Problem 36 - Algebra 1

Question

Evaluate the expression. $$ 2-(-4)-7 $$

Step-by-Step Solution

Answer

Therefore, the evaluation of the expression \(2-(-4)-7\) is -1.

Step 1: Identify the Negative Operation

In the expression, \[2-(-4)-7\], there is a term, -(-4) which means we are subtracting a negative number. From the rules of mathematics, we know that 'subtracting a negative' is the same as 'adding a positive'. So, -(-4) is equal to +4.

Step 2: Substitute and Simplify

Replace -(-4) with +4 in the expression. So the expression becomes \[2+4-7\]. Now follow the rule of operations (also known as BIDMAS/BODMAS/PEDMAS where the operations addition and subtraction must be carried out from left to right).

Step 3: Perform the Operations

Perform the addition operation first: 2+4 becomes 6. Then, substitute it in the expression. The expression now is \[6-7\]. Now, subtract 7 from 6 which yields -1.

Key Concepts

Negative Numbers

Understanding negative numbers is crucial not only for mathematics but also in real-life scenarios. Negative numbers are numbers less than zero. They are usually used to represent a deficit or a loss.
For instance:

• Temperature: -5°C (indicating 5 degrees below zero)
• Finance: -$20 (indicating a debt of 20 dollars)
• Elevation: -10 meters (indicating 10 meters below sea level)

When dealing with mathematical operations involving negative numbers, it’s important to remember:

• Subtracting a negative number is the same as adding its positive counterpart. For example, \(-(-4) = +4\).
• When two negative numbers are multiplied or divided, the result is positive. \(-3 \times -2 = 6\).
• Adding two negative numbers keeps the result negative. \(-3 + -2 = -5\).

Order of Operations

Order of operations dictates the sequence in which operations should be carried out in mathematical expressions. This ensures that everyone reads and calculates expressions in the same way. You might have heard of acronyms like BIDMAS, BODMAS, or PEDMAS used to remember the order:

• B/P: Brackets (Parentheses)
• I/O: Indices (Orders - powers and roots, etc.)
• DM: Division and Multiplication (from left to right)
• AS: Addition and Subtraction (from left to right)

In simpler terms, when you see an expression like \((2-(-4)-7)\), handle any operations inside brackets first, then move from left to right managing division and multiplication before tackling addition and subtraction. By following this rule, you'll reach the right answer each time.

Addition and Subtraction

Addition and subtraction are fundamental arithmetic operations but require careful consideration, especially when negative numbers are involved. In simple terms:

• Addition combines values. For instance, \(2 + 4\) combines to make 6.
• Subtraction removes or reduces a value from another, like \(6 - 7\) gives \(-1\).
• Remember, subtracting a negative is like adding a positive. So in \(2 - (-4)\), you get \(2 + 4 = 6\).

When processing expressions:

• Look left to right, performing addition and subtraction as they appear.
• Don't forget the rules of negative numbers, they can easily flip operations.

Such arithmetic operations are part of everyday calculations, whether in budgeting your finances or calculating distance, making their mastery essential.