Subtraction — Maths Topic Journey

Taking away and finding the difference

🟢 Foundation — Subtraction

Learn to subtract single-digit and teen numbers using counting back

Subtracting Single Digits

  • Subtraction means taking away.
  • When we subtract 7 - 3, we start with 7 and count back 3.
  • Example: 7 - 3 = 4
  • 9 - 2 = 7
  • 8 - 4 = 4
  • 10 - 5 = 5

Worked Example: 9 - 5 = ?

  1. Start at 9
  2. Count back: 8, 7, 6, 5, 4
  3. We counted back 5 numbers
  4. So 9 - 5 = 4

Answer: 4

Tip: Use your fingers to count back. Start at the bigger number and count down!

Counting Back from Teens

  • Taking away from 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
  • Example: 15 - 2
  • Start at 15, count back 2: 14, 13
  • 15 - 2 = 13
  • 18 - 3 = 15
  • 20 - 4 = 16

Worked Example: 17 - 5 = ?

  1. Start at 17
  2. Count back 5: 16, 15, 14, 13, 12
  3. We reached 12
  4. 17 - 5 = 12

Answer: 12

Tip: Count back carefully on your fingers. One finger for each number you count back.

Sharing and Grouping

  • Subtraction can also mean sharing things equally.
  • If we have 12 apples to share between 3 people, each person gets 4.
  • 12 shared by 3 = 4 each
  • We can write: 12 - 4 - 4 - 4 = 0
  • Subtraction helps us find groups and equal shares.

Worked Example: There are 16 sweets to share between 4 friends equally. How many does each get?

  1. Start with 16
  2. Give 1 to each friend (subtract 4): 16 - 4 = 12
  3. Give 1 more to each (subtract 4): 12 - 4 = 8
  4. Give 1 more to each (subtract 4): 8 - 4 = 4
  5. Give 1 more to each (subtract 4): 4 - 4 = 0
  6. Each friend got 4 sweets

Answer: 4

Tip: Sharing is dividing equally. It's the same as taking away groups.

Practice Problems

🟡 Intermediate — Subtraction

Master column subtraction with borrowing for 2 and 3-digit numbers

Introduction to Column Subtraction

  • Column subtraction means writing numbers in columns.
  • Ones go in the ones column.
  • Tens go in the tens column.
  • Subtract the ones first, then the tens.
  • Example: 45 - 23
  • 45
  • - 23
  • ----
  • 22

Worked Example: 56 - 34 = ?

  1. Write in columns: 56
  2. - 34
  3. Subtract ones: 6 - 4 = 2
  4. Subtract tens: 5 - 3 = 2
  5. Answer: 22

Answer: 22

Tip: Line up the numbers by place value. Ones under ones, tens under tens.

Subtraction with Borrowing

  • Sometimes we cannot subtract the ones.
  • When the ones on top are smaller, we borrow from the tens.
  • Example: 42 - 17
  • Ones: 2 is less than 7, so we borrow 1 ten
  • 2 becomes 12, and 4 tens becomes 3 tens
  • Now: 12 - 7 = 5 (ones) and 3 - 1 = 2 (tens)
  • Answer: 25

Worked Example: 53 - 28 = ?

  1. Write in columns: 53
  2. - 28
  3. Ones: 3 is less than 8, so borrow from tens
  4. Borrow 1 ten: 5 tens becomes 4 tens, and 3 becomes 13
  5. Subtract ones: 13 - 8 = 5
  6. Subtract tens: 4 - 2 = 2
  7. Answer: 25

Answer: 25

Tip: If you cannot subtract the ones, borrow 1 ten from the tens column.

3-Digit Subtraction

  • For 3-digit numbers, subtract ones, then tens, then hundreds.
  • Sometimes you need to borrow from hundreds to tens.
  • Example: 345 - 128
  • 345
  • - 128
  • -----
  • 217
  • Work from right to left: ones, tens, hundreds.

Worked Example: 312 - 147 = ?

  1. Write in columns: 312
  2. - 147
  3. Ones: 2 is less than 7, borrow from tens
  4. Tens: becomes 0, ones becomes 12. 12 - 7 = 5
  5. Tens: 0 is less than 4, borrow from hundreds
  6. Hundreds: becomes 2, tens becomes 10. 10 - 4 = 6
  7. Hundreds: 2 - 1 = 1
  8. Answer: 165

Answer: 165

Tip: Borrow from the next column if needed. Work right to left.

Practice Problems

🔴 Exam Ready — Subtraction

Subtract money, find differences, and solve word problems with change

Subtracting Money

  • Subtracting money works like subtracting decimals.
  • Line up the decimal points (the pounds and pence separator).
  • Example: £5.30 - £2.15
  • £5.30
  • - £2.15
  • -------
  • £3.15
  • Always write £ in the answer.

Worked Example: £7.45 - £3.28 = ?

  1. Write in columns: £7.45
  2. - £3.28
  3. Pence: 45 - 28 = 17 pence
  4. Pounds: 7 - 3 = 4 pounds
  5. Answer: £4.17

Answer: £4.17

Tip: Line up the decimal points. Always write £ in your answer.

Finding Differences and Change

  • Finding the difference is subtraction.
  • Change is the money you get back when you buy something.
  • Example: Item costs £2.50. You pay with £5.00.
  • Change = £5.00 - £2.50 = £2.50
  • If you buy for £3.75 and pay with £10.00:
  • Change = £10.00 - £3.75 = £6.25

Worked Example: A book costs £4.99. You pay with a £10 note. How much change do you get?

  1. £10.00
  2. - £4.99
  3. -------
  4. Pence: 100 - 99 = 1 pence (borrow 1 pound)
  5. Pounds: 9 - 4 = 5 pounds
  6. Answer: £5.01 change

Answer: £5.01

Tip: Change = money you give - money the item costs

Multi-Step Word Problems

  • Some problems need more than one step.
  • Read carefully to find what you need to do.
  • Example: You have £20. You buy a pen for £3.50 and a book for £5.25. How much do you have left?
  • Step 1: Find total spent: £3.50 + £5.25 = £8.75
  • Step 2: Find what's left: £20.00 - £8.75 = £11.25

Worked Example: Sarah has 8.75 meters of ribbon. She uses 3.20 meters for a project. How much ribbon does she have left?

  1. 8.75
  2. - 3.20
  3. ------
  4. Hundredths: 5 - 0 = 5
  5. Tenths: 7 - 2 = 5
  6. Ones: 8 - 3 = 5
  7. Answer: 5.55 meters

Answer: 5.55

Tip: Break word problems into steps. Do subtraction carefully with decimals.

Practice Problems

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