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Chapter 1: Problem 214

Simplify each expression. $$ -17+(-18)+6 $$

Short Answer

Expert verified
The simplified expression is -29.

Step by step solution

01

Rearrange the terms

Group the numbers to simplify the operations: -17 + (-18) + 6
02

Simplify the sum of negative numbers

Combine the negative numbers first: -17 + (-18) = -35
03

Add the remaining positive number

Now add the positive number: -35 + 6 = -29

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Key Concepts

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

Combining Like Terms
Combining like terms is a crucial step in simplifying expressions. Like terms are terms that contain the same variables raised to the same power. But in this exercise, we only have constants, so we are focusing on combining just the numbers.
For instance, in the expression given:
  • -17
  • -18
  • 6
When you are combining these terms, make sure to handle each number's sign carefully. First, group and combine the negative numbers:
  • -17 + (-18) = -35
Once combined, this sum then needs to be added to the remaining positive number.
  • -35 + 6 = -29
Negative Numbers
Negative numbers can sometimes be tough, but with practice, they become easier to handle. When dealing with negative numbers, always remember that adding two negative numbers together makes a bigger negative number.
For example:
  • -17 + (-18)
Here, you can think of it as losing 17 units and then losing another 18 units. Therefore, the total loss is 35 units, which is
  • -35
When working with negative numbers, it's important to keep track of your signs to avoid errors in your calculations.
Addition and Subtraction
Addition and subtraction are fundamental math operations, but they get trickier when involving negative numbers. When subtracting, think of it as adding a negative. When you see a problem like
  • -35 + 6
Imagine starting at -35 on a number line and moving 6 units to the right toward the positive side. One rule of thumb for combining positive and negative numbers is:
If the signs are different, subtract the smaller absolute value from the larger absolute value, and keep the sign of the number with the larger absolute value.
So, in
  • -35 + 6
we subtract 6 from 35 to get 29, and keep the negative sign because 35 is larger. Hence:
  • -35 + 6 = -29

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