NCERT Solutions for Class 2 Joyful Maths Chapter 08 Grouping and Sharing

Question. Look at the picture and fill in the blanks using the numbers and what you see. There are 2 + 2 + 2 + 2 = 8 wheels total. We can also say 4 groups of 2 give us 8, or 4 times 2 is 8.
Answer: In the street scene, we can count the wheels by grouping the vehicles. When we have 4 bicycles and each one has 2 wheels, we get 2 + 2 + 2 + 2 = 8 wheels in total. This is the same as saying 4 groups of 2 equals 8. When we use the multiplication symbol, we write 4 x 2 = 8. For the auto-rickshaws, there are 2 of them and each has 3 wheels. So the total is 3 + 3 = 6 wheels, which we can also say is 2 groups of 3 equals 6, or 2 x 3 = 6. For the 7 cars in the scene, with 4 wheels on each car, we add them up as 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28 wheels. This is the same as 7 groups of 4 equals 28, or 7 x 4 = 28.
In simple words: When you have many of the same thing, you can group them and multiply instead of adding many times. Grouping makes counting faster and easier.

Exam Tip: Always show both the repeated addition and the multiplication method - examiners want to see you can link the two ways of working together.

Question. Number of cars = _____. Number of wheels in each car = _____. Total wheels = _____ + _____ + _____ + _____ + _____ + _____ + _____ = _____. _____ times 4 is _____. 7 groups of _____ is _____. _____ x _____ = _____.
Answer: Number of cars = 7. Number of wheels in each car = 4. Total wheels = 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28. 7 times 4 is 28. 7 groups of 4 is 28. 7 x 4 = 28.
In simple words: We add 4 seven times to get 28. We can also call this 7 groups of 4, or write it as 7 x 4 = 28.

Exam Tip: Match the blanks carefully - the number of groups comes first, then the size of each group, then the total result.

Question. Number of butterflies = _____. Number of wings in each butterfly = _____. Total number of wings = _____ + _____ + _____ = _____. Or 3 groups of _____ is _____. _____ times 2 is 6. 3 twos are _____. _____ x _____ = _____.
Answer: Number of butterflies = 3. Number of wings in each butterfly = 2. Total number of wings = 2 + 2 + 2 = 6. Or 3 groups of 2 is 6. 3 times 2 is 6. 3 twos are 6. 3 x 2 = 6.
In simple words: When you add 2 three times, you get 6. You can also say 3 groups of 2 make 6, or simply write 3 x 2 = 6.

Exam Tip: Stay consistent with the wording - "groups of" and "times" mean the same thing in multiplication.

Question. Number of octopuses = _____. Number of legs in each octopus = _____. Total number of legs = _____ + _____ = _____. 2 groups of _____ is _____. 2 times _____ is 16. 2 eights are _____. _____ x _____ = _____.
Answer: Number of octopuses = 2. Number of legs in each octopus = 8. Total number of legs = 8 + 8 = 16. 2 groups of 8 is 16. 2 times 8 is 16. 2 eights are 16. 2 x 8 = 16.
In simple words: There are 2 octopuses, each with 8 legs. When you add 8 twice, the total is 16 legs. This is written as 2 x 8 = 16.

Exam Tip: Octopus facts are useful helpers - knowing that octopuses have 8 legs makes the grouping clear and easy.

Question. Number of lines = _____. Number of soldiers in each line = _____. Total number of soldiers = _____ + _____ + _____ + _____ = _____. _____ times _____ is 40. 4 tens are _____. _____ x _____ = _____.
Answer: Number of lines = 4. Number of soldiers in each line = 10. Total number of soldiers = 10 + 10 + 10 + 10 = 40. 4 times 10 is 40. 4 tens are 40. 4 x 10 = 40.
In simple words: When you add 10 four times, you get 40 soldiers standing in rows. The fast way to write this is 4 x 10 = 40.

Exam Tip: Use tens as a natural grouping tool - multiplication by 10 is often simpler because the pattern is clear and easy to count.

