95 | 150 | 199 | 425 | 500 | 111 | 205 | 250 |
| Flowers after magic | 46 | 20 | 102 | 190 | 300 | 398 | 850 | 1000 | 222 | 410 | 500 |
(iv) (a) 64
(b) 28
(c) 52
(d) 34
(e) 78
(f) 90
(NCERT Pg 134)
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) 47 ______
Answer:
(a) 6 [∵ 28 x 2 = 56, so the ones digit is 6]
(b) 2 [∵ 56 x 2 = 112, so the ones digit is 2]
(c) 0 [∵ 45 x 2 = 90, so the ones digit is 0]
(d) 4 [∵ 47 x 2 = 94, so the ones digit is 4]
Question 2 (i).
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 ______
(ii) Can we get 3, 5, 7, 9 as the ones digit after doubling?
What do we notice about the numbers that we get after doubling? Even or odd?
Answer:
(i) (a) 45
(b) 56
(c) 17
(d) 18
(e) 39
There are many more examples of this type of numbers. Students will do themselves.
(ii) We cannot get 3, 5, 7 or 9 as ones digit after doubling any whole number. Because doubling always gives even numbers like 0, 2, 4, 6 or 8 at the end. So, we noticed about the numbers that we got even number after doubling.
(NCERT Pg 135-136)
Question 3.
Fill each square in the chart by multiplying the row number by the column number.
(i) What do you notice about the numbers shaded in magenta? Why is this happening?
(ii) Share the patterns that you notice in the table.
(iii) Are the numbers in row 7 the same as the numbers in column 7? In general, there are the numbers in a given row the same as the numbers in the corresponding column? Why does this happen?
(iv) Is there a row where all answers (products) are even numbers? Which rows have this property?
(v) Is there a row having only odd numbers as products?
(vi) Are there rows that have both even and odd numbers? What do you notice? Why is it so?
(vii) Are there more even numbers in the chart or odd numbers? How do you know?
(viii) 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.
(ix) Observe the pattern in the ones digits of the products in row 5? Observe the ones digit of the products in other rows also. What patterns do you notice?
(x) Here, in 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 and 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____
(xi) 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?
(xii) Is there a row in which all the digits from 0 to 9 appear as the ones digit? Which rows have this property?
(xiii) 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.
(xiv) Is there a row in which 0 appears as the ones digit only once? Which rows have this property?
(xv) What do you notice about the answers for Questions XII and XIV? Share in the grade.
Answer:
(i) The numbers shaded in magenta on either side of the diagonal are exactly the same because of the commutative property of multiplication. The chart is symmetric across the diagonal.
(ii) The table has mirror-symmetry across the pink diagonal.
Because axb=bxa, the values above and below the diagonal are identical.
(iii) Yes, they are the same.
Let us list them
Row 7 ( 7 x1 to 7 x10 )
7,14,21,28,35,42,49,56,63,70
Column 7(1 x7 to 10 x7)
7,14,21,28,35,42,49,56,63,70
The numbers are exactly the same, just arranged differently.
Yes, the numbers in a given row are the same as the numbers in the corresponding column because multiplication is commutative.
That means a xb=b xa, so rows and columns for the same number will always contain the same values
(iv) Yes, there are rows where all the products are even numbers. The rows with this property are 2,4,6,8 and 10.
Because multiplying any number by an even number always gives an even number.
(v) No, there is no row in the multiplication table ( 1-10 ), where all the products are odd numbers.
(vi) Yes, many rows (especially rows with odd numbers like 1,3,5,7,9) have both even and odd products.
This happens because multiply with both even and odd these rows provide even and odd numbers both.
And Odd x Even = Even,
Odd x Odd = Odd
(vii) There are more even numbers than odd numbers in the multiplication chart. Because only 25 products are odd (from odd x odd), and the remaining 75 products are all even.
(viii) Do yourself.
