Addition & Subtraction (Edexcel GCSE Maths)

Revision Note

Jamie Wood

Written by: Jamie Wood

Reviewed by: Dan Finlay

Addition & Subtraction

How do I add large numbers without a calculator?

  • There are a variety of written methods that can be used to add large numbers

    • The order in which numbers are added is not important

  • The column method is the most commonly used hand written method

    • The numbers are written one number above the other,

      • Line up the digits using place value columns

    • Add each pair of corresponding digits from the top and bottom rows (work right to left)

    • If the result is a single digit

      • write the result in the relevant place value column below the line

    • If the result is a 2 digit number

      • the ones are written in the relevant place value column below the line

      • the tens are carried to the top of the next column

    • If the addition of the final pair of digits results in a 2 digit number 

      • write both digits below the line

  • For example, the addition 9789 + 563 = 10 352

How do I subtract large numbers?

  • A variety of written methods exist, but you only need to know one

    • The order in which two numbers are subtracted is important so ensure the calculation is the right way round

  • The column method is the most commonly used hand written method

    • The numbers are written one number above the other

      • Line up the digits using place value columns

      • The number being subtracted should be below the original amount

    • Subtract each digit in the bottom value from the corresponding digit in the top value (work right to left)

    • If the digit being subtracted is bigger than the one it is subtracted from

      •  "borrow ten" from the next column to the left

  • For example, 392 - 28 = 364

What words are used for addition and subtraction?

  • Addition may be phrased using the words: plus, total or sum

  • Subtraction may be phrased using the words: difference or take away

Examiner Tips and Tricks

  • A good way to check your answer without a calculator is to estimate it

    • e.g. if you work out 32 870 ÷ 865 to be 295, check by doing 30 000 ÷ 1 000 in your head which is 30, so your answer is probably wrong (the actual answer is 38)

Worked Example

(a) Find the sum of 3985 and 1273.

Notice that the word sum is used but this means add
Quickly estimate the answer

4000 + 1000 = 5000

Write the numbers in two rows and columns aligned

Start with the ones (units) column, writing the answer below the line but in the same column

Move on to the tens (next on the left) column
The sum is 15 so the 5 (ones) is written below the line and the 1 (tens) 'carries over' to the next (hundreds) column 

Next is the hundreds column which again results in a two-digit answer

Finally add the digits in the thousands column

Check the final answer is similar to your estimate; 5000 and 5258 are reasonably close

3985 + 1273 = 5258

(b) Find the difference between 506 and 28.

Notice that the word difference is used; this means subtract
Quickly estimate the answer

500 - 30 = 470

Write the numbers in two rows, column aligned, ensuring the top number is the number being subtracted from

In the ones (units) column, 6 is smaller than 8, so borrow from the next column (tens)
The tens column is 0, so borrow from the column to the left of that (hundreds)

This turns the 0 (in the tens column) into a 10 which we can then borrow from (for the ones column)

16 - 8 can be now be calculated in the ones column

Move onto the tens column which is 9 - 2 = 7
There is nothing to subtract in the last (hundreds) column (4 - 0 = 4)

Check the final answer is similar to the estimate; 470 and 478 are reasonably close

506 - 28 = 478

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Jamie Wood

Author: Jamie Wood

Expertise: Maths

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Author: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.