/*! 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 13 Simplify. $$[-5.53 \div(0.68+0... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 13

Simplify. $$[-5.53 \div(0.68+0.9)]+0.7 \sqrt{2.25}$$

Short Answer

Expert verified
Please follow the steps below to simplify the given expression: Step 1: Perform addition inside the parentheses (0.68 + 0.9) = 1.58 Step 2: Perform the division (-5.53 梅 1.58) 鈮� -3.5 Step 3: Calculate the square root 鈭�2.25 = 1.5 Step 4: Perform the multiplication 0.7 * 1.5 = 1.05 Step 5: Perform the final addition -3.5 + 1.05 = -2.45 The simplified answer is -2.45.

Step by step solution

01

Perform addition inside the parentheses

Firstly, we will calculate the sum inside the parentheses: $$(0.68 + 0.9) = 1.58$$ Now, the expression becomes: $$[-5.53 \div 1.58] + 0.7 \sqrt{2.25}$$
02

Perform the division

Next, we will calculate the division: $$\frac{-5.53}{1.58} \approx -3.5$$ Now, the expression becomes: $$[-3.5] + 0.7 \sqrt{2.25}$$
03

Calculate the square root

Now, let's find the square root of 2.25: $$\sqrt{2.25} = 1.5$$ Now, the expression becomes: $$[-3.5] + 0.7(1.5)$$
04

Perform the multiplication

Next, we will calculate the multiplication: $$0.7(1.5) = 1.05$$ Now, the expression becomes: $$[-3.5] + 1.05$$
05

Perform the final addition

Finally, let's find the sum of the two numbers: $$-3.5 + 1.05 = -2.45$$ The simplified answer is: $$-2.45$$

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Key Concepts

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

Simplification
Simplification in algebra involves condensing an expression into its simplest form. Our goal is to make the expression easier to understand and work with. We achieve this by performing arithmetic operations such as addition, subtraction, multiplication, and division, as well as reducing fractions or combining like terms. In this exercise, we take a complex expression \([-5.53 \div (0.68 + 0.9)] + 0.7 \sqrt{2.25}\) and systematically simplify it by following the order of operations. Breaking down these steps helps to clarify each part of the process, leading us to the final simple result.
Order of Operations
The order of operations is a set of rules that dictates the sequence in which operations should be performed to correctly solve an expression. It鈥檚 known by the acronym PEMDAS, which stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In our simplification task, we start with the operation inside the parentheses \((0.68 + 0.9)\) and then move on to division, square root, multiplication, and finally addition. Each step respects this specific order to ensure the expression is evaluated correctly.
Square Roots
Square roots are the numbers that, when multiplied by themselves, give the original number. Understanding square roots is essential to simplifying expressions that include them. In the expression provided, we encounter \(\sqrt{2.25}\). To find this, we determine which number, when multiplied by itself, results in 2.25. As illustrated in the solution, \(\sqrt{2.25} = 1.5\). Grasping this concept helps in performing calculations that involve square roots within larger algebraic contexts.
Division
In algebra, division is a fundamental operation used to divide one number by another. Proper handling of division in expressions is crucial for accurate simplification. In the previous example, the operation \(-5.53 \div 1.58\) was computed. By performing this division, we transform the expression to include simpler components that can be more easily manipulated. The division here results in approximately \(-3.5\), showing how larger numbers can be broken down into smaller, more manageable parts in algebraic simplification.
Addition
Addition combines two or more numbers to get a total sum. It is often one of the final steps in the simplification of expressions. In our exercise, the addition appears at the very end, where we need to sum \(-3.5 + 1.05\). This process brings together results from previous operations (like division and square root) to reach the simplest form (-2.45). Understanding and executing addition is pivotal as it concludes many algebraic simplifications by merging separate parts of the expression into a single, simplified result.

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