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Chapter 10: Problem 74

Simplify. $$ 81-(-20)-14-(-50)+53 $$

Short Answer

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Step by step solution

01

Simplify Double Negatives

Identify and simplify double negatives. These double negatives turn into addition: $$ \text{Simplified equation: } 81 + 20 - 14 + 50 + 53 $$
02

Perform Addition

Add the positive numbers together first. $$ 81 + 20 + 50 + 53 = 204 $$
03

Perform Subtraction

Subtract the remaining number from the result of the addition: $$ 204 - 14 = 190 $$

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Key Concepts

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

double negatives
A double negative happens when you subtract a negative number. It's like taking away a minus sign, which means adding. For example, in the expression \(81 - (-20)\), the double negative \(- (-20)\) becomes a \(+ 20\). This simplification makes the expression easier to solve. Always switch double negatives to additions for clarity.
addition
Addition is one of the basic arithmetic operations. When you simplify an expression, you often need to add several numbers together. In the simplified equation \(81 + 20 - 14 + 50 + 53\), you first add all the positive numbers. This means we combine \(81\), \(20\), \(50\), and \(53\) together to get \(204\). Adding numbers step-by-step can help prevent mistakes.
subtraction
Subtraction is another fundamental arithmetic operation. After adding up the positive numbers, you will need to subtract the remaining number. For our example, you subtract \(14\) from \(204\) to get \(190\). Remember, subtraction is taking away or reducing the value of a number.
arithmetic operations
Arithmetic operations include addition, subtraction, multiplication, and division. These basic operations are essential for solving math problems. In this exercise, we focused on addition and subtraction. Simplifying expressions correctly requires understanding and accurately performing these operations step-by-step. Practice with various problems to become proficient in these skills.

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