/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 43 Simplify each expression. $$(1... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 43

Simplify each expression. $$(10-2) 180$$

Short Answer

Expert verified
The simplified expression is 1440.

Step by step solution

01

Solve Inside the Parentheses

Begin by solving the expression inside the parentheses. The expression is \(10 - 2\). Subtract 2 from 10 to get \(8\).
02

Multiply with the Remaining Number

Now, take the result from Step 1, which is \(8\), and multiply it by 180. Calculate \(8 imes 180\).
03

Perform the Multiplication

Multiply \(8\) by \(180\):\[8 imes 180 = 1440\]

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Key Concepts

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

Simplifying Expressions
In mathematics, simplifying expressions involves reducing them to their simplest form. This simplifies calculations and makes it easier to understand and solve problems. Let鈥檚 break down the exercise example:
  • Start with the expression \( (10 - 2) \times 180 \, \).
  • The first step is simplifying inside the parentheses. Subtract 2 from 10, which gives us \( 8 \).
  • This simplifies the expression to \( 8 \times 180 \), which is much easier to handle.
Simplifying expressions often involves performing various operations like addition, subtraction, multiplication, or division to arrive at a more manageable form. By simplifying, we ensure that the expression is as concise and clear as possible before further calculations.
Order of Operations
The order of operations is crucial in ensuring calculations are performed correctly. The standard order is dictated by PEMDAS/BODMAS:
  • P/B: Parentheses/Brackets first
  • E/O: Exponents/Orders (like square roots or powers)
  • MD/DM: Multiplication and Division (from left to right)
  • AS: Addition and Subtraction (from left to right)
Following this order prevents ambiguity and ensures everyone solves problems the same way. In our example, \( (10-2) \times 180 \, \), the parentheses mean subtraction happens first, \( 10-2 = 8 \). Next, multiplication is performed, \( 8 \times 180 = 1440 \). By adhering to these rules, you avoid mistakes that could arise from solving expressions in the wrong sequence.
Basic Arithmetic
Basic arithmetic represents the fundamental operations of math: addition, subtraction, multiplication, and division. Mastering these concepts is crucial for tackling more complex problems. In the given exercise:
  • Subtraction reduces numbers to find a difference, such as \( 10 - 2 = 8 \).
  • Multiplication combines groups of a certain number鈥攁 faster way to add the same number repeatedly. Here, \( 8 \times 180 \) combines eight sets of 180.
These operations form the foundation for all calculations and expressions in mathematics. By understanding each function and how they interact, problem-solving becomes more intuitive and streamlined.

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