How do you solve brackets with integers?

Solving brackets with integers involves following the order of operations, often remembered by the acronym PEMDAS (or BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). The key is to simplify expressions inside the brackets before applying other operations.

Here’s a breakdown of how to approach it:

Order of Operations

1. Brackets/Parentheses First:

• Always start by simplifying the expressions within the brackets first. This may involve other operations within the brackets itself. For instance, if you have 2 * (3 + 4), you must calculate 3 + 4 first, resulting in 2 * 7.

2. Multiplication with Integers:

• Once brackets are simplified, multiply any numbers outside the bracket with the simplified contents of the bracket.

3. Examples using the information from reference

• The YouTube video "Grade 6 Math #9.10b, Solving integer operations" illustrates solving equations with integers inside and outside the brackets.
• Example:
  • Let's say you have -6 * x = -42 where the variable x is what you're trying to find.
  • In the video, the presenter explains that -6 multiplied by some number x would equal -42. To isolate x, you would divide both sides of the equation by -6. This means -42 / -6 = x, which results in x = 7.

Practical Steps

1. Identify Brackets:

   • Look for parentheses ( ), square brackets [ ], or curly braces { }.

2. Solve Inside Out:

   • If there are nested brackets, begin with the innermost set and work your way outwards.

3. Apply PEMDAS/BODMAS:

   • Within the brackets, follow the order of operations:
     • Exponents/Orders: Simplify any exponents or roots inside the brackets.
     • Multiplication and Division: Work from left to right for any multiplication or division.
     • Addition and Subtraction: Work from left to right for any addition or subtraction.

4. Apply Outside Operations:

   • Once the bracket contents are simplified, continue the operations outside the brackets again following the order of operations.

Examples

Equation	Step 1: Simplify Brackets	Step 2: Apply Multiplication	Step 3: Final Answer
2 * (3 + 4)	2 * (7)	2 * 7	14
(10 - 4) * 3	(6) * 3	6 * 3	18
5 + (2 * 6 - 10)	5 + (12 - 10)	5 + (2)	7
3 * [1 + (2 * 2)]	3 * [1 + (4)]	3 * [5]	15
( -2 + -3 ) * 5	(-5) * 5	-5 * 5	-25

Key Points

• Integer Rules: Remember the rules for integer operations, especially when multiplying or dividing positive and negative numbers.
• Distributive Property: When you have a number multiplied by a bracket (e.g. 2(x+1)), remember to distribute: 2x + 2.
• Careful Calculation: Take your time, and double-check each step to avoid errors.

By consistently applying these rules, you can confidently solve bracketed expressions involving integers.