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Chapter 2: Problem 8

For Exercises \(1-74,\) simplify. $$-30 \div 2 \cdot(-3)+21$$

Short Answer

Expert verified
Question: Simplify the given expression: $$-30 \div 2 \cdot(-3) + 21$$ Answer: 66

Step by step solution

01

Evaluate division and multiplication operations from left to right.

According to the order of operations (PEMDAS), the first step is to perform the division and multiplication: $$-30 \div 2 \cdot(-3) = (-15) \cdot(-3)$$
02

Complete the multiplication operation.

Now we can multiply -15 and -3, which results in a positive value: $$(-15) \cdot(-3)=45$$
03

Add the result of the multiplication to 21.

Lastly, we will complete the addition operation: $$45 + 21 = 66$$

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Key Concepts

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

Simplifying Expressions
When working with expressions like \[-30 \div 2 \cdot (-3) + 21\], it's essential to follow certain rules to simplify them properly. Simplifying involves reducing expressions to their simplest form, ensuring they are easy to understand and work with.

To simplify:
  • Identify operations within the expression.
  • Follow the set order of operations, commonly known by the acronym PEMDAS.
  • PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition, and Subtraction (from left to right).
  • Ensure accurate calculations by performing each operation in its specified order.
By following these steps, you'll prevent errors and make complex expressions manageable.
Division and Multiplication
Within the context of the order of operations, division and multiplication rank equally. However,
these operations are completed from left to right in the sequence they appear.

In our example, the division \(-30 \div 2\) comes before multiplication, so it is done first:
  • \(-30 \div 2 = -15\).
  • Next, perform the multiplication: \(-15 \cdot (-3)\).
  • This results in a positive outcome: \(45\).
Remember to always process operations in the order they appear left to right, not by preference of one over the other.
Integer Operations
The operation of integers follows specific rules, especially concerning positive and negative numbers.
Multiplying or dividing negative numbers requires a basic understanding of these rules:
  • When multiplying or dividing two negative numbers, the result is positive.
  • Conversely, when one number is positive and the other negative, the result is negative.
In our example, dividing a negative by a positive \((-30 \div 2)\) gives \(-15\). When you multiply two negatives, as in \(-15 \cdot (-3)\), you get a positive \(45\). Thus, knowing integer operation rules simplifies solving these expressions effectively. This allows for precise calculation and understanding of results by providing consistency and clear guidance.

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Most popular questions from this chapter

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