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Chapter 5: Problem 75

Simplify the given expression. \(1 .2+|8.74-16.5|\)

Short Answer

Expert verified
8.96

Step by step solution

01

Calculate the Absolute Value

First, we need to calculate the value inside the absolute value symbol: \( 8.74 - 16.5 \). Subtract 16.5 from 8.74: \( 8.74 - 16.5 = -7.76 \).The absolute value of \( -7.76 \) is \( 7.76 \).
02

Perform Addition

Now, add the result from Step 1 to 1.2: \(1.2 + 7.76 = 8.96 \).

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Key Concepts

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

Simplifying Mathematical Expressions
When you come across an expression that involves multiple operations, the goal is to simplify it. Simplification means transforming the expression into its simplest form.
This process often involves following a certain sequence to solve operations, which makes it easier to understand and interpret the expression's value.
For example, in the expression \(1.2 + |8.74 - 16.5|\), you must first handle the operations inside the absolute value before proceeding to addition.
By simplifying, we make complex problems easier to deal with and often more aesthetically pleasing, removing unnecessary components, which provides clarity.
  • Simplification often helps in comparing and evaluating expressions.
  • It assists in identifying properties and patterns hidden in more complex formulations.
Understanding Addition in Expressions
Addition is one of the basic operations in mathematics. It's used to combine numbers to get a sum. In an algebraic expression like our problem, addition is crucial in reaching the correct answer.
Once the expression inside the absolute value is simplified, addition is straightforward.
For example, in the problem, after finding that the absolute value is 7.76, you then add it to 1.2, which gives 8.96.
Understanding addition involves:
  • Knowing how to align numbers correctly when performing operations manually.
  • Being careful with decimals to maintain accuracy.
In some expressions, addition is not just adding singular numbers but might require combining like terms, especially in polynomials.
Expressions and Absolute Value
Expressions can include numbers, variables, and operators that represent a value. In math, handling expressions often involves solving or simplifying them.
An absolute value, denoted by vertical bars \,|\, is a special expression that always yields a non-negative result.
It signifies the distance a number is from zero, without considering direction.
For instance, the absolute value of \(-7.76\) in the expression \( |8.74 - 16.5| \) results in \(7.76\). This concept is critical because it always returns a non-negative value, simplifying problem-solving.
  • The absolute value removes negative signs, which can greatly simplify calculations.
  • Understanding this property is essential for solving equations and inequalities involving absolute terms.
Expressions that include absolute values demand careful execution of operations inside the bars before proceeding.

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Most popular questions from this chapter

A 10-foot ladder leans against the wall of a house. How close to the wall must the bottom of the ladder be in order to reach a window 8 feet above the ground?

Compute the exact square root. If the square root is undefined, write "undefined". \(-\sqrt{196}\)

Compute the exact value of the given expression. \(-\sqrt{625}-5 \sqrt{576}\)

In Exercises 71-76, complete the following tasks to estimate the given square root. a) Determine the two integers that the square root lies between. b) Draw a number line, and locate the approximate location of the square root between the two integers found in part (a). c) Without using a calculator, estimate the square root to the nearest tenth. \(\sqrt{58}\)

Complete the following tasks to estimate the given square root. a) Determine the two integers that the square root lies between. b) Draw a number line, and locate the approximate location of the square root between the two integers found in part (a). c) Without using a calculator, estimate the square root to the nearest tenth. \(\sqrt{44}\)
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