Simplification and Order of Operations
beginner24 min read
The VBODMAS order and how to apply it without slips, handling signs and nested brackets, keeping fractions and decimals under control, and the four algebraic identities that turn an ugly product into a two-step mental calculation.
What you will be able to do
- Apply the VBODMAS order, resolving 'of', division and multiplication correctly.
- Work through nested brackets and sign changes without error.
- Simplify an expression that mixes fractions and decimals.
- Use (a+b)², (a−b)², a²−b² and (a+b)(a−b) to speed up a product.
What is inside this lesson
- 1The VBODMAS order
- 2Signs and nested brackets
- 3Fractions and decimals under time pressure
- 4Four identities that speed up products
- 5Worked example: order and brackets
- 6Worked example: a fraction chain
- 7Worked example: identities for a product
- 8Common mistakes
- 9Quick revision
- 10Practice
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The VBODMAS order
Work an expression in this order:
- V — Vinculum: a bar over part of an expression, treated as a bracket. Resolve what is under it first.
- B — Brackets: innermost first — round, then curly, then square.
- O — Of: "3/5 of 40" means multiply, and it is done before ordinary division and multiplication.
- D and M — Division and Multiplication: together, left to right. Neither outranks the other.
- A and S — Addition and Subtraction: together, left to right.
The two points people get wrong: division and multiplication are equal (go left to right), and "of" is settled before them.
The lesson itself is for members
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