Adding and subtracting (Edexcel GCSE Maths): Revision Notes
Adding and subtracting
You need to master adding and subtracting numbers without using a calculator. This skill is essential for your GCSE maths exam and requires both mental methods and column methods.
Mastering these fundamental arithmetic skills without a calculator is crucial for GCSE success. The ability to add and subtract confidently will support you across all areas of mathematics.
Mental methods
Mental methods are quick strategies you can use to add and subtract numbers in your head. These techniques help you work faster and check your written calculations.
Addition mental methods
When adding numbers, you can break them into manageable parts to make the calculation easier in your head.
Worked Example: Adding 213 + 79
Step 1: Break down the second number into tens and units 79 = 70 + 9
Step 2: Add the tens first 213 + 70 = 283
Step 3: Add the units 283 + 9 = 292
Therefore: 213 + 79 = 292
Subtraction mental methods
For subtraction, the counting up method can be very effective, especially when the numbers are close together.
Worked Example: Subtracting 152 - 63
Step 1: Count up from the smaller number to the larger number From 63 to 152 in manageable jumps:
Step 2: Make the jumps
- From 63 to 70 (+7)
- From 70 to 100 (+30)
- From 100 to 152 (+52)
Step 3: Add up all the jumps 7 + 30 + 52 = 89
Therefore: 152 - 63 = 89
Column addition method
The column method is a systematic way to add larger numbers by working through each column from right to left. This method ensures accuracy and shows clear working.
Remember the golden rule: Always start with the units column and work towards the left. This prevents errors and ensures you handle carrying correctly.
Key steps for column addition
- Always start with the units column: Add all the digits in the rightmost column first
- Handle carrying: If the sum is 10 or more, write down the units digit and carry the tens digit to the next column
- Move to the tens column: Add the tens digits plus any carried amount
- Continue left: Repeat for hundreds, thousands, and any remaining columns
Worked Example: Column Addition 285 + 56 + 1091
285
56
+1091
-----
1432
Step 1: Units column 5 + 6 + 1 = 12 (write 2, carry 1)
Step 2: Tens column
8 + 5 + 9 + 1 (carried) = 23 (write 3, carry 2)
Step 3: Hundreds column 2 + 0 + 0 + 2 (carried) = 4 (write 4)
Step 4: Thousands column 1 (write 1)
Answer: 1432
Column subtraction method
The column method for subtraction also works from right to left, but uses exchanging (also called borrowing) when the top digit is smaller than the bottom digit.
Critical concept: When you can't subtract because the top digit is smaller, you must exchange from the column to the left. This is often where mistakes happen, so take extra care!
Key steps for column subtraction
- Always start with the units column: Subtract the bottom digit from the top digit
- Use exchanging when needed: If the top digit is smaller, borrow 10 from the next column to the left
- Adjust the borrowed column: Reduce the digit you borrowed from by 1
- Continue left: Work through tens, hundreds, and remaining columns
Worked Example: Column Subtraction 418 - 62
418
- 62
----
356
Step 1: Units column 8 - 2 = 6 (write 6)
Step 2: Tens column 1 is smaller than 6, so we need to exchange
- Exchange 1 hundred for 10 tens (making 11 tens)
- Now: 11 - 6 = 5 (write 5)
Step 3: Hundreds column
4 - 1 = 3 (write 3, remembering we used 1 hundred for exchanging)
Answer: 356
Exam tips
Essential Exam Strategies
- Show your working: Column methods make your working clear for exam markers to follow and award partial marks
- Check your answers: Use mental methods to roughly verify if your answer makes sense
- Start right, work left: Always begin with the units column in both addition and subtraction
- Line up place values: Make sure digits are properly aligned in columns to avoid errors
- Handle money carefully: When working with pounds and pence, remember to give your final answer with appropriate units (£ and p)
Key Points to Remember:
- Mental methods help you work quickly and check answers
- Column methods provide a systematic approach for larger calculations
- Always start with the units column and work left
- In addition, carry forwards any extra tens
- In subtraction, exchange from the left when the top digit is too small
- Practice both methods regularly to build confidence and speed