Question. Complete The Table.
Answer:
Row 1 (4 stars): 3 + 3 + 3 + 3, 4 times 3, 4 x 3 = 12 Stars
Row 2 (3 hands): 5 + 5 + 5, 5 times 3, 5 x 3 = 15 Fingers
Row 3 (6 bananas): 3 + 3 + 3 + 3 + 3 + 3, 6 times 3, 6 x 3 = 18 Bananas
Row 4 (4 oranges): 4 + 4 + 4 + 4, 4 times 4, 4 x 4 = 16 Oranges
Row 5 (10 pencils): 5 + 5, 2 times 5, 2 x 5 = 10 Pencils
Row 6 (15 balls): 5 + 5 + 5, 3 times 5, 3 x 5 = 15 Balls
In simple words: For each row, count how many groups there are, then count what is in each group. Multiply the two numbers to get the answer.

Exam Tip: Complete all three columns for each row - the repeated addition, the word form, and the multiplication form show that all three ways are the same.

Question. Match the Following.
Answer: 9 + 9 + 9 matches to 3 x 9 and equals 27. 5 + 5 + 5 + 5 + 5 + 5 + 5 matches to 7 groups of 5 and equals 35. 3 + 3 + 3 + 3 + 3 matches to 3 x 5 and equals 40 (Note: 3 x 5 = 15, but checking the source: 3 + 3 + 3 + 3 + 3 = 15, which matches 5 times 3). 10 + 10 + 10 + 10 matches to 4 groups of 10 and equals 40. 8 + 8 + 8 matches to 3 x 8 and equals 24. 7 + 7 matches to 2 sevens are and equals 14. 5 times 3 matches with the remaining value 15.
In simple words: Look at each addition line and count how many numbers are added. Then match it to the multiplication sentence that shows the same amount.

Exam Tip: Count the number of addends to find how many groups there are, then the addend itself tells you the size of each group.

Question. Complete the Table of 2.
Answer:
2 ones are 2, 2 x 1 = 2
2 twos are 4, 2 x 2 = 4
2 threes are 6, 2 x 3 = 6
2 fours are 8, 2 x 4 = 8
2 fives are 10, 2 x 5 = 10
2 sixes are 12, 2 x 6 = 12
2 sevens are 14, 2 x 7 = 14
2 eights are 16, 2 x 8 = 16
2 nines are 18, 2 x 9 = 18
2 tens are 20, 2 x 10 = 20
In simple words: The 2 times table shows what you get when you take 2 of something, over and over, from 1 to 10 times.

Exam Tip: Learn this table by heart - the 2 times table is one of the most important to master early, as it appears in many problems.

Question. Complete the Table of 3.
Answer:
3 ones are 3, 3 x 1 = 3
3 twos are 6, 3 x 2 = 6
3 threes are 9, 3 x 3 = 9
3 fours are 12, 3 x 4 = 12
3 fives are 15, 3 x 5 = 15
3 sixes are 18, 3 x 6 = 18
3 sevens are 21, 3 x 7 = 21
3 eights are 24, 3 x 8 = 24
3 nines are 27, 3 x 9 = 27
3 tens are 30, 3 x 10 = 30
In simple words: The 3 times table shows what you get when you take 3 of something, ten times in a row, starting from 1 up to 10.

Exam Tip: Notice that each answer is 3 more than the one before - this pattern helps you remember and check your work.

Question. Complete the Table of 5.
Answer:
5 ones are 5, 5 x 1 = 5
5 twos are 10, 5 x 2 = 10
5 threes are 15, 5 x 3 = 15
5 fours are 20, 5 x 4 = 20
5 fives are 25, 5 x 5 = 25
5 sixes are 30, 5 x 6 = 30
5 sevens are 35, 5 x 7 = 35
5 eights are 40, 5 x 8 = 40
5 nines are 45, 5 x 9 = 45
5 tens are 50, 5 x 10 = 50
In simple words: The 5 times table is easy to spot - every answer ends in either 5 or 0.

Exam Tip: The 5 times table has a clear pattern - answers alternate between ending in 5 and ending in 0, which helps you catch mistakes.

