Grouping and Sharing (Multiplication and Division)

Given: Number of bicycles = 4, wheels on each bicycle = 2.

Total wheels = $2 + 2 + 2 + 2 = 8$

We are adding 2 four times, so: $4 \times 2 = 8$

Total wheels = 8

Given: Number of autorickshaws = 2, wheels on each = 3.

Total wheels = $3 + 3 = 6$

$2 \times 3 = 6$

Total wheels = 6

Given: Number of cars = 7, number of wheels in each car = 4.

Total wheels = $4 + 4 + 4 + 4 + 4 + 4 + 4 = 28$

We are adding 4 seven times.

7 times 4 is 28

7 groups of 4 is 28

$$7 \times 4 = 28$$

How many fours are you adding? 7

We can write it as: 7 fours are 28.

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

$$3 \times 2 = 6$$

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

$$2 \times 8 = 16$$

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

$$4 \times 10 = 40$$

Step 1 — Calculate each sum:

$9 + 9 + 9 = 27$ → This is $3 \times 9$ → 27

$5+5+5+5+5+5+5 = 35$ → This is 7 fives are → 35

$3+3+3+3+3 = 15$ → This is 5 times 3 → 15

$10+10+10+10 = 40$ → This is 4 groups of 10 → 40

$8+8+8 = 24$ → This is $3 \times 8$ → 24

$7+7 = 14$ → This is 2 sevens are → 14

Matches:
- $9+9+9$ ↔ $3 \times 9$ ↔ 27
- $5+5+5+5+5+5+5$ ↔ 7 fives are ↔ 35
- $3+3+3+3+3$ ↔ 5 times 3 ↔ 15
- $10+10+10+10$ ↔ 4 groups of 10 ↔ 40
- $8+8+8$ ↔ $3 \times 8$ ↔ 24
- $7+7$ ↔ 2 sevens are ↔ 14

Using the pattern: $2 \times n = n + n$

| Dots | Words | Multiplication |
|------|-------|----------------|
| ●● ●● | 2 ones are 2 | $2 \times 1 = 2$ |
| ●●● ●●● | 2 twos are 4 | $2 \times 2 = 4$ |
| ●●●● ●●●● | 2 threes are 6 | $2 \times 3 = 6$ |
| | 2 fours are 8 | $2 \times 4 = 8$ |
| | 2 fives are 10 | $2 \times 5 = 10$ |
| | 2 sixes are 12 | $2 \times 6 = 12$ |
| | 2 sevens are 14 | $2 \times 7 = 14$ |
| | 2 eights are 16 | $2 \times 8 = 16$ |
| | 2 nines are 18 | $2 \times 9 = 18$ |
| | 2 tens are 20 | $2 \times 10 = 20$ |

Using the pattern: $3 \times n =$ sum of $n$ threes

| Words | Multiplication |
|-------|----------------|
| 3 ones are 3 | $3 \times 1 = 3$ |
| 3 twos are 6 | $3 \times 2 = 6$ |
| 3 threes are 9 | $3 \times 3 = 9$ |
| 3 fours are 12 | $3 \times 4 = 12$ |
| 3 fives are 15 | $3 \times 5 = 15$ |
| 3 sixes are 18 | $3 \times 6 = 18$ |
| 3 sevens are 21 | $3 \times 7 = 21$ |
| 3 eights are 24 | $3 \times 8 = 24$ |
| 3 nines are 27 | $3 \times 9 = 27$ |
| 3 tens are 30 | $3 \times 10 = 30$ |

Using the pattern: $5 \times n =$ sum of $n$ fives

| Words | Multiplication |
|-------|----------------|
| 5 ones are 5 | $5 \times 1 = 5$ |
| 5 twos are 10 | $5 \times 2 = 10$ |
| 5 threes are 15 | $5 \times 3 = 15$ |
| 5 fours are 20 | $5 \times 4 = 20$ |
| 5 fives are 25 | $5 \times 5 = 25$ |
| 5 sixes are 30 | $5 \times 6 = 30$ |
| 5 sevens are 35 | $5 \times 7 = 35$ |
| 5 eights are 40 | $5 \times 8 = 40$ |
| 5 nines are 45 | $5 \times 9 = 45$ |
| 5 tens are 50 | $5 \times 10 = 50$ |

Using the pattern: $10 \times n =$ sum of $n$ tens

| Words | Multiplication |
|-------|----------------|
| 10 ones are 10 | $10 \times 1 = 10$ |
| 10 twos are 20 | $10 \times 2 = 20$ |
| 10 threes are 30 | $10 \times 3 = 30$ |
| 10 fours are 40 | $10 \times 4 = 40$ |
| 10 fives are 50 | $10 \times 5 = 50$ |
| 10 sixes are 60 | $10 \times 6 = 60$ |
| 10 sevens are 70 | $10 \times 7 = 70$ |
| 10 eights are 80 | $10 \times 8 = 80$ |
| 10 nines are 90 | $10 \times 9 = 90$ |
| 10 tens are 100 | $10 \times 10 = 100$ |

Ram: 4 groups of 3 flowers → $4 \times 3 = 12$ flowers.

