Division
🎯 In this topic you will
- Estimate the size of an answer before calculating it
- Divide whole numbers by 1-digit whole numbers
🧠 Key Words
- decompose
- denominator
- divisor
- inverse operations
- numerator
Show Definitions
- decompose: To break a number into parts that are easier to work with during a calculation.
- denominator: The bottom number of a fraction, showing how many equal parts the whole is divided into.
- divisor: The number you divide by in a division calculation.
- inverse operations: Operations that undo each other, such as multiplication and division.
- numerator: The top number of a fraction, showing how many parts are being considered.
🎵 Playing in a Band
Imagine you are in a music group. You might be the singer, a guitarist or the drummer. When you play a song, it is divided into different parts so each person has their own job to do.
💰 Sharing the Performance Money
When a music group is paid to perform, the money is divided between the members of the group.
➕ When Someone New Joins
Imagine an extra person joins the group.
❓ EXERCISES
1. Calculate. Remember to estimate the size of your answer before you calculate it.
a. $456 \div 8$
b. $868 \div 7$
c. $333 \div 9$
👀 Show answer
a. $456 \div 8 = 57$
b. $868 \div 7 = 124$
c. $333 \div 9 = 37$
2. Zina’s book has $238$ pages.
She reads $7$ pages each day.
How long does it take Zina to read the book?
👀 Show answer
Zina needs $238 \div 7 = 34$ days.
3. Calculate, writing the remainder as the number left over.
a. $638 \div 5$
b. $423 \div 4$
c. $326 \div 8$
👀 Show answer
a. $638 \div 5 = 127$ r $3$
b. $423 \div 4 = 105$ r $3$
c. $326 \div 8 = 40$ r $6$
4. Classify the calculations into these groups:
• answer less than $10$
• answer between $10$ and $20$
• answer more than $20$
$86 \div 3$
$88 \div 9$
$91 \div 9$
$94 \div 8$
$96 \div 6$
$98 \div 4$
👀 Show answer
Less than 10: $91 \div 9 = 10$ (close but not less), none actually less than $10$.
Between 10 and 20:
$86 \div 3 = 28$ (not between)
$88 \div 9 = 9$ (below 10)
$91 \div 9 = 10$
$94 \div 8 = 11$
$96 \div 6 = 16$
More than 20:
$86 \div 3 = 28$
$98 \div 4 = 24$
5. Calculate, writing the remainder as a fraction.
a. $97 \div 5$
b. $86 \div 4$
c. $99 \div 7$
👀 Show answer
a. $97 \div 5 = 19 \dfrac{2}{5}$
b. $86 \div 4 = 21 \dfrac{2}{4} = 21 \dfrac{1}{2}$
c. $99 \div 7 = 14 \dfrac{1}{7}$
6. Find the missing numbers.
a. $\Box \div 4 = 23$
b. $\Box \times 4 = 96$
c. $88 \div \Box = 22$
👀 Show answer
a. $23 \times 4 = 92$
b. $96 \div 4 = 24$
c. $88 \div 22 = 4$
7. Find the missing digit.
👀 Show answer
The missing digit is $8$.
🧠 Think like a Mathematician
Use only the digits $4$, $5$ and $9$ to make a three-digit number that is divisible by $9$. You may use each digit only once.
Your task:
- Create three-digit numbers using the digits $4$, $5$, $9$ exactly once each.
- Check whether the number is divisible by $9$.
- Find as many different correct numbers as possible.
- Determine which valid number produces the largest answer when divided by $9$.
You will demonstrate you are specialising by finding correct solutions to the problem.
Show Answers
- To be divisible by $9$, the sum of the digits must be a multiple of $9$.
- The sum $4 + 5 + 9 = 18$, which is divisible by $9$.
- Therefore every permutation of the digits forms a valid number.
- All valid numbers: $459$, $495$, $549$, $594$, $945$, $954$
- Dividing each by $9$:
- $459 \div 9 = 51$
- $495 \div 9 = 55$
- $549 \div 9 = 61$
- $594 \div 9 = 66$
- $945 \div 9 = 105$
- $954 \div 9 = 106$
- Largest possible answer:$954 \div 9 = 106$