Question. Complete the Table of 10.
Answer:
10 ones are 10, 10 x 1 = 10
10 twos are 20, 10 x 2 = 20
10 threes are 30, 10 x 3 = 30
10 fours are 40, 10 x 4 = 40
10 fives are 50, 10 x 5 = 50
10 sixes are 60, 10 x 6 = 60
10 sevens are 70, 10 x 7 = 70
10 eights are 80, 10 x 8 = 80
10 nines are 90, 10 x 9 = 90
10 tens are 100, 10 x 10 = 100
In simple words: The 10 times table is the simplest one - just put a 0 at the end of any number to multiply it by 10.

Exam Tip: This table is the easiest to learn because every answer is just the number with a zero added to the end.

Question. Test your observation with other examples.
Answer: The pictures show two different ways of grouping the same 20 items. On the left, we have 4 groups of 5 items each. We can count this as 5 + 5 + 5 + 5 = 20, or we say 4 times 5 is 20, or write 4 x 5 = 20. There are 20 gulab jamuns in total. On the right, we have 5 groups of 4 items each. We count this as 4 + 4 + 4 + 4 + 4 = 20, or we say 5 times 4 is 20, or write 5 x 4 = 20. There are also 20 gulab jamuns here. This shows that 4 x 5 and 5 x 4 both give the same answer - 20. The order of the numbers does not change the result.
In simple words: When you multiply two numbers, swapping them around gives you the same answer. 4 x 5 = 20 and 5 x 4 = 20.

Exam Tip: This is called the commutative property of multiplication - knowing it helps you check your work and understand that grouping can be done in different ways.

Question. 6 groups of 4 - times 4 is ____
Answer: 6 times 4 is 24. When you put together 6 separate groups, each containing 4 items, the total becomes 24. We can also write this as 6 × 4 = 24.
In simple words: When you have 6 groups and each group has 4 things in it, you get 24 things altogether.

Exam Tip: Remember that grouping and multiplication show the same idea - if you have equal groups, multiply the number of groups by the number in each group.

Question. 4 groups of 6 - times 6 is ____
Answer: 4 times 6 is 24. When you arrange items into 4 equal groups with 6 items in each group, the total is 24. This is written as 4 × 6 = 24.
In simple words: If you make 4 groups and put 6 things in each group, you will have 24 things in total.

Exam Tip: Notice that 6 × 4 and 4 × 6 both give 24 - multiplication works the same way no matter which number comes first.

Question A. There are 8 packets of bindis. Each packet has 5 bindis. Find: Number of packets, Number of bindis in each packet, and total bindis.
Answer: Number of packets = 8. Number of bindis in each packet = 5. There are 8 groups of 5 bindis. Using the multiplication formula: 8 × 5 = 40 bindis in total.
In simple words: You have 8 packets. Each packet holds 5 bindis. When you count all the bindis from all packets together, you get 40 bindis.

Exam Tip: Always identify the number of groups first, then the size of each group, then multiply to get the total.

Question B. Bharti puts 4 buttons on each shirt. She wants to put buttons on 7 shirts. Find how many buttons are needed.
Answer: Number of shirts = 7. Number of buttons on each shirt = 4. There are 7 groups of 4 buttons. Using multiplication: 7 × 4 = 28 buttons are required in total.
In simple words: Bharti has 7 shirts. She puts 4 buttons on every shirt. So she needs 28 buttons altogether.

Exam Tip: In word problems, look for the phrases "on each" or "in each" to find the group size - this number gets multiplied by the count of groups.

Question C. Rita bought 6 pencils of Rs. 4 each. How much money will she give to the shopkeeper?
Answer: Number of pencils = 6. Cost of 1 pencil = Rs. 4. The total cost is found by adding: 4 + 4 + 4 + 4 + 4 + 4. Using multiplication: 6 × 4 = Rs. 24. Rita will pay Rs. 24 to the shopkeeper.
In simple words: Each pencil costs Rs. 4. If Rita buys 6 pencils, she pays 6 times 4, which equals Rs. 24.

Exam Tip: For money problems, remember that multiplying the quantity by the price per item gives you the total cost to pay.

Question D. Five people can sit in a car. How many people can sit in 8 such cars?
Answer: Number of people sitting in 1 car = 5. Number of people sitting in 8 cars = ?. We multiply: 8 × 5 = 40. Therefore, 40 people can sit in 8 cars.
In simple words: Each car holds 5 people. If you have 8 cars, the total number of people you can fit is 40.

Exam Tip: When you need to find a total from equal groups, multiplication is the quickest method instead of repeated addition.

Making Multiplication Table

Question. Rudra is making multiplication table of 4 using the table of 2. Complete the table.
Answer: By adding the Table of 2 to itself (or doubling it), we get the Table of 4. This works because 4 = 2 + 2. So each entry in Table of 4 is twice the entry in Table of 2. Starting with Table of 2 (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) and adding the same sequence again gives us Table of 4 (4, 8, 12, 16, 20, 24, 28, 32, 36, 40).
In simple words: Table of 4 is made by doubling the numbers in Table of 2, or you can add Table of 2 twice to get Table of 4.

Exam Tip: This method shows that multiplication tables are related - knowing one table helps you find another without memorizing everything separately.

Question. Complete the table: Making Table of 6 from Table of 3.
Answer: When we add the Table of 3 to itself, we get the Table of 6. This is because 6 = 3 + 3. The entries are: Table of 3 is 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Adding these values again produces Table of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.
In simple words: To make Table of 6, take Table of 3 and add it to itself, or double every number in Table of 3.

Exam Tip: Tables of even numbers are often double the tables of their half - this pattern helps you construct and remember multiplication tables faster.

Project Work

Question. Collect 24 small objects like buttons, bottle caps, pebbles, etc. Arrange them in different arrays and write the related multiplication facts. How many of these facts can you find? Record your answers in the table given below.
Answer: You can form several arrays with 24 objects. The possible groupings are: 3 groups of 4 (3 × 4), 4 groups of 3 (4 × 3), 8 groups of 3 (8 × 3), 3 groups of 8 (3 × 8), 2 groups of 12 (2 × 12), and 12 groups of 2 (12 × 2). Each arrangement shows a different way to multiply and get 24 as the result.
In simple words: With 24 objects, you can arrange them in many different ways - such as rows and columns - and each way shows a different multiplication fact that equals 24.

Exam Tip: Try to find as many factor pairs as you can - these are all the different ways a number can be broken into equal groups, and they all multiply back to give that number.

Question. How many gulab jamuns were there in total?
Answer: There were 8 gulab jamuns in total.
In simple words: When we count all the gulab jamuns in the story, there are 8 of them altogether.

Exam Tip: Always read the story carefully to find numbers that are stated directly in the text.

Question. Have they shared equally?
Answer: Yes, they shared equally. Both children received the same number of gulab jamuns (4 each).
In simple words: Equal sharing means both people get the same amount. In this case, each child got 4 gulab jamuns, so yes, they divided them fairly.

Exam Tip: To check if something is shared equally, count how many each person got - if the amounts are the same, then it is equal sharing.

Question. How many gulab jamuns did each of them get?
Answer: Each child got 4 gulab jamuns. When 8 gulab jamuns are divided equally between 2 children, each one receives 8 ÷ 2 = 4 gulab jamuns.
In simple words: If you split 8 gulab jamuns between 2 people equally, each person gets 4 gulab jamuns.

Exam Tip: Division is the opposite of multiplication - to share equally, divide the total number by how many people are sharing.

Question A. Complete Ritu's art and craft project by drawing 12 bindis equally on 2 ice cream cones as cherries.
Answer: To divide 12 bindis equally between 2 ice cream cones, place 6 bindis on each cone. This way, each ice cream cone gets the same number of bindis as a cherry decoration.
In simple words: Split the 12 bindis into 2 equal parts. Each part has 6 bindis, so put 6 bindis on each cone.

Exam Tip: When dividing into equal parts, count the total items and divide by the number of parts to find how many go in each part.

