Subtraction
Method 1 - Counting Backwards Using a Number Line
A number line can be used to take one number away from another.
e.g. 34 - 6
Step 1: Start by marking the number 34 on the number line:
Step 2: Count back to the nearest ten, which in this case is 30. This takes 4 steps.
Step 3: To count back 6, we need to count back a further 2 steps.
We have now counted back 6 steps, which shows the answer as 28.
Method 2 - Counting Forward Using a Number Line
A number line can also be used to subtract by counting forward from the smaller number to the larger number.
e.g. 34 - 26
Step 1: Start by marking the numbers 0, 34 and 26 on the number line:
Method 2 - Counting Forward Using a Number Line
A number line can also be used to subtract by counting forward from the smaller number to the larger number.
e.g. 34 - 26
Step 1: Start by marking the numbers 0, 34 and 26 on the number line:
Step 2: Count forward to the nearest ten, which in this case is 30. This takes 4 steps.
Step 3: We need to count how many more steps we need to take to reach 34. We need to take 4 more steps.
Step 4: Add up the total number of jumps:
From 26 to 30 = 4 jumps
From 30 to 34 = 4 jumps
Total number of jumps between 26 and 34 = 8
Method 3 - Subtraction of Large Numbers Using a Number Line
e.g. 878 - 49
Step 1: Start by marking the numbers 0, 49 and 878 on the number line:
From 26 to 30 = 4 jumps
From 30 to 34 = 4 jumps
Total number of jumps between 26 and 34 = 8
Method 3 - Subtraction of Large Numbers Using a Number Line
e.g. 878 - 49
Step 1: Start by marking the numbers 0, 49 and 878 on the number line:
Step 2: Start with the largest number when adding to find the total, eg:
Move to the next largest number:
Move to the next largest number, and so on until all jumps have been made between 49 and 878.
Step 3: To find the difference between 878 and 49, add up the number of jumps:
Total number of jumps = 700 + 70 + 50 + 8 + 1
= 829
Method 4 - Decomposition
In subtraction using decomposition, each number is split up into hundreds, tens and units, and each part of one number is taken away from each part of the other.
e.g. 878 - 49
Step 1: Partition the numbers into hundreds, tens and units:
H T U
878 = 800 70 8 49 = 0 40 9
Step 2: Subtract the units: 8 - 9
As we cannot subtract 9 from 8, we borrow one ten from the tens column and add it onto the 8 in the
units column to give us 18. As we have borrowed one ten, we must also reduce the tens column
by ten.
Subtracting the units now becomes: 18 - 9
H T U
60 18
800 70 8
0 40 9 -
9
Step 3: Subtract the tens: 60 - 40
H T U
60 18
800 70 8
0 40 9 -
20 9
Step 4: Subtract the hundreds: 800 - 0
H T U
60 18
800 70 8
0 40 9 -
800 20 9
Step 5: Recombine the numbers in the hundreds, tens and units columns to give the answer:
800 + 20 + 9 = 829
This method can be shortened, using vertical subtraction and carrying tens, hundreds etc where appropriate.
e.g. 878 - 49
Step 1: Subtract the units: 8 - 9
Again, as we cannot subtract 9 from 8, we must borrow a ten from the tens column, to give 18 - 9.
6 1
8 7 8
4 9 -
9
Step 2: Subtract the tens: 6 - 4
6 1
8 7 8
4 9 -
2 9
Step 3: Subtract the hundreds: 8 - 0
6 1
8 7 8
4 9 -
8 2 9
Total number of jumps = 700 + 70 + 50 + 8 + 1
= 829
Method 4 - Decomposition
In subtraction using decomposition, each number is split up into hundreds, tens and units, and each part of one number is taken away from each part of the other.
e.g. 878 - 49
Step 1: Partition the numbers into hundreds, tens and units:
H T U
878 = 800 70 8 49 = 0 40 9
Step 2: Subtract the units: 8 - 9
As we cannot subtract 9 from 8, we borrow one ten from the tens column and add it onto the 8 in the
units column to give us 18. As we have borrowed one ten, we must also reduce the tens column
by ten.
Subtracting the units now becomes: 18 - 9
H T U
60 18
800 70 8
0 40 9 -
9
Step 3: Subtract the tens: 60 - 40
H T U
60 18
800 70 8
0 40 9 -
20 9
Step 4: Subtract the hundreds: 800 - 0
H T U
60 18
800 70 8
0 40 9 -
800 20 9
Step 5: Recombine the numbers in the hundreds, tens and units columns to give the answer:
800 + 20 + 9 = 829
This method can be shortened, using vertical subtraction and carrying tens, hundreds etc where appropriate.
e.g. 878 - 49
Step 1: Subtract the units: 8 - 9
Again, as we cannot subtract 9 from 8, we must borrow a ten from the tens column, to give 18 - 9.
6 1
8 7 8
4 9 -
9
Step 2: Subtract the tens: 6 - 4
6 1
8 7 8
4 9 -
2 9
Step 3: Subtract the hundreds: 8 - 0
6 1
8 7 8
4 9 -
8 2 9