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Chapter 2: Problem 37

simplify. $$-6-(-38) \quad$$

Short Answer

Expert verified
-6 - (-38) = 32

Step by step solution

01

Identify the operators

Recognize the negative signs in the expression. The expression is -6 - (-38) .
02

Simplify the double negative

Convert the double negative into a positive. Using the rule that subtracting a negative is equivalent to adding, we get -6 + 38 .
03

Perform the arithmetic

Add the numbers together: -6 + 38 = 32.

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Key Concepts

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

Negative Numbers
Negative numbers can seem confusing at first, but they are very important in mathematics. A negative number is any number less than zero. You can recognize negative numbers by the minus sign (-) placed in front of the number. For example, -1, -6, and -38 are negative numbers.
Negative numbers are used in various real-life situations, such as temperatures below freezing, depths below sea level, or financial debts. When working with negative numbers, it's essential to understand how they interact with positive numbers during arithmetic operations.
Double Negative
The concept of double negative might sound complicated, but it is quite simple. A double negative occurs when you have two negative signs together. For example, in the expression ( -6 - (-38) ), you can see a double negative at (-(-38)).
By mathematical rules, a double negative turns into a positive. Think of it as the negatives canceling each other out. So, (-(-38)) becomes +38.
This is an essential rule to remember when simplifying expressions involving negative numbers. It helps make the calculations much more straightforward.
Arithmetic Operations
Arithmetic operations impact how we work with numbers. The basic arithmetic operations include addition, subtraction, multiplication, and division.
In the exercise, we dealt with addition and subtraction involving negative numbers. The key steps are:
  • Identify the operators: Look for the signs and understand what operation you need to perform.
  • Simplify the double negatives: Convert subtracting a negative to adding a positive.
  • Perform the arithmetic: After simplifying, complete the addition or subtraction calculation.

Let's go through the example again:
Start with the expression (-6 - (-38)).
Change the double negative to positive: -6 + 38.
Finally, add the numbers: (-6 + 38) = 32.
Following these steps will help you simplify expressions involving negative numbers.

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