Study P2 Mathematics Multiplication and Division 2 - Geniebook

# Multiplication And Division 2

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 $$6$$ balloons equally between two children.

How many balloons does each child get?

Solution:

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

Each child gets $$3$$ balloons.

$$3$$ 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.

(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 $$3 = 9$$

(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. $$16 \div 4$$

(2) $$16 \div 4$$

1. How many candies are there in each group above?

1. $$8$$
2. $$12$$
3. $$3$$
4. $$4$$

Solution:

$$16 \div 4 = 4$$

(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:

$$15 \div 3 = 5$$

(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:

$$10 \div 5 = 2$$

(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 $$3 = 18$$

(2) $$2$$

Question 2:

Look at the picture below.

1. How many groups of $$5$$ are there?

1. $$5$$
2. $$10$$
3. $$3$$

Solution:

(3) $$3$$

1. 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:

$$15 \div 5 = 3$$

(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. $$2 \div 12$$

(1) $$12 \div 2$$

1. How many groups of apples are there?

1. $$6$$
2. $$2$$
3. $$10$$
4. $$4$$

Solution:

$$12 \div 2 = 6$$

(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:

$$12 \div 6 = 2$$

(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:

$$21 \div 7 = 3$$

(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:

$$24 \div 3 = 8$$

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

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

1. Which two division equations best represent the picture above?

1. $$2 \times 5 = 10$$ and $$5 \times 2 = 10$$
2. $$10 \div 5 = 2$$ and $$10 \div 2 = 5$$

(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 $$16$$

(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 $$Y$$,

$$5 \times 8 = 40$$

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

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Numbers To 1000 Multiplication And Division 1
Multiplication And Division 2 Addition And Subtraction 1
Addition And Subtraction 2 Fractions 1
Length 1 Mass 1
Volume 1 Money 1
Time 1 Shapes And Patterns
Picture Graphs 1 Model Drawing 1
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Picture Graphs 1
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