Question B. Pooja has 2 plates. Each plate has a different number of laddoos in it. Help her divide the laddoos equally in 3 plates. You can draw and colour the laddoos.
Answer: Count the total laddoos from both of Pooja's plates. Then divide this total equally into 3 new plates. If the first plate has 8 laddoos and the second plate has 8 laddoos, the total is 16. Dividing 16 laddoos equally among 3 plates gives approximately 5 laddoos in each plate (with some remaining). For perfect equal division, you could use 15 total laddoos (5 in each of 3 plates).
In simple words: Add up all the laddoos, then share them evenly into 3 plates so each plate has the same amount.

Exam Tip: Sometimes items may not divide evenly - when this happens, distribute as equally as possible, noting any remainder.

Let Us Make

Question A. Each string has 7 beads. How many strings can we make with 21 beads?
Answer: To find how many strings can be made, divide the total number of beads by the beads needed for one string. We have 21 beads and each string needs 7 beads. So, 21 ÷ 7 = 3. We can make 3 strings with 21 beads.
In simple words: If one string needs 7 beads and you have 21 beads total, you can make 3 strings because 21 split into groups of 7 gives you 3 groups.

Exam Tip: Division helps us find how many equal groups we can form - this is the reverse of grouping in multiplication.

Question B. There are 54 flowers. Join 9 flowers to make 1 bracelet. How many bracelets can we make with 54 flowers?
Answer: To find the number of bracelets, divide the total flowers by the flowers needed for each bracelet. We have 54 flowers and each bracelet needs 9 flowers. So, 54 ÷ 9 = 6. We can make 6 bracelets with 54 flowers.
In simple words: If each bracelet uses 9 flowers and you have 54 flowers, you can make 6 bracelets because 54 split into groups of 9 gives you 6 groups.

Exam Tip: For "how many groups can we make" questions, always divide the total by the size of one group.

Question C. There are 25 roses. 5 roses can be placed in 1 vase. How many vases are needed for placing 25 roses?
Answer: To find the number of vases needed, divide the total roses by the roses that fit in each vase. We have 25 roses and each vase holds 5 roses. So, 25 ÷ 5 = 5. Therefore, 5 vases are needed.
In simple words: Each vase can hold 5 roses. With 25 roses total, you need 5 vases to place all the roses, with each vase holding the same number.

Exam Tip: Read carefully whether you are finding "how many in each group" (division) or "how many groups total" (also division, but a different setup).

Question D. There are 27 candles. Put them equally in 3 boxes. How many candles will be in each box?
Answer: To find how many candles go in each box, divide the total candles by the number of boxes. We have 27 candles and 3 boxes. So, 27 ÷ 3 = 9. There will be 9 candles in each box.
In simple words: When you share 27 candles equally among 3 boxes, each box gets 9 candles.

Exam Tip: For "equal sharing" problems, divide the total amount by the number of people or containers to find what each one gets.

Question E. A tailor puts 6 buttons on one shirt. Here are 30 buttons. How many shirts can the tailor make?
Answer: To find how many shirts the tailor can make, divide the total buttons by the buttons needed for one shirt. We have 30 buttons and each shirt needs 6 buttons. So, 30 ÷ 6 = 5. The tailor will be able to put 30 buttons on 5 shirts.
In simple words: If one shirt needs 6 buttons and you have 30 buttons, you can make 5 shirts because 30 split into groups of 6 gives you 5 groups.

Exam Tip: When you know the total amount and how much is needed per item, divide to find how many items you can make or complete.

Question F. Share 24 bananas equally among 3 monkeys.
Answer: To find how many bananas each monkey gets, divide the total bananas by the number of monkeys. We have 24 bananas and 3 monkeys. So, 24 ÷ 3 = 8. Each monkey will get 8 bananas.
In simple words: If you divide 24 bananas equally among 3 monkeys, each monkey receives 8 bananas.

Exam Tip: Equal sharing always uses division - divide the total by the number of receivers to find the fair share for each.

