Source: https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-1-method-a-decomposition-method

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# Method A - Decomposition Method

CPD: A Compendium of Mathematical Methods (By Jo Morgan), topic 2.1.1

## Decomposition Method: 753 − 491

### Step 1

![Step 1](https://image-v2.cdn.app.senecalearning.com/2020-04/914f3793-4662-4de9-a705-d9b522fcc103/Method%20A%20-%20Example%201.png)

- 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

![Step 2](https://image-v2.cdn.app.senecalearning.com/2020-04/a79d7bfb-7b1f-49fa-b14f-7a2dc1fcc7df/Method%20A%20-%20Example%201%20(1).png)

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

### Step 3

![Step 3](https://image-v2.cdn.app.senecalearning.com/2020-04/a5abfbca-2d44-4d16-a9d0-f7f919adfaf4/Method%20A%20-%20Example%201%20(2).png)

- 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

![Step 4](https://image-v2.cdn.app.senecalearning.com/2020-04/bed95ed1-be8f-4488-bc6d-bd9010d6fa9d/Method%20A%20-%20Example%201%20(3).png)

- 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

![Step 5](https://image-v2.cdn.app.senecalearning.com/2020-04/d4d384c4-7d96-47e9-a50b-e82abc920e1b/Method%20A%20-%20Example%201%20(4).png)

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

### Step 6

![Step 6](https://image-v2.cdn.app.senecalearning.com/2020-04/88450277-736b-4184-81db-365b0fa9acf7/Method%20A%20-%20Example%201%20(5).png)

- 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

![Breaking down the maths](https://image-v2.cdn.app.senecalearning.com/2020-04/0238b64f-0003-4893-a318-b5ec61c5db24/Method%20A%20-%20Example%201%20(5).png)

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

## Test yourself on Method A - Decomposition Method

- Which digit do students need to exchange (i.e. cross out and replace) in the top line of this subtraction?
- Which digit do students add a small 1 to, when using the decomposition method to perform this calculation?
- What calculation can a student do to immediately check that 9610 is the correct answer to 9875 − 265?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/d0e67498-99c8-47d2-ada7-cd629abed70c/section/4c5f120f-eeaf-4418-b9ba-3a4c6839523c/session)

- Previous topic: [1.1.1 Introduction to the Course & Common Questions](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/1-1-1-introduction-to-the-course-and-common-questions.md)
- Next topic: [2.1.2 Method B - Equal Addition Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-2-method-b-equal-addition-method.md)

## CPD: A Compendium of Mathematical Methods (By Jo Morgan) contents

### 1 Course Overview
- 1.1 Course Structure & Commonly Asked Questions
  - [1.1.1 Introduction to the Course & Common Questions](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/1-1-1-introduction-to-the-course-and-common-questions.md)

### 2 Subtraction: KS2/3
- 2.1 Subtraction Methods
  - [2.1.1 Method A - Decomposition Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-1-method-a-decomposition-method.md)
  - [2.1.2 Method B - Equal Addition Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-2-method-b-equal-addition-method.md)
  - [2.1.3 Method C - Expanded Form Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-3-method-c-expanded-form-method.md)
  - [2.1.4 Method D - Partitioning Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-4-method-d-partitioning-method.md)
  - [2.1.5 Method E - Counting-Up Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-5-method-e-counting-up-method.md)
  - [2.1.6 Method F - Constant Difference Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-6-method-f-constant-difference-method.md)
  - [2.1.7 Method G - Partial Differences Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-7-method-g-partial-differences-method.md)
  - [2.1.8 Method H - Complementary Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-8-method-h-complementary-method.md)
  - [2.1.9 Method I - Nines Complement Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/2-1-9-method-i-nines-complement-method.md)

### 3 Expanding Double Brackets: KS3/4
- 3.1 Expansion Methods
  - [3.1.1 Method A - Grid Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/3-1-1-method-a-grid-method.md)
  - [3.1.2 Method B - Each by Each](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/3-1-2-method-b-each-by-each.md)
  - [3.1.3 Method C - Distributive Law](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/3-1-3-method-c-distributive-law.md)
  - [3.1.4 Method D - Inspection](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/3-1-4-method-d-inspection.md)
  - [3.1.5 Method E - Column Method](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/3-1-5-method-e-column-method.md)
  - [3.1.6 Method F - Vertical & Crosswise](https://senecalearning.com/en-gb/revision-notes/teacher-cpd/cpd-a-compendium-of-mathematical-methods-seneca-certified/3-1-6-method-f-vertical-and-crosswise.md)