(ix) Row 5=5,10,15,20,25,30,35,40,45,50
Ones digits
5,0,5,0,5,0,5,0,5,0
Pattern Alternates between 5 and 0
Do yourself for other rows.
(x) 8,16,24,32,40,48,56,64,72,80
Ones digits
8,6,4,2,0,8,6,4,2,0
Pattern 8→6 → 4 → 2 →0, then repeats.
So, yes there is repeating pattern in this row.
Now,
11 x 8=88 →Ones digit =8
12 x 8=96 → Ones digit =6
13 x 8=104 → Ones digit =4
(xi) Ones digits in Row 8
8,6,4,2,0
Digits that do not appear
1,3,5,7,9
(xii) Yes – Row 7
7,14,21,28,35,42,49,56,63,70
Ones digits 7,4,1,8,5,2,9,6,3,0
All digits from 0 to 9 appear once.
(xiii) From Row 8
40 ends with 0
and 80 ends with 0
So, 5 x 8=40
10 x 8=80
Five examples of such numbers
5,10,15,20,25 (Multiples of 5)
Any number ending in 5 or 0 when multiplied by even gives 0 at the end. Five numbers that give 0 as the ones digit when multiplied by 8
5,10,15,20,25
(xiv) Yes; For example, Try Row 1
1,2,3,4,5,6,7,8,9,10
Only 10 ends in 0
So, Row 1 has 0 once and Row 3, Row 7, Row 9 have same property.
(xv) We have noticed in Row 7, all digits from 0-9 appear once at the end.
In Row 5 and Row 10, only 0 appears two times at the end.
This shows how some rows have repeating patterns, while others (like 7) have complete digit coverage.
Multiples of Tens (NCERT Pg 137)
Question 1.
Let us count the number of wheels in tricycles.
(i) Number of wheels in 10 tricycles with 3 wheels in each is 10 × 3 wheels = ………… wheels.
(ii) Number of wheels in 10 more tricycles with 3 wheels in each is 10 × 3 wheels = ………… wheels.
(iii) Number of wheels in 20 tricycles with 3 wheels in each is 20 × 3 wheels = ………… + …………= …………wheels.
Answer:
(i) 30
(ii) 30
(iii) 30+30=60
Question 2.
Let us count the number of wheels in cars.
(i) Number of wheels in 10 cars with 4 wheels in each is 10 × 4 wheels = ________wheels.
Number of wheels in 10 tricycles with 3 wheels in each is 10 × 3 wheels = ________ wheels.
(ii) Number of wheels in 10 more tricycles with 3 wheels in each is 10 × 3 wheels = ________wheels.
(iii) Number of wheels in 20 tricycles with 3 wheels in each is 20 ×3 wheels = ________ + ________ = ________ wheels.
Answer:
(i) 30
(ii) 30
(iii) 30+30=60
Question 2.
Let us count the number of wheels in cars.
(i) Number of wheels in 10 cars with 4 wheels in each is 10 × 4 wheels = ……………….. wheels.
(ii) Number of wheels in 30 cars with 4 wheels in each is 30 ×4 wheels = ……….. + ……….. + ……….. = ……….. wheels.
10 ×4= ………….
30 ×4= …………
(iii) What happens when the number of groups is a multiple of 10 ?
(iv) 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= ………..
(f) 60 ×8= ………..
(g) 4 ×6= ………..
(h) 40 ×8= ………..
Answer:
(i) 40
(ii) 40+40+40=120
10 ×4=40
30 ×4=120
(iii) Multiplying by 10,20,30,40, ………… just means multiplying first, then adding the zero at the end.
(iv) (a) 60
(b) 240
(c) 80
(d) 480
(e) 48
(f) 480
(g) 24
(h) 320
Multiplying Using 10s (NCERT Pg 138)
Question 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 x 4 cupcakes.
(i) 10 boxes with 4 cupcakes in each contain 10×4 cupcakes = ——– cupcakes.
(ii) 8 boxes with 4 cupcakes in each contain 8×4 cupcakes = ——– cupcakes.
(iii) 18 boxes with 4 cupcakes in each contain ——– +——– cupcakes =——– cupcakes.
Answer:
(i) 40
(ii) 32
(iii) 40+32=72
Question 28.
bamboo rods are needed to make a bullock cart. How many bamboo rods are needed for 23 carts?
One car needs 8 bamboo rods. 23 carts need 23×8 rods.
(i) 20 carts with 8 rods in each need 20 × 8 rods = ………. rods.
(ii) 3 carts with 8 rods in each need 3 × 8 rods = ………. rods.
Answer:
(i) 160
(ii) 24
Let Us Solve (NCERT Pg 139)
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?
Answer:
Geese have 2 legs each.
Sheep have 4 legs each.
Geese legs =25 × 2=50 legs
Sheep legs =12 × 4=48 legs
Total legs =50+48=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?
Answer:
Given that 8 children are sitting in each row and number of rows is 15 .
So, total children = Number of rows × Number of children in each row =15 × 8=120 children
Question 3.
A book shop has kept 9 books in each pile. There are 14 such piles. How many books does the shop have?
Answer:
Given that number of books in each pile =9 and number of piles =14
So, total books = Number of piles × Number of books in each pile =14 × 9=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 magenta colour beads and white colour beads has he used in making this patch work?
Answer:
From the image, each row has 16 beads and there are 10 rows.
Magenta and white beads used in manner alternate that means half are magenta and half are white.
So, total beads = Number of rows
Number of beads
= 10 x 16
= 160
Therefore, he used 80 magenta and 80 white colour beads.
Question 5.
For each of the following multiplication problems, make your own stories as above. Then, find out the product.
(a) 34 x 3
(b) 75 x 5
(c) 46 x 6
(d) 50 x 9
Answer:
(a) Do yourself.
(b) Do yourself.
(c) Do yourself.
(d) Do yourself.
Division (NCERT Pg 140-141)
Question 1.
A factory has ordered 58 wheels for the small tempos that they make. Each tempo has 3 wheels In how many tempos can they fix the wheels? Discuss your thinking in each step.
(i) Number of tempos is 58 ÷ 3.
30 wheels are needed for 10 tempos. ……….. wheels are left.
(ii) 15 wheels are needed for ……….. tempos……….. wheels are left.
(iii) 9 wheels are needed for ……….. tempos………… wheels are left.
(iv) ……….. wheels are needed for ……….. tempos. ……….. wheels are left. Can we make another tempo?
(v) How many total tempos can the factory make using the 58 wheels?
Answer:
(i) 0
With 30 wheels, we can make 10 tempos.
No wheel is left.
(ii) 5 ; 0
With 15 wheels, we can make 5 tempos No wheel is left.
(iii) 3 ; 0
As [9 ÷3=3, remainder 0 ]
No, wheel is left.
(iv) Do yourself.
(v) 19
With 58 wheels, we can make 19 tempos. 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.
(i) (a) Number of legs of a cow is ………..
(b) Number of cows is 88÷………..
(ii) Show your work using the table below
Hint Taking out groups of 10 s is easy.
Total number of cows =_______
Answer:
(i) (a) 4
(b) 88÷ 4=22
Total number of cows =22
Let Us Solve (NCERT Pg 141)
Question 1.
In a big aquarium, Jolly fish sees 72 legs of octopuses. How many octopuses are there in the aquarium?
Answer:
We know that each octopus has 8 legs. So, number of octopuses =72 ÷ 8=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?
Answer:
50 ÷ 4=12, remainder 2
So, they will need 13 boxes ( 12 full boxes + 1 more for the remaining 2 shuttlecocks to pack all of them).
No, they cannot pack all the shuttlecocks in the boxes.
12 full boxes, 2 shuttlecocks are left.
Question 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:
Given that total saplings are 75 and each row has 5 saplings.