Question. Look at the street scene with many vehicles. Count how many cars there are. How many wheels does each car have? Find the total number of wheels by adding them together. You can also write this as groups of 4, where each group has 4 wheels. How many groups of 4 are you adding? Write this as multiplication.
Answer: Number of cars = 7. Each car has 4 wheels. Total wheels = 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28. This is the same as 7 groups of 4, which equals 28. We write this as 7 × 4 = 28. When we multiply, we're just counting how many times we add the same number. So 7 times 4 means we're adding four, seven times over, which gives us 28.
In simple words: When you have 7 cars and each one has 4 wheels, you can find the total by adding 4 seven times, or by saying 7 times 4 equals 28.

Exam Tip: Multiplication is a faster way to add the same number over and over. Always link the groups (how many) to what's in each group (how many in each).

Question. There are 3 butterflies. Each butterfly has 2 wings. Work out the total number of wings. Write this as a repeated addition first, then as groups, and finally as multiplication.
Answer: Number of butterflies = 3. Each butterfly has 2 wings. Total wings = 2 + 2 + 2 = 6. This is 3 groups of 2, which equals 6. We can write this as 3 times 2 equals 6, or 3 × 2 = 6. Each time we add the same number repeatedly, we can show it using multiplication instead.
In simple words: When you add the same number many times, you can write it as multiplication. Three groups of 2 is the same as 3 × 2, which equals 6.

Exam Tip: Show the three stages clearly - first the addition, then the groups, then the multiplication sentence - this shows you understand how multiplication connects to adding.

Question. There are 2 octopuses. Each octopus has 8 legs. Find the total number of legs using addition. Then write this as groups and finally as a multiplication sentence.
Answer: Number of octopuses = 2. Each octopus has 8 legs. Total legs = 8 + 8 = 16. This is 2 groups of 8, which equals 16. We write this as 2 times 8 is 16, or 2 × 8 = 16. When we repeat an addition with the same number, we use multiplication to show it more quickly.
In simple words: Two octopuses, each with 8 legs, give us 16 legs altogether. We can write 8 + 8 the fast way as 2 × 8 = 16.

Exam Tip: Match the number of groups to how many times you're adding, and match the group size to what you're adding.

Question. There are 4 lines of soldiers. Each line has 10 soldiers. Find the total number of soldiers by adding them. Then express this as groups and write the multiplication sentence.
Answer: Number of lines = 4. Soldiers in each line = 10. Total soldiers = 10 + 10 + 10 + 10 = 40. This represents 4 groups of 10, which equals 40. We can write this as 4 times 10 is 40, or 4 × 10 = 40. Grouping helps us see that repeating the same number four times gives us the same result as multiplying 4 by 10.
In simple words: Four lines with 10 soldiers each means 40 soldiers in total. Instead of adding 10 four times, we simply say 4 × 10 = 40.

Exam Tip: Always identify both the number of groups and the size of each group before writing the multiplication sentence.

Question. Complete The Table
Answer:

Exam Tip: Each column shows a different way to say the same idea - the picture shows the groups, the addition shows the repeated adding, the words describe how many times, and the multiplication is the fastest way to write it.

Question. Match The Following
Answer:
9 + 9 + 9 matches with 3 × 9 and also with 27
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 matches with 4 groups of 10 and also with 40
3 + 3 + 3 + 3 + 3 matches with 5 times 3 and also with 15
10 + 10 + 10 + 10 matches with 3 × 8 and also with 24
8 + 8 + 8 matches with 2 sevens are and also with 14
7 + 7 matches with 7 fives are and also with 35
In simple words: Match each addition sentence (on the left) to both its multiplication statement (in the middle) and its answer (on the right). The same total can be written three different ways.

Exam Tip: Count how many numbers you're adding to find the first number in the multiplication, and look at which number you're adding to find the second number.

Question. Complete The Table of 2
Answer:

Exam Tip: Notice that each answer goes up by 2 - this makes it easy to remember the 2 times table without memorizing each fact.

Question. Complete The Table of 3
Answer:

Exam Tip: The pattern in the table of 3 shows each answer is 3 more than the previous one - learning to spot patterns helps you remember multiplication facts faster.

Question. Complete The Table of 5
Answer:

Exam Tip: The table of 5 always ends in either 5 or 0 - odd numbers paired with 5 give answers ending in 5, and even numbers paired with 5 give answers ending in 0.

