Multiplication And Division 2

In this article, we will be learning about Multiplication and Division and the learning objectives are:

1. Understanding division as equal sharing
2. Understanding division as equal grouping
3. Relating multiplication and division

Topic Recap:

Understanding division as equal sharing

• We divide when we share equally.
• Sharing equally means each group gets the same number of objects.
• To find the number of objects in each group, we need:

1. The total number of objects
2. The total number of groups

Start by distributing 1 object to each group.

Example: 

Share $\small{6}$ balloons equally between two children.

How many balloons does each child get?

Solution:

Let’s begin by giving $\small{1}$ balloon to each child. Repeat until all the balloons have been equally distributed. 

Each child gets $3$ balloons.

Answer:

$3$ balloons

Question 1:

Share $10$ lollipops equally between two children. How many lollipops does each child get? 

1. $5$
2. $6$
3. $3$
4. $4$

Solution: 

Start by distributing $1$ lollipop to each child. Repeat until all the lollipops have been equally distributed. 

Answer:

(1) $5$

Question 2:

Put $9$ bunches of grapes equally into $3$ baskets. How many bunches of grapes are there in each basket?

$3$ groups of _________ $= 9$

1. $6$
2. $2$
3. $3$
4. $4$

Solution: 

Begin by putting $1$ bunch of grapes in each basket. Repeat until all the bunches of grapes have been equally distributed. 

$3$ groups of $3 = 9$

Answer:

(3) $3$

1. Maths concept: Understanding division as equal sharing

Example:

Divide $14$ balloons into $2$ equal groups.

Sharing equally means that each group will get the same number of items.

When you share $14$ balloons equally into two groups, there will be $7$ balloons in each group.

This can be represented as:

$14 \div 2 = 7$

‘$\div$’ means divided by.

We read the division equation above as ‘fourteen divided by two equals seven’. We can also say ‘Divide $14$ by $2$’.

This can also be represented as:

$2$ groups of $7 = 14$

$2 \times 7 = 14$

Question 1: 

Look at the following.

Divide $16$ candies into $4$ equal groups. 

1. Choose the correct option to represent the sentence above.
    
   1. $4 \div 16$
   2. $16 \div 4$

Answer:

(2) $16 \div 4$

2. How many candies are there in each group above?
   1. $8$
   2. $12$
   3. $3$
   4. $4$

Solution: 

$16 \div 4 = 4$

Answer:

(4) $4$

Question 2: 

Divide $15$ crayons into $3$ equal groups. How many crayons are there in each group?

1. $5$
2. $6$
3. $3$
4. $12$

Solution: 

$15 \div 3 = 5$

Answer:

(1) $5$

Question 3: 

$5$ boys went fishing. They caught 10 fish altogether. Each boy caught the same number of fish. How many fish did each boy catch?

1. $5$
2. $2$
3. $10$
4. $50$

Solution: 

$10 \div 5 = 2$

Answer:

(2) $2$

Topic Recap: 

Understanding division as equal grouping

• We divide by equal grouping when we put objects into groups of the same number.
• Equal grouping means to divide a number of objects into groups of the same number.
• To find the number of groups, we need:

1. The total number of objects, and
2. The total number of objects to be put in each group

Example 1:

Divide the elephants into equal groups.

There are $12$ elephants.

Start by identifying how many elephants are to be put in each group.

If we divide the elephants into groups of $3$,

There will be $4$ groups of $3$. 

This also means that $4 \times 3 = 12$.

Similarly, if we divide these $12$ elephants into groups of $4$,

There will be $3$ groups of $4$ elephants each.

This also means that $3 \times 4 = 12$.

Question 1: 

Divide $18$ strawberries into groups of $3$. How many groups of strawberries are there?

__________ groups of $3 = 18$

1. $5$
2. $6$
3. $7$
4. $8$

Solution: 

$18 ÷ 3 = 6$

$6$ groups of $3 = 18$

Answer:

(2) $2$

Question 2: 

Look at the picture below. 

1. How many groups of $5$ are there?
2. $5$
3. $10$
4. $3$

Solution:

Answer:

(3) $3$

2. Max wants to pack $5$ cookies in each bag. How many bags does he need to pack the cookies above?
   1. $5$
   2. $10$
   3. $3$

Solution: 

$15 \div 5 = 3$

Answer:

(3) $3$

2. Understanding division as equal grouping

Divide $20$ toy planes into groups of $5$.

There are $4$ groups of toy planes.

We write a division equation to find the number of groups:

$20 \div 5 = 4$

Total number of objects Number of objects in each group $=$ Number of groups

We can also say that:

$4$ groups of $5 = 20$

$4 \times 5 = 20$

Question 1: 

Divide $12$ apples in groups of $2$.

1. Choose the correct option that represents the statement above.
    
   1. $12 \div 2$
   2. $2 \div 12$

Answer:

(1) $12 \div 2$

2. How many groups of apples are there?
    
   1. $6$
   2. $2$
   3. $10$
   4. $4$

Solution: 

$12 \div 2 = 6$

Answer:

(1) $6$

Question 2: 

Divide $12$ children into groups of $6$. How many groups of children are there?

1. $6$
2. $2$
3. $3$
4. $12$

Solution: 

$12 \div 6 = 2$

Answer:

(2) $2$

Question 3: 

Mr Ng prepared $21$ sandwiches for a party. He puts $7$ sandwiches on each tray. How many trays did he need? 

1. $7$
2. $2$
3. $3$
4. $4$

Solution: 

$21 \div 7 = 3$

Answer:

(3) $3$

Question 4: 

Lindy uses $3$ ice cream sticks to form a triangle. How many such triangles can she form using $24$ sticks?

1. $7$
2. $2$
3. $3$
4. $8$

Solution: 

$24 \div 3 = 8$

Answer:

(4) $8$

3. Relating multiplication and division

There are $3$ pots.

There are $5$ flowers in each pot.

There are $15$ flowers in all. 

From the given picture, we can write $2$ multiplication and $2$ division equations:

• $5 \times 3 = 15$ and $3 \times 5 = 15$
• $15 \div 3 = 5$ and $15 \div 5 = 3$

Question 1: 

Ron collected $10$ bottles for recycling.

1. Which two multiplication equations best represent the picture above?
    
   1. $2 \times 5 = 10$ and $5 \times 2 = 10$
   2. $10 \times 2 = 5$ and $10 \times 5 = 2$

Answer:

(1) $2 \times 5 = 10$ and $5 × 2 = 10$

2. Which two division equations best represent the picture above?
    
   1. $2 \div 5 = 10$ and $5 \div 2 = 10$
   2. $10 \div 5 = 2$ and $10 \div 2 = 5$

Answer:

(2) $10 \div 5 = 2$ and $10 \div 2 = 5$

Question 2: 

What is the missing number?

1. $6$
2. $2$
3. $16$
4. $4$

Solution: 

$\begin{align}​​ 2 \times 8 &= 16 \\[2ex] 8 \times 2 &= 16 \end{align}$

The missing number is $16$. 

Answer:

(3) $16$

Question 3: 

What are the values of $X$ and $Y$?

1. $X = 8, Y = 5$
2. $X = 8, Y = 40$
3. $X = 5, Y = 40$

Solution: 

To find $X$, 

$40 \div 5 = 8$

To find $Y$,

$5 \times 8 = 40$

Answer:

(2) $X = 8, Y = 40$

In this article, we learnt division: