Division — Maths Topic Journey

Sharing equally and grouping

🟢 Foundation — Division

Learn halving, sharing equally, and grouping using division as the opposite of multiplication

Halving and Sharing

  • Division means sharing or grouping.
  • Halving means dividing by 2.
  • Half of 8 is 4
  • Half of 10 is 5
  • Half of 12 is 6
  • Half of 16 is 8
  • ÷ means divide (share)

Worked Example: Share 12 sweets between 2 children equally. How many does each get?

  1. We have 12 sweets
  2. Share between 2 children
  3. Each child gets 6 sweets
  4. 12 ÷ 2 = 6

Answer: 6

Tip: Halving is the same as dividing by 2. Half of 12 is 6.

Sharing Equally

  • To share equally, we split into groups.
  • 15 ÷ 3 means share 15 between 3 people
  • Each person gets 5
  • 20 ÷ 4 means share 20 between 4 people
  • Each person gets 5
  • 18 ÷ 6 means share 18 between 6 people
  • Each person gets 3

Worked Example: 16 apples to share between 4 people. How many each?

  1. We have 16 apples
  2. Share between 4 people
  3. Count: 4 people get 1, 4 people get 1 more...
  4. Each person gets 4
  5. 16 ÷ 4 = 4

Answer: 4

Tip: Give everyone 1, then 1 more, and keep counting until they are all shared out.

Grouping and Division as Opposite of Multiplication

  • Division is the opposite of multiplication.
  • If 3 × 5 = 15, then 15 ÷ 5 = 3
  • If 4 × 6 = 24, then 24 ÷ 6 = 4
  • 20 ÷ 5 = 4 because 4 × 5 = 20
  • Use times tables to help with division!

Worked Example: 24 ÷ 8 = ?

  1. Think: 8 times what equals 24?
  2. From times tables: 8 × 3 = 24
  3. So 24 ÷ 8 = 3

Answer: 3

Tip: If you know your times tables, you know division! 5 × 6 = 30 means 30 ÷ 6 = 5.

Practice Problems

🟡 Intermediate — Division

Master short division (bus stop method) with and without remainders for 2-digit ÷ 1-digit

Short Division Introduction

  • Short division is also called the bus stop method.
  • We write the numbers like this:
  • 42 ÷ 2
  • It looks like a bus stop symbol
  • Divide the tens first, then the ones
  • Example: 42 ÷ 2 = 21

Worked Example: 63 ÷ 3 = ?

  1. Write: 3 | 63
  2. Divide tens: 6 ÷ 3 = 2 (write 2)
  3. Divide ones: 3 ÷ 3 = 1 (write 1)
  4. Answer: 21

Answer: 21

Tip: The bus stop method divides left to right: tens first, then ones.

Division with Remainders

  • Sometimes numbers don't divide exactly.
  • A remainder is what is left over.
  • Example: 17 ÷ 5 = 3 remainder 2
  • We write: 17 ÷ 5 = 3 r 2
  • 25 ÷ 4 = 6 r 1
  • 19 ÷ 3 = 6 r 1

Worked Example: 26 ÷ 6 = ?

  1. How many 6s in 26?
  2. 6 × 4 = 24
  3. 26 - 24 = 2 left over
  4. 26 ÷ 6 = 4 remainder 2
  5. Written: 4 r 2

Answer: 4 r 2

Tip: The remainder is the number left over. It's always smaller than the divisor.

Using Bus Stop with Remainders

  • When dividing doesn't work exactly, we get a remainder.
  • Example: 47 ÷ 3
  • Tens: 4 ÷ 3 = 1 remainder 1
  • Bring down the 7: becomes 17
  • Ones: 17 ÷ 3 = 5 remainder 2
  • Answer: 15 r 2

Worked Example: 35 ÷ 4 = ?

  1. Tens: 3 ÷ 4 = 0 remainder 3
  2. Bring down 5: becomes 35
  3. Ones: 35 ÷ 4 = 8 remainder 3
  4. 35 ÷ 4 = 8 r 3

Answer: 8 r 3

Tip: When the tens digit is smaller than the divisor, it becomes a remainder you bring down.

Practice Problems

🔴 Exam Ready — Division

Master 3-digit ÷ 1-digit long division, interpret remainders in context, and solve word problems

3-Digit Division

  • Long division for 3-digit numbers follows the same pattern.
  • Example: 156 ÷ 3
  • Hundreds: 1 ÷ 3 = 0 remainder 1
  • Bring down 5: 15 ÷ 3 = 5
  • Bring down 6: 6 ÷ 3 = 2
  • Answer: 52

Worked Example: 234 ÷ 2 = ?

  1. Hundreds: 2 ÷ 2 = 1
  2. Tens: 3 ÷ 2 = 1 remainder 1
  3. Bring down 4: 14 ÷ 2 = 7
  4. Answer: 117

Answer: 117

Tip: Work left to right: hundreds, tens, ones. Bring down remainders.

Interpreting Remainders

  • Sometimes you need to interpret what the remainder means.
  • If 23 apples share among 4 people: 23 ÷ 4 = 5 r 3
  • Each person gets 5 apples, and 3 are left over.
  • If 23 pounds buys items costing 4 pounds each:
  • 23 ÷ 4 = 5 r 3, so you can buy 5 items and have £3 left.
  • In context matters!

Worked Example: A coach has 47 children to transport in minibuses that hold 8 children each. How many minibuses needed?

  1. 47 ÷ 8 = 5 r 7
  2. This means 5 buses are full
  3. But 7 children are still waiting
  4. Need 1 more bus, so 6 buses total

Answer: 6 buses

Tip: Sometimes you round up the remainder. A remainder of 1 person still needs a bus!

Word Problems with Division

  • Read carefully to understand what division you need.
  • Look for words like: share, distribute, split, divide, each, per
  • Example: 144 books in a library to arrange in 6 shelves equally.
  • 144 ÷ 6 = 24 books per shelf
  • Another: 250 pencils in packs of 10.
  • 250 ÷ 10 = 25 packs

Worked Example: A factory makes 360 toys per day. They pack them in boxes of 8. How many boxes?

  1. Divide total toys by toys per box
  2. 360 ÷ 8 = 45
  3. They make 45 boxes per day

Answer: 45 boxes

Tip: Find: what number are you dividing? What number are you dividing by?

Practice Problems

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