Source: 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

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# Method I - Nines Complement Method

CPD: A Compendium of Mathematical Methods (By Jo Morgan), topic 2.1.9

## Nines Complement Method: 753 − 491

### Step 1

![Step 1](https://image-v2.cdn.app.senecalearning.com/2020-04/2ab37d71-cdcb-438b-b038-03a1d6bed172/Copy%20of%20Method%20H%20-%20Example%201.png)

- Instead of subtracting from 753, we start by subtracting 491 from 999. It is easy to subtract any number from 999.

### Step 2

![Step 2](https://image-v2.cdn.app.senecalearning.com/2020-04/01a03fa7-5055-45e0-b970-a5fa5e2140db/Method%20I%20-%20Example%201.png)

- 508 is the ‘9s complement’ of 491. 
- Now add 508 to 753.

### Step 3

![Step 3](https://image-v2.cdn.app.senecalearning.com/2020-04/a74fe405-f116-411a-a79a-22b5a5a2e054/Method%20I%20-%20Example%201-Answer.png)

- Subtract 1000 from the total, then add 1. 
- This is equivalent to subtracting 999.

## Test yourself on Method I - Nines Complement Method

- Which student has done the first step of the calculation 792,836 − 284,756 correctly?
- Which student has done the final step of the calculation 792,836 − 284,756 correctly?

[Practise this topic for free](https://app.senecalearning.com/classroom/course/d0e67498-99c8-47d2-ada7-cd629abed70c/section/e64a86b9-0597-45a1-be4c-c14e7a3b131d/session)

- Previous topic: [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)
- Next topic: [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)

## 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)