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Chapter 2: Problem 45

Simplify each of the numerical expressions. $$0.76(0.2+0.8)$$

Short Answer

Expert verified
The simplified expression is 0.76.

Step by step solution

01

Understand the Expression

We are given the expression \(0.76(0.2+0.8)\). Our goal is to simplify this expression by performing basic arithmetic operations.
02

Simplify Inside the Parentheses

First, simplify the expression inside the parentheses. Add \(0.2\) and \(0.8\): \[0.2 + 0.8 = 1.\]
03

Multiply by the Factor Outside the Parentheses

Now, multiply the result from Step 2 by the number outside the parentheses: \[0.76 imes 1 = 0.76.\]
04

Conclude the Simplification

We have simplified the expression to \(0.76\). There are no further operations to perform.

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Key Concepts

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

Simplifying Expressions
Simplifying expressions is like tidying up a messy room. You want to make everything as simple and neat as possible. In mathematics, simplifying involves reducing the expression to its simplest form without changing its value. This can involve:
  • Performing arithmetic operations like addition or subtraction.
  • Breaking down complex sections using multiplication or division.
  • Combining like terms if possible.
In our given expression, simplifying sheds any unnecessary complexity so that the core value becomes clear. Simplification is a fundamental math skill that helps make expressions easier to interpret and use in further calculations.
Arithmetic Operations
Arithmetic operations are the basic building blocks of math. They include addition, subtraction, multiplication, and division. It鈥檚 like having a toolkit to solve various math puzzles. For our expression, these operations play key roles:
  • Addition: Combines values. Used to simplify inside the parentheses.
  • Multiplication: Scales one number by another. Applied after simplifying inside the parentheses.
When you handle an expression with numbers, you're looking to execute these operations in a sequence that makes it as simple to read and use as possible. Practicing arithmetic operations helps in quick and accurate computation.
Parentheses in Mathematics
Parentheses are crucial in math as they indicate what should be calculated first in an expression. Think of them as priority signals, ensuring that operations inside occur before dealing with anything outside. For example:
  • In the expression \(0.76(0.2 + 0.8)\), the parentheses tell us to add \(0.2\) and \(0.8\) before multiplying by \(0.76\).
Remembering the function of parentheses is vital for the correct simplification of expressions. They set the rules for operation precedence, avoiding confusion in complex mathematical problems.

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Most popular questions from this chapter

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(3.4 x-1.9 x+5.2 x\) for \(x=0.3\)

Do you think that \(2 \sqrt{2}\) is a rational or an irrational number? Defend your answer.

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