Division (2)
In this topic you will
- Build division tables using related multiplication tables.
- Connect multiplication and division facts that produce the same value.
- Explain how halving relates to dividing by 2, and how finding a quarter relates to dividing by 4.
Key Words
- quotient
Show Definitions
- quotient: The result of a division calculation (the number you get when one number is divided by another).
Division and equal groups
Division is all about equal groups, just like multiplication.
Using multiplication facts
You can use a multiplication fact to find a division fact.
Halves and quarters
Finding a half or a quarter is the same as dividing by $2$ and $4$.
Making connections
You don’t have to learn everything in mathematics, there are so many connections to use.
EXERCISES
1. Complete the multiplication table for $5$. Use it to write the division facts for $5$.
$5 \times 1 = 5$
$5 \times 2 = 10$
$5 \times 3 =$
$5 \times 4 =$
$5 \times 5 =$
$5 \times 6 =$
$5 \times 7 =$
$5 \times 8 =$
$5 \times 9 =$
$5 \times 10 =$
$5 \times 11 =$
$5 \times 12 =$
$5 \div 5 = 1$
👀 Show answer
Multiplication table for $5$:$5 \times 1 = 5$, $5 \times 2 = 10$, $5 \times 3 = 15$, $5 \times 4 = 20$, $5 \times 5 = 25$, $5 \times 6 = 30$, $5 \times 7 = 35$, $5 \times 8 = 40$, $5 \times 9 = 45$, $5 \times 10 = 50$, $5 \times 11 = 55$, $5 \times 12 = 60$.
Division facts for $5$:$5 \div 5 = 1$, $10 \div 5 = 2$, $15 \div 5 = 3$, $20 \div 5 = 4$, $25 \div 5 = 5$, $30 \div 5 = 6$, $35 \div 5 = 7$, $40 \div 5 = 8$, $45 \div 5 = 9$, $50 \div 5 = 10$, $55 \div 5 = 11$, $60 \div 5 = 12$.
2. Write the inverse division fact for each multiplication fact.
a. $2 \times 6 = 12$$\rightarrow$
b. $1 \times 8 = 8$$\rightarrow$
c. $10 \times 4 = 40$$\rightarrow$
d. $5 \times 3 = 15$$\rightarrow$
👀 Show answer
a.$12 \div 6 = 2$
b.$8 \div 8 = 1$
c.$40 \div 4 = 10$
d.$15 \div 3 = 5$
3. When a product and a quotient have the same value, the facts are equal in value.
You can join them using the equals sign, for example, $6 \times 1 = 12 \div 2$.
Write a multiplication or division fact with the same value as the given fact. Write a multiplication fact if the given fact is a division, and a division fact if the given fact is a multiplication.
a. $2 \times 4 =$
b. $1 \times 3 =$
c. $14 \div 2 =$
d. $30 \div 5 =$
👀 Show answer
a.$2 \times 4 = 8$, so one matching division fact is $8 \div 2 = 4$.
b.$1 \times 3 = 3$, so one matching division fact is $3 \div 3 = 1$.
c.$14 \div 2 = 7$, so one matching multiplication fact is $7 \times 2 = 14$.
d.$30 \div 5 = 6$, so one matching multiplication fact is $6 \times 5 = 30$.
4. Is each division fact the equivalent to finding $\frac{1}{2}$ or $\frac{1}{4}$?
| Division fact | Equivalent to finding $\frac{1}{2}$ or $\frac{1}{4}$? |
|---|---|
| $8 \div 2 = 4$ | |
| $12 \div 4 = 3$ | |
| $20 \div 4 = 5$ | |
| $10 \div 2 = 5$ |
👀 Show answer
$8 \div 2$ is finding $\frac{1}{2}$.
$12 \div 4$ is finding $\frac{1}{4}$.
$20 \div 4$ is finding $\frac{1}{4}$.
$10 \div 2$ is finding $\frac{1}{2}$.
Think like a Mathematician
Investigation: Grandma is buying Zara and her 3 brothers some chocolate. They can each have a small bar like this, or a larger bar like this one to share.
Task: Which bar should they choose? Why?
Method:
- Count how many children will share the chocolate: Zara + 3 brothers = 4 children.
- Count how many chocolate pieces are in the small bar.
- Count how many chocolate pieces are in the large bar.
- Work out how many pieces each child would get in each option.
- Write number sentences to show your thinking, then choose the better option and explain why.
Follow-up: Write some number sentences to show how you found your answer.
👀 show answer
Counts from the picture:
- Small bar: 4 pieces.
- Large bar: 20 pieces.
Number sentences (examples):
- Children: $1 + 3 = 4$
- If everyone gets a small bar: $4 \times 4 = 16$ pieces in total.
- If they share the large bar: $20 \div 4 = 5$ pieces each.
- Compare per child: small gives $4$ each, large gives $5$ each, and $5 > 4$.
Decision: They should choose the large bar, because sharing it gives 5 pieces each, which is more than the 4 pieces each from the small bars.
EXERCISES
$5$. Write some division facts to connect with this multiplication fact.
I know that $10 \times 2 = 20$ so I also know that …
👀 Show answer
$20 \div 2 = 10$
$20 \div 10 = 2$
$20 \div 1 = 20$
$6$. Write $4$ multiplication, division or fraction facts about this array.
👀 Show answer
$2 \times 2 = 4$
$4 \times 5\text{c} = 20\text{c}$
$20\text{c} \div 4 = 5\text{c}$
$20\text{c} \div 5\text{c} = 4$
$7$. Make up a question like question $6$ using your own currency. Swap questions with a friend and answer it. Ask your friend to check that you were correct.
👀 Show answer
Example question: Write $4$ multiplication, division or fraction facts about an array of $6$ coins worth $\pounds 1$ each, arranged in $3$ rows of $2$.
Facts:
$3 \times 2 = 6$
$6 \div 3 = 2$
$6 \div 2 = 3$
$6 \times \pounds 1 = \pounds 6$