Gopal: 3 groups of 4 flowers → $3 \times 4 = 12$ flowers.

Observation: Even though the groups are arranged differently, the total is the same. $4 \times 3 = 3 \times 4 = 12$. This shows that the order of multiplication does not change the answer (Commutative Property of Multiplication).

(i) 4 groups of 5:

4 times 5 is 20

$$4 \times 5 = 20$$

There are 20 gulab jamuns.

(ii) 5 groups of 4:

5 times 4 is 20

$$5 \times 4 = 20$$

There are 20 gulab jamuns.

Observation: $4 \times 5 = 5 \times 4 = 20$

(i) 6 groups of 4:

6 times 4 is 24

$$6 \times 4 = 24$$

There are 24 flowers.

(ii) 4 groups of 6:

4 times 6 is 24

$$4 \times 6 = 24$$

There are 24 flowers.

Given:
Number of packets = 8
Number of bindis in each packet = 5

8 groups of 5 bindis.

$$8 \times 5 = 40 \text{ bindis}$$

There are 40 bindis in all.

Given:
Number of shirts = 7
Number of buttons on each shirt = 4

7 groups of 4 buttons.

$$7 \times 4 = 28 \text{ buttons}$$

Bharti needs 28 buttons.

Given:
Number of pencils = 6
Cost of 1 pencil = ₹4

Cost of 6 pencils = $4 + 4 + 4 + 4 + 4 + 4$

$$6 \times 4 = 24$$

Rita will give ₹24 to the shopkeeper.

Given:
Number of people sitting in 1 car = 5
Number of cars = 8

Number of people sitting in 8 cars:

$$8 \times 5 = 40$$

40 people can sit in 8 cars.

Step 1 — Complete the Table of 3:

$3 \times 1=3,\ 3 \times 2=6,\ 3 \times 3=9,\ 3 \times 4=12,\ 3 \times 5=15,\ 3 \times 6=18,\ 3 \times 7=21,\ 3 \times 8=24,\ 3 \times 9=27,\ 3 \times 10=30$

Top row: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Second row (same table of 3): 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Step 2 — Add both rows to get Table of 6:

$3+3=6,\ 6+6=12,\ 9+9=18,\ 12+12=24,\ 15+15=30,\ 18+18=36,\ 21+21=42,\ 24+24=48,\ 27+27=54,\ 30+30=60$

Table of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Given: Total objects = 24.

We find all ways to arrange 24 objects in equal groups:

| Number of groups | Multiplication fact |
|-----------------|--------------------|
| 3 groups of 8 | $3 \times 8 = 24$ |
| 8 groups of 3 | $8 \times 3 = 24$ |
| 4 groups of 6 | $4 \times 6 = 24$ |
| 6 groups of 4 | $6 \times 4 = 24$ |
| 2 groups of 12 | $2 \times 12 = 24$ |
| 12 groups of 2 | $12 \times 2 = 24$ |
| 1 group of 24 | $1 \times 24 = 24$ |
| 24 groups of 1 | $24 \times 1 = 24$ |

We can find 8 multiplication facts for 24.

From the picture context (gulab jamuns shared equally among children), the total number of gulab jamuns is 20.

*(Note: The exact number depends on the figure. A common version of this problem uses 20 gulab jamuns shared among 4 children.)*

Total gulab jamuns = 20

Yes, they have shared equally — each child gets the same number of gulab jamuns.

Total gulab jamuns = 20, shared among 4 children.

$$20 \div 4 = 5$$

Each child got 5 gulab jamuns.

Given: Total bindis = 12, number of cones = 2.

$$12 \div 2 = 6$$

Each ice cream cone gets 6 bindis (cherries).

Draw 6 dots on each of the 2 cones.

Given: Total laddoos on 2 plates = 12 (assumed from standard version of this problem), number of plates to share into = 3.

$$12 \div 3 = 4$$

Each of the 3 plates gets 4 laddoos.

Draw and colour 4 laddoos on each of the 3 plates.

Given: Total beads = 21, beads per string = 7.

$$21 \div 7 = 3$$

We can make 3 strings with 21 beads.

Given: Total flowers = 54, flowers per bracelet = 9.

$$54 \div 9 = 6$$

We can make 6 bracelets with 54 flowers.

Given: Total roses = 25, roses per vase = 5.

$$25 \div 5 = 5$$

5 vases are needed.

Given: Total candles = 27, number of boxes = 3.

$$27 \div 3 = 9$$

There will be 9 candles in each box.

Given: Total buttons = 30, buttons per shirt = 6.

$$30 \div 6 = 5$$

The tailor will be able to put 30 buttons on 5 shirts.

Given: Total bananas = 24, number of monkeys = 3.

$$24 \div 3 = 8$$

Each monkey will get 8 bananas.