Method A - Decomposition Method

Test yourself

Decomposition Method: 753 − 491

Step 1

Write out the subtrahend under the minuend.
Line up the digits so that the hundreds, tens and ones digits of each number are in the same columns.

Step 2

Start at the right. Subtract 1 from 3.
Write the difference at the bottom, in the ones column.

Step 3

Now we want to ‘subtract 9 from 5'. Note that because we’re in the tens column now, we’re actually subtracting 90 from 50.
To do this without using negatives, we exchange the 700 (i.e. we see 700 as 600 + 100). We do this by crossing out the 7 in the hundreds column and replacing it with a 6.

Step 4

Then we write a small 1 to the left of the 5 in the tens column, giving us 15 tens.
What we’ve done is add one of our hundreds to the 50, meaning we can now to subtract 90 from 150.

Step 5

Now, we subtract 9 from 15 which gives a difference of 6 for the tens column (i.e. 150 − 90= 60).

Step 6

Finally, we subtract the digits in the hundreds column.
We’ve used one of our hundreds already, so we have 6 left. We do 6 − 4 and write a 2 at the bottom. (This actually means 600 − 400 = 200.)

Breaking down the maths

What we effectively did here was rewrite 753 as 600 + 150 + 3.

1Course Overview

1.1Course Structure & Commonly Asked Questions

1.1.1Introduction to the Course & Common Questions

2Subtraction: KS2/3

2.1Subtraction Methods

2.1.1Method A - Decomposition Method

2.1.2Method B - Equal Addition Method

2.1.3Method C - Expanded Form Method

2.1.4Method D - Partitioning Method

2.1.5Method E - Counting-Up Method

2.1.6Method F - Constant Difference Method

2.1.7Method G - Partial Differences Method

2.1.8Method H - Complementary Method

2.1.9Method I - Nines Complement Method

3Expanding Double Brackets: KS3/4

3.1Expansion Methods

3.1.1Method A - Grid Method

3.1.2Method B - Each by Each

3.1.3Method C - Distributive Law

3.1.4Method D - Inspection

3.1.5Method E - Column Method

3.1.6Method F - Vertical & Crosswise

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