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Chapter 5: Problem 243

Simplify. 10\((25.1-43.8)\)

Short Answer

Expert verified
The simplified result is -187.

Step by step solution

01

Identify the Expression Inside the Parentheses

First, locate the expression inside the parentheses that needs to be simplified, which is \(25.1 - 43.8\).
02

Perform the Subtraction Inside the Parentheses

Subtract 43.8 from 25.1. This can be calculated as: \[25.1 - 43.8 = -18.7\].
03

Multiply the Result by 10

After getting the result from the subtraction, multiply it by 10. This can be calculated as: \[10 \times (-18.7) = -187\].

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Key Concepts

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

Parentheses in Math
In math, parentheses are used to group parts of an expression that should be dealt with first. Think of them as a way to prioritize certain operations.
For instance, in the exercise, the expression inside the parentheses is \(25.1 - 43.8\). Before doing anything else, you need to simplify what's inside the parentheses. This is because parentheses operate like a signal, telling you what math to do first.
Ignoring them or doing operations out of order can lead to the wrong answer. In our example, if you didn't handle the subtraction inside the parentheses first, you'd get a completely different result.
Subtraction
Subtraction is taking one number away from another. In this exercise, you need to subtract 43.8 from 25.1.

Here is how you can think about it: What is \(25.1 - 43.8\)? Feel free to use a calculator or line up the numbers vertically to ensure accuracy. When you subtract these numbers, you find \(-18.7\).

One easy way to handle the subtraction is:
  • Align the decimal points in both numbers.
  • Since 43.8 is larger than 25.1, the result will be negative.
  • Subtract as if they are positive numbers, and then place a negative sign at the end.

So, \(43.8 - 25.1 = 18.7\), but since 43.8 was larger, you add a negative sign: \(-18.7\).
Multiplication
Once you have simplified the inside of the parentheses, the next step in this exercise involves multiplication.
Your expression is now \(10 \times (-18.7)\). Multiplication is all about taking one number and adding it to itself a certain number of times.
Here, you are multiplying 10 by \(-18.7\), which means you are essentially adding \(-18.7\) to itself 10 times.
To solve this, you can just multiply the magnitudes and then apply the sign:
  • Multiply 10 by 18.7, which equals 187.
  • Since one of the numbers is negative, the result will be negative.

So, \(10 \times (-18.7)\) becomes \(-187\).
Therefore, multiplying gets you the final result of \(-187\).

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