So, on dividing 75 ÷ 5=15
Rakul Chachi has planted 15 rows of saplings.
Question 4.
Make stories for the following problems and solve them.
(i) 70 ÷ 5
(ii) 84 ÷ 7
(iii) 69 ÷ 3
(iv) 93 ÷ 6
Answer:
(i) 70 ÷ 5=14
Story There are 70 chairs to be placed in rows of 5 each → 14 rows are needed.
(ii) 84 ÷ 7=12
Story There are 84 pencils to be packed in packets of 7 each →12 packets are needed.
(iii) 69 ÷ 3=23
Story There are 69 marbles to be shared among 3 children → each child get 23 marbles.
(iv) 93 ÷ 6=15, remainder 3
Story There are 93 laddus into plates with 6 each → 15 full plates are needed, 3 laddus are left.
Multiples of 100 (NCERT Pg 142-143)
Question 5.
(i) 100 bikes with 2 people on each have 100 x 2 people =………. people.
(ii) 200 bikes with 2 people on each have……….. people. How did you find it?
(iii) 100 cars with 4 people in each have 100× 4 people = ……………… people.
(iv) 500 cars with 4 people in each have………… people. How did you find it?
(v) What do you notice about multiplying by multiples of 100s?
Answer:
(i) 200
(ii) 400
We found the answer by using multiplication.
(iii) 400
(iv) 2000
We found the answer by using multiplication.
Total number of people = Number of cars x Number of people in each car
(v) When we multiply by 100, we usually add two zeroes at the end of number.
Question 6.
Observe the pattern and complete the answers.
Answer:
The pattern shows how multiplying by multiples of 10 (i.e. 10, 100) affects the product. When multiplying by 10 , a zero is added to the end of the product and when multiplying by 100 , two zeroes are added at the end.
More Multiplication (NCERT Pg 143-144)
Question 1.
Big electric autorickshaws 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 is 125 × 8.
(i) 100 autorickshaws with 8 passengers in each have 100 × 8 passengers = ——— passengers.
(ii) 20 autorickshaws with 8 passengers in each have 20 × 8 passengers = ——— passengers.
(iii) 5 autorickshaws with 8 passengers in each have 5 × 8 passengers = ——— passengers.
(iv) 125 autorickshaws with 8 passengers in each have ——— + ——— + ——— = ——— passengers.
(i) 800
(ii) 160
(iii) 40
(iv) 800+160+40=1000
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? The total number of kulhads is …………
Answer:
They pack 6 kulhads in a box and have packed 174 boxes for delivery.
So, number of kulhads they made
= Number of boxes
× Number of kulhads in a box
= 174 × 6=1044
The total number of kulhads is 1044
Let Us Solve (NCERT Pg 144-145)
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?
Answer:
Each student gets =2 pencils
Number of students =465
We need to calculate total number of pencils needed
=Required number of pencils x number of students
=2 x 465
Let us use simple multiplication
=2 x465=930
The school needs to buy 930 pencils.
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?
Answer:
234 children are organising a school mela. Each child contributes ₹ 5
We need to calculate 234 x5
So, 234 x5=1170
The children collect ₹ 1170 in total.
Question 3.
Make stories for the following problems and solve them.
(i) 439 x4
(ii) 514 x8
(iii) 356 x5
(iv) 623 x7
Answer:
(i) 439 x4
Story A publisher prints 439 invitation cards per day.
How many cards are printed in total in 4 days?
Solution 439 x4=1756
The publisher prints 1756 invitation cards.
(ii) 514 x8
Story A factory produces 514 toy cars per day.
How many toy cars are made in 8 days?
Solution 514 x8=4112
4112 toy cars
(iii) 356 x5
Story There are 356 books on each shelf. If there are 5 shelves.
How many books are there in total?
Solution 356 x5=1780
1780 books
(iv) 623 x7
Story A shop sells 623 chocolates every day.
How many chocolates are sold in 7 days?
