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Chapter 3: Problem 44

Find the value of each of the following expressions. $$ 14-(-20) $$

Short Answer

Expert verified
Answer: The value of the expression $$14 - (-20)$$ is $$34$$.

Step by step solution

01

Identify the operation

In the given expression, we can notice there is only one operation: subtraction. We have to subtract the numbers to simplify the expression. Remember that when dealing with negative numbers, we have to follow certain rules.
02

Observe the negative sign

There is a negative number in the expression, which can be identified by the presence of the negative sign before the number.
03

Change the subtraction to addition

When subtracting a negative number, it is easier to convert this operation into an addition problem. We can do this by changing the subtraction sign to an addition sign and changing the sign of the second number: $$ 14 - (-20) = 14 + 20 $$
04

Add the numbers

Now we have an addition problem. To find the value of the expression, we simply add the two numbers: $$ 14 + 20 = 34 $$
05

Write the final answer

The simplified value of the given expression is 34. So, the value of the expression $$14 - (-20)$$ is $$34$$.

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Key Concepts

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

Subtracting Negative Numbers
Understanding how to subtract negative numbers is essential when working with integer operations. It might seem a bit confusing at first, but here's a simple way to approach it:

  • Instead of seeing the subtraction sign, think of it as adding the opposite of the number.
  • In the expression \(14 - (-20)\), consider the negative sign before 20. In the real world, it's like removing a debt, which increases your amount.

By this logic, subtracting a negative number such as -20 is equivalent to adding its positive counterpart, making \(14 - (-20) = 14 + 20\). This simple transformation helps to simplify the process and avoid errors.
Addition
Handling addition in integer operations is straightforward once you're familiar with the basic rules. Remember, adding a positive number means moving further to the right on a number line.

  • When you rewrite \(14 - (-20)\) as \(14 + 20\), you are dealing with straightforward addition.
  • Add the numbers as you would normally: start from 14 and move 20 steps to the right.

For example, starting from 14 and adding 20, you would reach the number 34. This simple process confirms that addition can effectively simplify our expressions.
Simplification of Expressions
Simplifying expressions is a key concept in algebra, allowing you to write complex equations more simply. By systematically handling operations like subtraction of negatives and straightforward addition, this process can become intuitive.

  • Always begin by identifying the types of numbers and operations involved.
  • Use rules such as turning subtraction of a negative into addition to help simplify the problem.

In the case of \(14 - (-20)\), changing it to \(14 + 20\) reduces the problem to a simple addition task. You end up with 34, the simplified and final value of the expression. This approach not only makes solving such problems easier but also strengthens your understanding of integer operations.

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