Playing with multiplication and division
🎯 In this topic you will
- Multiply numbers in any order.
- Multiply numbers up to 20 by 2, 3, 4, or 5.
- Record what is left over after division (remainders).
🧠 Key Words
- distributive
- quotient
- remainder
- simplify
Show Definitions
- distributive: A rule that lets you multiply or divide across brackets, such as breaking one calculation into smaller parts.
- quotient: The answer you get when one number is divided by another.
- remainder: The amount left over after a division that does not divide evenly.
- simplify: To make a calculation or expression easier by reducing it to its simplest form.
🔄 Changing Order in Calculations
M ultiplication is commutative, just like addition. This means you can multiply numbers in any order, so you can rearrange a calculation to make it easier. Division sometimes leaves part of the whole left over. You will learn how to show this in your calculation.
❓ EXERCISES
1. Multiply each set of three numbers in any order to simplify the calculation and find the product.
a. $5 \times 4 \times 3$
b. $6 \times 5 \times 3$
c. $6 \times 4 \times 2$
d. $8 \times 3 \times 2$
👀 Show answer
a) $5 \times 4 \times 3 = 20 \times 3 = 60$
b) $6 \times 5 \times 3 = 30 \times 3 = 90$
c) $6 \times 4 \times 2 = 24 \times 2 = 48$
d) $8 \times 3 \times 2 = 24 \times 2 = 48$
2. Choose one of the sets of numbers from question $1$. Simplify the calculation in a different way to check that the product is the same.
👀 Show answer
Example using part d:
$8 \times 3 \times 2 = 8 \times 6 = 48$
This matches the previous result, so the product is still $48$.
❓ EXERCISES
3. Simplify each multiplication to help you find the product.
a. $13 \times 4 =$
b. $18 \times 5 =$
c. $12 \times 2 =$
d. $15 \times 3 =$
👀 Show answer
a) $13 \times 4 = 52$
b) $18 \times 5 = 90$
c) $12 \times 2 = 24$
d) $15 \times 3 = 45$
4. Complete each division. Make sure that you include any remainders.
a. $28 \div 4 =$
b. $25 \div 2 =$
c. $53 \div 5 =$
d. $32 \div 4 =$
e. $10 \div 4 =$
f. $46 \div 3 =$
👀 Show answer
a) $28 \div 4 = 7$
b) $25 \div 2 = 12\text{ r }1$
c) $53 \div 5 = 10\text{ r }3$
d) $32 \div 4 = 8$
e) $10 \div 4 = 2\text{ r }2$
f) $46 \div 3 = 15\text{ r }1$
5. Four children share a bag of $30$ sweets between them equally. How many sweets does each child get? Write the division calculation that shows the result.
👀 Show answer
$30 \div 4 = 7\text{ r }2$
Each child gets $7$ sweets, with $2$ left over.
🧠 Think like a Mathematician
Challenge: Find a number between $10$ and $20$ that always leaves a remainder when you divide by $2$, $3$, $4$, and $5$.
Method:
- List the numbers from $11$ to $19$.
- Test each number by dividing it by $2$, $3$, $4$, and $5$.
- Remove any number that divides exactly (with no remainder).
- Keep the numbers that leave a remainder every time.
Follow-up Questions:
👀 show answer
- 1. The numbers are $11$, $13$, $17$, and $19$.
- 2. None of these numbers are divisible by $2$, $3$, $4$, or $5$, so each division leaves a remainder.
- 3. Yes — there is more than one correct answer because several numbers in this range are not multiples of $2$, $3$, $4$, or $5$.