The question "How to do bracket integers?" is a bit vague. It's likely asking about how to solve math problems that include integers (positive and negative whole numbers) within brackets, often involving multiplication, division, addition, or subtraction, and sometimes even solving for an unknown variable. We'll address this by explaining the order of operations and incorporating how to handle negative numbers as suggested by the video reference.
Here's a breakdown of how to handle bracketed integers:
Understanding the Order of Operations
Before we dive into bracketed integers, let's recap the order of operations, often remembered by the acronym PEMDAS or BODMAS:
- Parentheses / Brackets
- Exponents / Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
This order tells you which operations to perform first. Brackets always come first.
Solving Integer Problems with Brackets
- Simplify inside the brackets: Perform all operations inside the innermost brackets first, following PEMDAS/BODMAS.
- Handle negatives correctly:
- When multiplying or dividing integers with different signs, the result is negative (e.g., -2 * 3 = -6).
- When multiplying or dividing integers with the same sign, the result is positive (e.g., -2 * -3 = 6).
- When adding a negative number this is the same as subtracting the positive form of the number (e.g., 5 + -2 is the same as 5-2 = 3).
- When subtracting a negative number, this is the same as adding its positive form (e.g., 5 - -2 is the same as 5 + 2 =7).
- Work outwards: Once you've simplified inside brackets, move outwards to perform other operations according to PEMDAS.
- Solve for unknowns: If there are unknowns, as the example provided in the video, work to isolate the variable.
Example 1: Simple Brackets
(5 + -2) * -3
- Solve inside the brackets: 5 + -2 = 3
- Multiply: 3 * -3 = -9
Example 2: Nested Brackets
2 [ 10 - ( 4 -2)]
- Solve inside the inner brackets: 4 * -2 = -8
- Rewrite the equation: 2 * [10 - (-8)]
- Simplify: 10 - (-8) = 10 + 8 = 18
- Multiply: 2 * 18 = 36
Example 3: Solving with Unknowns
Based on the YouTube video excerpt, solving "negative 42 is equal to negative 6 times something" can be shown as:
-42 = -6 * x
- Divide both sides by -6: -42 / -6 = x
- Simplify: 7 = x
Key Takeaways
- Always follow the order of operations (PEMDAS/BODMAS).
- Pay close attention to positive and negative signs when operating with integers.
- Work from the innermost brackets outward.
- When solving for an unknown variable, work to isolate the variable using inverse operations.
By following these steps, you can effectively solve problems involving bracketed integers, whether they are simple computations or more complex equations with unknowns.
