1. Subtraction Using Pencil & Paper Methods
Mathematics
Subtraction Using Pencil & Paper Methods

2. The aim of this powerpoint is to teach you pencil & paper methods for subtracting large numbers or decimals.
EITHER
Take notes as you go along, include some examples and write down any questions and your answers (which you can mark as you go along) OR
At the end of the powerpoint, printout the notes called Calc4b

3. Pencil & Paper – Whole Numbers
For small numbers, you should be able to subtract these in your head or jot down things to help you work it out quickly.
For larger numbers you will need to use ‘pencil & paper’ methods which involving writing the numbers in columns (one on top of the other).
When you write them in columns MAKE SURE that the correct column values of each number all match up – i.e. all the units values should be in one straight column.
It might help to write Th H T U etc. out and then write the numbers below these column value headings.

4. Borrowing…
Starting from the smallest column on the RIGHT, take the bottom digit away from the top digit.
If this is not possible (because the top digit is smaller than the bottom digit), you will need to borrow 1 from the next column on the left, which is worth 10 of the column we are in.
Remember borrowing 1 = 10 in the next column on its right but you cannot jump columns – see example 2!

5. Example 1
Lets do: 467 – 123
H T U
Step 3: Subtract the tens next (top – bottom) 
Step 2: Start on the right and move left. Subtract the units first (top – bottom) 
Step 1: Write them in column form 
Step 4: Now subtract the hundreds 
4 6 7
– 1 2 3
4 6 7
– 1 2 3
4 6 7
– 1 2 3
4 6 7
– 1 2 3 3 4 4
There was no need to borrow in this example!
Check using rounded numbers for 467 and 123 in your head:
= or – 100 = 400 both are close to 344!
You can also check by adding back on to see whether you get back to the number you started with… = 467

6. Example 2 Lets do: 4018 – 1436 Step 4: Now the hundreds are 9 – 4 
Step 5: Now the thousands are 3 – 1 
Step 3: subtract the tens but you can’t do 1 – 3! 
You need to borrow 1 from the hundreds but it’s a zero so
the hundreds column needs to borrow 1 from the thousands…
so now we have 11 – 3 in the tens…
Step 2: Start with the units (top – bottom) 
Step 1: Write them in column form 
Th H T U 3 9 1 1 – – – – – 2 5 8 2
Check using rounded numbers for 4018 and 1436 in your head:
= or – 1400 = both are close to 2582!
You can also check by adding back on to see whether you get back to the number you started with… = 4018

7. Example 3 – Last one!!! YOU try: 7465 – 1328 Th H T U
First write them in column form 
– ________
Try to do this yourself on paper before clicking on the next slide.
Remember to check your answer makes sense by doing a mental version in your head using ‘rounded’ numbers!

8. Example 3 – Answer Th H T U 7 4 6 5 – 1 3 2 8 6 1 3 7 5 1
Check by using rounded numbers for 7465 and 1328
in your head: 7500 – 1300 = or – 1000 = 6000
The answer should be about 6000 and it is, it’s 6137!
You could also check by adding back on: = 7465 1 6 1 3 7

9. Practice
Showing your workings, in your books work out the answers to the following calculations.
At the end of each one show what mental calculation you used to check your answer!
1) 87 – 42 =
2) 56 – 34 =
3) 34 – 28 =
4) 238 – 152 =
5) 738 – 351 =
6) 663 – 55 =
7) 426 – 138 =
8) 7268 – 4277 =
9) 6504 – 2255 =
10) 5000 – 2781 =

