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Chapter 10: Problem 73

Simplify. $$ 132-(-21)+45-(-21) $$

Short Answer

Expert verified
The simplified result is 219.

Step by step solution

01

Understand the Problem

The goal is to simplify the expression \(132 - (-21) + 45 - (-21)\). Notice that there are two subtractions involving negative numbers.
02

Simplify Negative Subtractions

When subtracting a negative number, it is equivalent to adding the positive version of that number. Therefore, \(132 - (-21)\) becomes \(132 + 21\), and \(45 - (-21)\) becomes \(45 + 21\).
03

Perform the Additions

Calculate the new additions: \(132 + 21\) and \(45 + 21\).
04

Add the Results

Sum the results of the additions from Step 3. So, \(132 + 21 = 153\) and \(45 + 21 = 66\). Then add these two results together: \(153 + 66\).
05

Final Calculation

Finally, calculate \(153 + 66\) to get the simplified result.

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Key Concepts

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

Addition of Integers
Adding integers is simple once you understand the basic rules. When you add positive numbers together, the result is always positive.
For example, if you add 5 and 3, you get 8 \(5 + 3 = 8\).

This rule also applies to larger numbers. Just combine their values. In our exercise, we have two sums:

  • \(132 + 21\)

  • \(45 + 21\)

When you calculate these, you get:

\(132 + 21 = 153\)
\(45 + 21 = 66\)

These results will be important for the next steps.
Subtraction of Negative Numbers
Subtracting a negative number can be tricky, but it's easier if you remember one key fact:
Subtracting a negative is the same as adding a positive.

Let's visualize it. If you see \( -(-21) \), you can think of it as adding 21.

In our exercise, you encounter:

  • \(132 - (-21)\)

  • \(45 - (-21)\)


This becomes:

  • \(132 + 21\)

  • \(45 + 21\)

So, we just change the negative subtraction into addition, making the problem easier to solve.
Simplification Steps
Simplifying expressions means breaking them down into their simplest form.

We often do this in multiple steps. For our exercise, follow these steps:

  • First, transform the subtractions of negative numbers into additions
    \(132 - (-21) + 45 - (-21) \) becomes \(132 + 21 + 45 + 21 \)

  • Next, perform the additions. Break them into smaller sums:
    \(132 + 21 = 153\)
    and
    \(45 + 21 = 66\)

  • Finally, combine final sums:
    \(153 + 66\)


In the example, this gives you:
\[ 153 + 66 = 219 \]

So, the simplified form of \(132 - (-21) + 45 - (-21)\) is 219.

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