Adding and subtracting Revision Notes for AQA GCSE Maths

Adding and subtracting

You need to be able to add and subtract numbers without a calculator. This is a fundamental skill that appears frequently in GCSE Foundation Maths exams.

infoNote

Adding and subtraction without a calculator is one of the most essential skills in GCSE Foundation Maths. These methods will save you valuable time in exams and build your number confidence.

Mental methods

Mental methods help you add and subtract quickly in your head using number sense and place value understanding. These techniques allow you to perform calculations efficiently without writing anything down.

Quick addition strategies

When adding numbers mentally, break them down into manageable parts:

Split larger numbers into tens and units
Add the easier numbers first, then combine
Use number bonds you know well

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Worked Example: Mental Addition

Calculate $213 + 79$ using mental methods:

Step 1: Split the second number $213 + 79 = 213 + 70 + 9$

Step 2: Add the easier number first $213 + 70 = 283$

Step 3: Add the remaining amount $283 + 9 = 292$

Therefore, $213 + 79 = 292$

Quick subtraction strategies

For mental subtraction, you can count up from the smaller number:

Find the difference by counting in steps
Use place value to make calculations easier
Bridge through multiples of 10 or 100

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Worked Example: Mental Subtraction by Counting Up

Calculate $152 - 63$ using the counting up method:

Step 1: Count from 63 to the next multiple of 10 $63 → 70$ (difference of 7)

Step 2: Count from 70 to the next multiple of 100 $70 → 100$ (difference of 30)

Step 3: Count from 100 to 152 $100 → 152$ (difference of 52)

Step 4: Add all the differences $7 + 30 + 52 = 89$

Therefore, $152 - 63 = 89$

Column method for addition

The column method is a systematic way to add larger numbers by organising them in place value columns. This method ensures accuracy when dealing with multiple large numbers.

chatImportant

Key Rule for Column Addition Always start from the units column (right-hand side) and work systematically from right to left. This ensures you handle carrying correctly.

Step-by-step process

Always add the units column first: Start from the right-hand side
Add each column systematically: Work from right to left
Carry over when needed: If a column total is 10 or more, write down the units digit and carry the tens digit to the next column
Include carried numbers: Don't forget to add any numbers you've carried over

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Worked Example: Column Addition

Calculate $285 + 56 + 1091$ using the column method:

   285
    56
+ 1091
______
  1432

Step 1: Add the units column $5 + 6 + 1 = 12$ Write down 2, carry 1

Step 2: Add the tens column $8 + 5 + 9 + 1 \text{ (carried)} = 23$ Write down 3, carry 2

Step 3: Add the hundreds column $2 + 0 + 0 + 2 \text{ (carried)} = 4$ Write down 4

Step 4: Add the thousands column $1$ (no other digits to add) Write down 1

Therefore, $285 + 56 + 1091 = 1432$

Column method for subtraction

Column subtraction uses place value columns but requires exchanging when the top digit is smaller than the bottom digit. This is also called "borrowing" from the next column.

chatImportant

Critical Rule for Column Subtraction When the top digit is smaller than the bottom digit, you must exchange (borrow) from the column to the left. Never try to subtract a larger number from a smaller one.

Step-by-step process

Always subtract the units column first: Start from the right
Check if exchange is needed: If the top number is smaller than the bottom number, you must exchange
Exchange from the next column: Borrow 10 from the next column to the left
Continue column by column: Work systematically from right to left

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Worked Example: Column Subtraction with Exchange

Calculate $418 - 62$ using the column method:

  ³⁴1̱8̱
-   62
______
   356

Step 1: Subtract the units column $8 - 2 = 6$ ✓

Step 2: Subtract the tens column $1 - 6$ is not possible, so exchange 1 hundred for 10 tens This gives us $11 - 6 = 5$

Step 3: Subtract the hundreds column $4$ becomes $3$ after exchanging, and there's nothing to subtract Write down $3$

Therefore, $418 - 62 = 356$

Practical applications

Adding and subtracting skills are essential for real-world problems, especially with money calculations. These skills help you manage finances and solve everyday mathematical problems.

Money problems

When working with money:

You can work in pence to avoid decimal numbers
Always give your final answer in the correct format
Remember to include units (£ or p) in your answer

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Converting to pence eliminates decimal points and makes calculations easier. For example, £4.45 becomes 445p, which is much simpler to work with in column methods.

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Worked Example: Money Problem

Joe buys a magazine costing £4.45 and birthday cards costing £1.99 each. He buys two cards and pays with a £10 note. How much change does he receive?

Solution working in pence:

Step 1: Convert all amounts to pence

Magazine: £4.45 = 445p
Each card: £1.99 = 199p
Payment: £10.00 = 1000p

Step 2: Calculate total cost of cards $199p + 199p = 398p$

Step 3: Calculate total purchase cost $445p + 398p = 843p$

Step 4: Calculate change $1000p - 843p = 157p$

Step 5: Convert back to pounds and pence $157p = £1.57$

Therefore, Joe receives £1.57 change.

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Key Points to Remember:

Always start with the units column when using column methods for both addition and subtraction
Mental methods save time - use number bonds and place value to calculate quickly
Exchange carefully in subtraction when the top digit is smaller than the bottom digit
Check your work by estimating whether your answer is reasonable
Practice regularly - these skills improve with repetition and are essential for GCSE success

Adding and subtracting (AQA GCSE Maths): Revision Notes