10. Answers 1) 87 – 42 = 45 (Check: 90 – 40 = 50) 2) 56 – 34 = 22
1) 87 – 42 = 45
(Check: 90 – 40 = 50)
2) 56 – 34 = 22
(Check: = 30)
3) 34 – 28 = 6
(Check: 30 – 30 = 0)
4) 238 – 152 = 86
(Check: 240 – 150 = 90)
5) 738 – 351 = 387
(Check: 740 – 350 = 390)
6) 663 – 55 = 608
(Check: 670 – 60 = 610)
7) 426 – 138 = 288
(Check: 430 – 140 = 290)
8) 7268 – 4277 = 2991
(Check: 7300 – 4300 = 3000)
9) 6504 – 2255 = 4249
(Check: 6500 – 2300 = 4200)
10) 5000 – 2781 = 2219
(Check: 5000 – 2800 = 2200)

11. Alternative Check…
Don’t forget you can check your answers by adding back on to see if you get back to the value you started with!
1) 87 – 42 = (Check: = 87)
2) 56 – 34 = 22 (Check: = 56)
3) 34 – 28 = 6 (Check: = 34)
4) 238 – 152 = 86 (Check: = 238)
5) 738 – 351 = 387 (Check: = 738)
6) 663 – 55 = 608 (Check: = 663)
7) 426 – 138 = 288 (Check: = 426)
8) 7268 – 4277 = (Check: = 7268)
9) 6504 – 2255 = (Check: = 6504)
10) 5000 – 2781 = (Check: = 5000)

12. What next?
If you haven’t made any notes or copied any examples, questions and answers out during this part of the presentation, print out the notes called Calc4b. Read through them and make sure you answer any questions on subtracting integers.
Work through the MyMaths lesson (and then the online homework) called Subtraction Columns found at:
Save and complete the worksheet called IntS-S1.xlsx
Now continue working through the rest of this powerpoint..

13. Pencil & Paper – Decimals
The pencil & paper methods for subtracting decimal numbers is the same as for subtracting whole numbers but you MUST...
…make sure that the correct column values of each number all match up – i.e. all the units values should be in one straight column, the decimal points should be lined up and so on…
…write a decimal point AFTER any whole numbers
…line up all the numbers on the right hand side by writing extra zeros on the end of each number (AFTER the decimal point) where needed.

14. Example Let’s do: 8 – 4.708 U . tth…
First write them in column form 
– _________
Now add decimal points and extra zeros as needed.
At the end, remember to check your answer makes sense by doing a mental version in your head using ‘rounded’ numbers!
Mental Check: I expect the answer to this question to be about 8 – 5 = 3

15. Answer 7 –
Once we have borrowed 1 from the 8, the other columns can then borrow from their previous columns – watch carefully!
The first column we can borrow from is the 8 in the units column BUT 1 in this column is 10 in the next column on its right. We do NOT jump three columns!
First: We need to do 0 – 8
but we can’t so we need to borrow from the next column on the left but this is ALSO zero, as is the next column on it’s left. 9 9 1 1 1
3 . 2 9 2
Now we can do the subtraction and check that the answer is about 3!

16. Practice
Showing your workings, in your books work out the answers to the following calculations.
At the end of each one show what mental calculation you used to check your answer!
1) 8.7 – 3.4 =
2) – 4.1 =
3) 11.5 – 3.26 =
4) 0.07 – =
5) 25 – =

17. Answers
1) 8.7 – 3.4 = 5.3
(Check: 9 – 3 = 6 OR = 8.7)
2) – 4.1 = 8.28
(Check: 12 – 4 = 8 OR = 12.38)
3) 11.5 – 3.26 = 8.24
(Check: 12 – 3 = 9 OR = 11.50)
4) 0.07 – =
(Check: 0.07 – 0.01 = 0.06 OR = 0.070)
5) 25 – =
(Check: 25 – 12 = 13 OR = 25.00)

18. What next?
If you haven’t made any notes or copied any examples, questions and answers out during this half of the presentation, print out the notes called Calc4b. Read through them and make sure you answer all of the questions.
Work through the MyMaths lesson (and then the online homework) called Add and Subtract Decimals found at:
Save and complete the worksheet called DecS-NS1.xlsx
Now move on to the Calc5a-IntroM powerpoint