Solution 623 x7=4361
4361 chocolates
Patterns in Division (NCERT Pg 146)
Question 4.
How much money will each get? Draw arrows linking the money and the children to answer the questions.
(i) ₹ 30 shared equally among 3 children
(ii) ₹ 900 shared equally among 3 children
Answer:
(i) ₹ 10 each
[∵ 30 ÷ 3=10]
(ii) ₹ 300 each
[∵ 900 ÷ 3=300]
Question 5.
Using the above way of thinking, solve the following problems. Observe and explain the patterns that you notice below.
Answer:
The pattern shows that when we divide a number (i.e. dividend) by another number, we find
‘As the clividend is multiplied by 10 or 100 , the quotient (result) is also multiplied by 10 or 100’
(NCERT Pg 148)
Question 1.
A load carrying truck has 6 tyres.
Chippi the lizard sees 60 tyres.
How many trucks are there?
Answer:
Each truck has 6 tyres and total tyres which Chippi the lizard sees is 60.
So, the number of trucks =60 ÷ 6=10
There are 10 trucks.
Question 2.
Chippi sees 80 wheels in a car parking space. How many cars are standing in the parking space?
Answer:
Each car has 4 wheels and total wheels are 80.
So, the number of cars which are standing in the parking =80 ÷ 4=20
There are 20 cars in the parking space.
Question 3.
Chippi sees 600 legs of ants walking towards the anthill. How many ants are there?
Answer:
Each ant has 6 legs and total legs are 600. So, the number of ants =600 ÷ 6=100 There are 100 ants walking toward the anthill.
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?
Answer:
Each packet has 4 rubber bands and total rubber bands are 800
So, the number of packets of rubber
=800÷4=200
The shop has 200 packets of rubber bands.
Let Us Solve (NCERT Pg 147-148)
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 travelling in each bus?
Answer:
Total children =245
Number of buses =7
So, the number of children who is travelling in each bus =245 ÷ 7=35
35 children are travelling in each bus.
Question 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:
Number of days in 1 week =7 days Distance per day covered by train =88km
So, the total distance travel by train in a week = 88 x 7=616
The toy train travels 616 km in a week.
Question 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:
Venture Out took 259 people for river rafting.
Each raft holds 7 people.
So, the number of rafts =259 ÷7=37
The company used 37 rafts.
Question 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:
(a) Given that Anu saves ₹ 45 every month. So, the money saved by Anu in 6 months
=₹ 45 x 6=₹ 270
(b) Anu saved ₹ 270 in 6 months.
So, the money each friend get after distribution =₹ 270 ÷6=₹ 45
(c) If Anu distributes her saved money of 6 months in 3 friends, then each friend get
=₹ 270 ÷3=₹ 90
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?
Answer:
(a) It can not be exactly calculated because we are not told how much he earns per trip, so we cannot determine his daily earnings.
(b) It can be exactly calculated.
Number of trips in a day =8
So, total number of trips in 7 days
= 8 x 7=56 trips
(c) It can not be exactly calculated because we are not given any information about time, so we cannot find the duration of one trip.
(d) It can be exactly calculated.
We know,
1 week = 7 days
So, total numbers of trips in 4 weeks
= 4 x Number of trips in 1 week
= 4 x 56
= 224 trips
Only (b) and (d) can be exactly calculated.
Question 6.
Solve
(a) 45 x 9
(b) 507 x 7
(c) 94 ÷ 4
(d) 778 ÷ 6
(e) 94 x 5
(f) 396 x 4
(g) 83 ÷ 3
(h) 635 ÷ 5
Answer:
(a) 405
(b) 3549
(c) 23, remainder 2
(d) 129, remainder, 4
(e) 470
(f) 1584
(g) 27, remainder 3
(h) 127
Question 7.
In Mathematics, some statements are always true, some are sometimes true and some are never true. Tick (✓) in the appropriate column.
Answer:
