Problem 43 Simplify. See Examples 1 through... [FREE SOLUTION]

Chapter 2: Problem 43

Simplify. See Examples 1 through $10$. $$ (-12-20) \div 16-25 $$

Short Answer

Expert verified

The simplified expression is $-27$.

Step by step solution

Simplify the Expression inside Parentheses

The expression inside the parentheses is $(-12 - 20)$. Start by simplifying this: $-12 - 20 = -32$. So now the expression becomes $(-32) \div 16 - 25$.

Perform the Division

Next, divide $-32$ by $16$. This gives:$-32 \div 16 = -2$. Now the expression is $-2 - 25$.

Perform the Subtraction

Subtract $25$ from $-2$: $-2 - 25 = -27$. This is the final simplified expression.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Basic Arithmetic Operations

Understanding basic arithmetic operations is crucial for simplifying expressions like the one in this exercise. Arithmetic involves four basic operations:

Addition: Combining two numbers to get a sum.
Subtraction: Taking one number away from another to find the difference.
Multiplication: Increasing a number by repeating it a certain number of times.
Division: Splitting a number into equal parts.

Example:
In our original expression, we start with subtraction inside the parentheses. Subtracting 20 from -12 yields -32.
Then, we proceed with division. Dividing -32 by 16 results in -2.
Lastly, subtracting 25 from -2 gives us -27. These operations help reduce complex problems into simpler steps.

Order of Operations

When solving expressions, the order of operations is key to achieving the correct answer. This ruleset tells us which mathematical operations to perform first. Remember the acronym PEMDAS to help with this:

P: Parentheses first.
E: Exponents (i.e., powers and roots, etc.).
M/D: Multiplication and Division (left to right).
A/S: Addition and Subtraction (left to right).

Example:
In our exercise, we first simplify the contents of the parentheses, (-12 - 20), resulting in -32.
Next, we perform division, dividing -32 by 16 to get -2.
Finally, we finish with subtraction, calculating -2 - 25 to reach the simplified expression of -27.

Negative Numbers

Dealing with negative numbers in arithmetic can initially be confusing, but understanding some basic principles can help. Negative numbers represent values less than zero, and they follow certain rules during arithmetic operations:

When subtracting negative numbers, think of it as adding the opposite.
The product or quotient of two negative numbers is positive.
The product or quotient of a positive and a negative number is negative.

Example:
In the problem, we first deal with the negative numbers: -12 and -20 being subtracted. Instead of getting larger, our negative result grows, reaching -32.
Then, dividing -32 (a negative number) by 16 (a positive number) gives us -2. Finally, subtracting 25 (a positive number) from -2 results further in the negative direction, yielding -27. Understanding these rules helps simplify and properly evaluate expressions with negative numbers.

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91影视

Simplify. See Examples 1 through \(10\). $$ (-12-20) \div 16-25 $$

Short Answer

Step by step solution

Simplify the Expression inside Parentheses

Perform the Division

Perform the Subtraction

Key Concepts

Basic Arithmetic Operations

Order of Operations

Negative Numbers

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