Written Strategies

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We can add and subtract using mental and written strategies. We can add two, three or four digit numbers using a range of strategies.
In this chapter we are going to look at some written methods for adding two, three and four digit numbers.

Firstly let’s look at adding the most significant digits first.

96

+ 35

90
30
11
131

Let’s look at another example adding the most significant digits first.

789

+ 663

700
600
140
12
1452

We can use the partitioning method for addition and subtraction. Let’s have a look at some examples.

879 + 456 =
We need to partition the numbers by using expanded notation.
800 + 70 + 9
400 + 50 + 6

Now we can add these numbers easily.
800 + 400 = 1200
70 + 50 = 120
9 + 6 = 15

1200 + 120 + 15 = 1335

Let’s use the partitioning method to subtract these numbers.

8987 – 2341 =
We need to partition the numbers first by using expanded notation.
8000 + 900 + 80 + 7
2000 + 300 + 40 + 1

Now we can subtract these numbers easily.
8000 – 2000 = 6000
900 – 300 = 600
80 – 40 = 40
7 – 1 = 6

6000 + 600 + 40 + 6 = 6646

Now let’s look at the Standard Written Method for addition and subtraction.

 H T U We start by adding the units column first: 1 + 3 = 4We then add the tens: 40 + 20 = 60 we put 6 tens in the tens columnLastly we add the hundreds: 700 + 0 = 700 we put 7 hundreds in the hundreds column. 7 4 1 + 2 3 7 6 4

 T H T U We add the units first: 3 + 4 = 7We then add the tens: 10 + 90 = 100 so we put 0 in the tens column and carry the 1 hundred to the hundreds column.We then add the hundreds: 200 + 600 + 100 = 900Lastly we add the thousands: 3000 + 0 = 3000 3 2 1 3 + 6 9 4 3 9 0 7

 H T U We start by subtracting the units column first: 7 – 2 = 5We then subtract the tens: 30 - 20 = 10 we put 1 ten in the tens columnLastly we subtract the hundreds: 300 – 100 = 200 we put 2 hundreds in the hundreds column. 3 3 7 - 1 2 2 2 1 5

Now let us have a look at the decomposition method or trading method. We use this method for subtraction only. In this method we borrow a multiple of 10 from the digit to the left when the top number is smaller than the bottom number.

 T H T U We subtract the units first: 2 – 1 = 1We then subtract the tens: 70 – 80 we can’t do because 70 is smaller than 80. We need to borrow from the hundreds column. We bring over 100 from the hundreds column (10 tens are 100) Now 10 tens + 7 tens – 8 tens is the same as 170 – 80 = 90 so we put 9 in the tens column.Because we borrowed one hundred we need to strike out the 4 in the hundreds column and leave 3 hundreds. 300 – 200 = 100 so we put 1 in the hundreds column.Lastly we subtract the thousands column. 3000 – 1000 = 2000 3 10 3 4 7 2 - 1 2 8 1 2 1 9 1

The Equal addends method is another method for completing a subtraction problem.

 Step 1: We cannot subtract 4 from 3. We add ten ones to make 13 and add one to the 7 at the bottom of the next column. 13 subtract 4 equals 9.Step 2: We cannot subtract 7 (+1) from 6. We add ten to make 16 and add one to the 3 at the bottom of the next column. 16 subtract 8 (7+1) equals 8.Step 3: 7 subtract 4 (3+1) equals 3.

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