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Chapter 10: Problem 41

Simplify each expression. $$(5-2) 180$$

Short Answer

Expert verified
The simplified expression is 540.

Step by step solution

01

Understand the Expression

The expression given is \[(5 - 2) imes 180 \]It involves subtraction inside the parentheses and multiplication outside.
02

Perform the Subtraction Inside the Parentheses

Calculate the expression inside the parentheses first. Subtract 2 from 5:\[5 - 2 = 3\]
03

Multiply the Result by 180

Now multiply the result from the subtraction by 180:\[3 imes 180 = 540\]

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Key Concepts

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

Order of Operations
When faced with mathematical problems, especially with more than one operation, it's crucial to follow the **Order of Operations**. This order is often remembered by the acronym PEMDAS:
  • Parentheses (P)
  • Exponents (E)
  • Multiplication and Division (MD) from left to right
  • Addition and Subtraction (AS) from left to right
In the exercise, \[(5 - 2) \times 180\]we start by looking inside the parentheses. Parentheses are at the top of the order, indicating that whatever is inside should be calculated first. Once that's solved, you can move on to multiplication or any other operation that follows. By sticking with this order, you'll always be sure you are simplifying expressions accurately.
Subtraction
Subtraction, quite simply, is the operation of taking one number away from another. It's essential to perform this step correctly as it sets the stage for any remaining operations. Here, inside the expression \(5 - 2\), subtraction happens first because it is within parentheses, positioning it at the forefront of our calculations.
Let's take it step by step:
  • Identify what operation is inside the parentheses. Here it is subtraction.
  • Subtract the smaller number from the larger: \[5 - 2 = 3\]
Notice that subtraction can change the number significantly by decreasing its value. Always double-check your subtraction to make sure you got this critical step correct.
Multiplication
After handling any subtraction or addition inside parentheses, the next step in simplifying an expression often involves **multiplication**. Multiplication is essentially repeated addition. In the exercise, after obtaining the value from the subtraction operation \(5-2\), we proceed to multiply the result by 180.
Here's how multiplication fits as the next step:
  • Take the result from the subtraction, which is 3.
  • Multiply it by 180: \[3 \times 180 = 540\]
Multiplication tends to increase the value (unless one of the numbers is zero). In our expression, it takes the simple result from our subtraction and scales it, producing a final simplified version of the entire expression.

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Most popular questions from this chapter

Make a drawing of each quadrilateral. Then classify each quadrilateral using the name that best describes it. In quadrilateral \(\mathrm{CDEF}, \overline{\mathrm{CD}}\) and \(\overline{E F}\) are parallel, and \(\overline{C F}\) and \(\overline{D E}\) are parallel. Angle \(C\) is not congruent to \(\angle D\).

Make a drawing of each quadrilateral. Then classify each quadrilateral using the name that best describes it. In quadrilateral \(J K L M, m \angle J=90^{\circ}, m \angle K=50^{\circ}, m \angle L=90^{\circ},\) and \(m \angle M=130^{\circ}\)

Use a protractor to draw an angle having each measurement. (pp. \(757-758\) ) $$65^{\circ}$$

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Graph each point on a coordinate plane. $$J(-1,3)$$
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