Question. Complete The Table of 10
Answer:

Exam Tip: All answers in the table of 10 end with zero, making this the simplest table to memorize - multiplying by 10 means just adding a zero to the number.

Question. Test your observation with other examples. Look at the two arrays shown. For the first array, count 4 groups of 5, find how many times you add 5, work out the total, and write it as multiplication. For the second array, count 5 groups of 4, find how many times you add 4, work out the total, and write it as multiplication. What do you notice?
Answer: In the first array, there are 4 groups of 5. The number 4 tells us how many times we add. So 4 times 5 is 20. We write this as 4 × 5 = 20. In the second array, there are 5 groups of 4. The number 5 tells us how many times we add. So 5 times 4 is 20. We write this as 5 × 4 = 20. When we compare the two, we see that 4 × 5 and 5 × 4 both give the same answer - 20. The order of the numbers does not matter in multiplication. Changing which number comes first still gives the same result. This property is called the commutative property of multiplication.
In simple words: When you multiply, you can swap the two numbers and still get the same answer. 4 × 5 equals 5 × 4, which is 20.

Exam Tip: This property - that order doesn't matter in multiplication - can help you if you know one fact, you automatically know another. For instance, if you know 3 × 7 = 21, then you also know 7 × 3 = 21.

Question. 6 groups of 4 - times 4 is ____. 6 × 4 = ____. There are ____ flowers.
Answer: 6 groups of 4 - times 4 is 24. 6 × 4 = 24. There are 24 flowers.
In simple words: When you count 6 groups with 4 flowers in each group, you get 24 flowers total.

Exam Tip: Show grouping clearly and count all items - do not skip or miscount any group.

Question. 4 groups of 6 - times 6 is ____. 4 × 6 = ____. There are ____ flowers.
Answer: 4 groups of 6 - times 6 is 24. 4 × 6 = 24. There are 24 flowers.
In simple words: When you arrange 4 groups with 6 flowers in each group, you get 24 flowers in total.

Exam Tip: Notice that 6 × 4 and 4 × 6 both give the same answer - this shows the commutative property of multiplication.

Question A. There are 8 packets of bindis. Each packet has 5 bindis.
Answer:
Number of packets = 8
Number of bindis in each packet = 5
8 groups of 5 bindis.
8 × 5 = 40 bindis
In simple words: You have 8 packets. Each packet holds 5 bindis. So altogether you have 40 bindis.

Exam Tip: Always identify the number of groups and the number of items in each group before multiplying.

Question B. Bharti puts 4 buttons on each shirt. She wants to put buttons on 7 shirts.
Answer:
Number of shirts = 7
Number of buttons on each shirt = 4
7 groups of 4 buttons
7 × 4 = 28 buttons
In simple words: There are 7 shirts, and each one gets 4 buttons. So you need 28 buttons altogether.

Exam Tip: Write the multiplication sentence in order - number of groups first, then items per group.

Question C. Rita bought 6 pencils of Rs.4 each. How much money will she give to the shopkeeper?
Answer:
Number of pencils = 6
Cost of 1 pencil = 4
Cost of 6 pencils = 4 + 4 + 4 + 4 + 4 + 4
6 × 4 = 24
So, Rita will give Rs. 24 to the shopkeeper.
In simple words: Rita buys 6 pencils. Each pencil costs 4 rupees. So she must pay 24 rupees in total.

Exam Tip: Show repeated addition first, then convert it to multiplication - this demonstrates the meaning of multiplication.

Question D. Five people can sit in a car. How many people can sit in 8 such cars?
Answer:
Number of people sitting in 1 car = 5
Number of people sitting in 8 cars = 40
8 × 5 = 40
40 people can sit in 8 cars.
In simple words: Each car holds 5 people. With 8 cars, you can fit 40 people altogether.

Exam Tip: Set up the multiplication correctly - multiply the number of cars by people per car, not the other way around.

Making Multiplication Table
Rudra is making multiplication table of 4 using the table of 2.

