Addition & Subtraction
What kind of addition or subtraction questions could I be asked?
- Adding and subtracting could be a part of any question within your IGCSE course
- Adding areas or volumes together in geometry questions
- Working with estimated mean or other averages
- Any problem solving questions in a variety of contexts
- A variety of vocabulary can be used to imply you must add or subtract values
- For adding the word plus may be used or you could be asked to find the total or find the sum
- For subtracting the word minus or take away may be used or you could be asked to find the difference
- Although you will have a calculator to carry out these sums on, you could be asked to show a non calculator method
- You should be especially confident showing methods for adding and subtracting large numbers and decimals
How do I add large numbers?
- You will almost always be able to use your calculator in the exam, you only need to show a full column method if the question tells you to
- If the question states without using your calculator then you must show a full written method, but you should still check your answer on your calculator
- To add large numbers without a calculator
- Write one number above the other in two rows, making sure that all the ones, tens, hundreds, and so on, are lined up in the same columns
- Add the numbers in each column, writing the answer below the line
- If your sum is a two digit number, split it into ones and tens, writing the value of the ones below the line, and the value of the tens at the top of the next column
- If the sum of the last column is a 2 digit number, you can write the entire number below the line
- this is effectively the same as writing it at the top of the next column, but it would be the only number in that column
How do I subtract large numbers?
- Again, use your calculator in the exam unless the question tells you not to
- If the question states without using your calculator then you must show a full written method, but you should still check your answer on your calculator
- To subtract large numbers without a calculator
- Write one number above the other in two rows, making sure that all the ones, tens, hundreds, and so on, are lined up in the same columns
- Subtract the bottom number in each column from the top number in each column, starting with the units column
- If your subtraction produces a negative number, we can avoid this by “borrowing” a ten from the next column to the left
- If you need to borrow from a column, but it is a zero, you can borrow a ten from the next column to the left; turning the 0 into a 10, which you can then borrow from
- Repeat this for each of the next columns, until complete
How do I add or subtract with decimals?
- If the numbers involve decimals, make sure the decimal points are lined up in a column of their own and keep the decimal point in the answer in this column too
- You may need to add zeros before or after the decimal point to keep everything in line
- Again, check your answer with your calculator!
Examiner Tip
- Even if a question asks you to perform a calculation without your calculator, still use it to check your work, the examiner will not know unless you do not show enough working!
- Make sure you show all the 'non calculator' steps clearly
Worked example
(a)
Find the sum of 3985 and 1273.
Notice that the word sum requires you to add the numbers together.
Begin by estimating the answer.
4000 + 1000 = 5000
so the answer should be a little more than 5000
Write one number above the other.
Add the digits in the ones column.
Add the digits in the tens column, writing the 1 above the next column.
Add the digits in the hundreds column, including the extra 1.
Add the digits in the thousands column, including the extra 1.
Check the final answer is similar to your estimate.
5258
(b)
Find the difference between 506 and 28.
Notice that the word difference requires you to subtract the second number from the first.
Begin by estimating the answer.
500 - 30 = 470
so the answer should be about 470
Write one number above the other, be careful to line up the columns correctly.
6 - 8 would be negative, so we need to borrow from the next column.
However the next column is 0, so we will borrow from the column to the left of it.
This turns the 0 into a 10.
We can then borrow from the tens column.
So we can now find 16 - 8 for the ones column.
For the second column (tens) we can do 9 - 2 = 7 and finally in the hundreds column, 4 - 0 = 4.
Check that your answer is similar to your estimate.
478
(c)
Without using your calculator, calculate 32.5 - 1.74.
You must show all your working.
Begin by estimating the answer.
32.5 is about 33 and 1.74 is about 2
33 - 2 = 31
So the answer should be about 31
Write one number above the other, be careful to line up the columns correctly, putting the decimal point in a column of its own and filling in the spaces with zeros.
Consider the hundredths column; 0 - 4 is negative, so we need to borrow from the next column.
Consider the tenths column, 4 - 7 would be negative, so we need to borrow from the next column.
We can now do 14 - 7 = 7, and continue subtracting in the other columns.
Remember to put the decimal point in line in the answer with those in the question.
Check that this is similar to your original estimate.
30.76