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 GCSE course, some examples are
- Adding areas or volumes together in geometry questions
- Working with estimated mean or other averages
- Any problem solving questions in a variety of contexts
- Simply showing that you have the skills to carry out these calculations without a calculator
- 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
- You must be confident with non calculator methods for adding and subtracting large numbers and decimals
How do I add large numbers?
- Write one number above the other in a column, making sure that all the ones, tens, hundreds, and so on, are lined up in the same columns
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- For example, 382 + 943
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- Add the numbers in each column, beginning with the units and working through the columns to the left
- Write each answer as a single digit 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
- For example, in the sum 382 + 943, the sum of the middle column is 12
- Put the 2 below the line and the 1 above the 3
- Repeat this for all columns, until complete
- 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
- For example when adding the 3 and 9 in the sum below
How do I subtract large numbers?
- Write one number above the other in a column, making sure that all the ones, tens, hundreds, and so on, are lined up in the same columns
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- For example, 435 − 183
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- Subtract the bottom number in each column from the top number in the same column, starting with the ones (units)
- If your subtraction produces a negative number “borrow” a ten from the column to the left
- For example in the middle column of the difference between 435 and 183, the difference between 3 and 8 is negative, so borrow a ten from the 4 in the hundreds column
- Repeat this for each of the next columns, until complete
- For example
- If you need to borrow from the next column, but the next column is a zero, you can borrow a ten from the column to the left of this
- This will turn the 0 into a 10, which you can then borrow from
- For example, in the problem 303 - 56
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- the units column cannot borrow from the tens as it is a zero, so the tens must borrow from the hundreds first
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, estimate the answer by rounding to sensible values to check your answer makes sense
Examiner Tip
- Before performing the calculation, estimate the answer
- This will help you spot any errors you might make with place value
- 4321-284 is roughly 4300-300 so the answer should be approximately 4000
- After finding the answer to a subtraction, turn it into an addition to check your answer
- If you find 303-56=247, then 247+56 should be 303
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