Question. Complete the multiplication table of 6 using the table of 3.
Answer:

Exam Tip: Doubling one times table is a quick way to build the next even-numbered table.

Project Work
Collect 24 small objects like buttons, bottle caps, pebbles, etc. Arrange them in different arrays and write the related multiplication facts. How many of these facts can you find? Record your answers in the table given below.

Exam Tip: List all factor pairs of 24 - this reinforces both grouping and the commutative property of multiplication.

Let us Share
This section shows children how to divide 8 gulab jamuns equally among 2 people by sharing one at a time: "I will share 1 by 1. See, 1 for you, 1 for me." The sharing continues until all are distributed, resulting in each person getting 4 gulab jamuns.
Answer:
A. How many gulab jamuns were there in total? 8
B. Have they shared equally? Yes
C. How many gulab jamuns did each of them get? 4
In simple words: When 8 gulab jamuns are shared equally between 2 people, each one gets 4.

Exam Tip: Division means sharing or grouping - always check that the answer makes sense by multiplying back.

Question A. Complete Ritu's art and craft project by drawing 12 bindis equally on 2 ice cream cones as cherries.
Answer: Draw 6 bindis on each ice cream cone, so that the total is 12 bindis spread equally between the 2 cones.
In simple words: Divide 12 by 2 to get 6 - put 6 bindis on each cone.

Exam Tip: Verify your answer by adding back - 6 + 6 = 12 confirms the sharing is correct.

Question B. Pooja has 2 plates. Each plate has a different number of laddoos in it. Help her divide the laddoos equally in 3 plates. You can draw and colour the laddoos.
Answer: Count the total laddoos from both plates, then divide equally among 3 plates - draw the same number of laddoos in each of the 3 empty plates so that the distribution is even across all three.
In simple words: Add up all the laddoos from the 2 plates. Then put the same number into each of the 3 empty plates.

Exam Tip: First find the total, then divide by the number of plates - this two-step process prevents mistakes.

Let us Do
Question A. Each string has 7 beads. How many strings can we make with 21 beads?
Answer: How many strings can we make with 21 beads? 3
In simple words: If each string needs 7 beads and you have 21 beads, you can make 3 strings.

Exam Tip: Divide the total beads by the beads per string - 21 ÷ 7 = 3.

Question B. There are 54 flowers. Join 9 flowers to make 1 bracelet. How many bracelets can we make with 54 flowers?
Answer: How many bracelets can we make with 54 flowers? 6
In simple words: You have 54 flowers. Each bracelet takes 9 flowers. So you can make 6 bracelets.

Exam Tip: Division questions like this are about grouping - divide the total by the group size: 54 ÷ 9 = 6.

Question C. There are 25 roses. 5 roses can be placed in 1 vase. How many vases are needed for placing 25 roses?
Answer: 5 vases are needed.
In simple words: You have 25 roses. Each vase holds 5 roses. So you need 5 vases.

Exam Tip: This is a grouping division - count how many groups of 5 fit into 25: 25 ÷ 5 = 5.

Question D. There are 27 candles. Put them equally in 3 boxes. How many candles will be in each box?
Answer: There will be 9 candles in each box.
In simple words: Share 27 candles evenly among 3 boxes. Each box gets 9 candles.

Exam Tip: This is a sharing division - divide the total by the number of boxes: 27 ÷ 3 = 9.

Question E. A tailor puts 6 buttons on one shirt. Here are 30 buttons. The tailor will be able to put 30 buttons on ____ shirts.
Answer: The tailor will be able to put 30 buttons on 5 shirts.
In simple words: There are 30 buttons. Each shirt needs 6 buttons. So you can make 5 shirts.

Exam Tip: Divide the total buttons by buttons per shirt: 30 ÷ 6 = 5.

Question F. Share 24 bananas equally among 3 monkeys. Each monkey will get ____ bananas.
Answer: Each monkey will get 8 bananas.
In simple words: When you divide 24 bananas among 3 monkeys equally, each gets 8 bananas.

Exam Tip: Sharing equally means dividing - 24 ÷ 3 = 8, and check: 8 × 3 = 24.