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Chapter 2: Problem 16

Write as an equivalent addition; then evaluate. $$-19-(-24)$$

Short Answer

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Question: Rewrite the expression $$-19-(-24)$$ as an equivalent addition and evaluate it. Answer: The equivalent addition of the given expression is $$-19+24$$, and its value is 5.

Step by step solution

01

Rewrite the expression as an equivalent addition

To rewrite $$-19-(-24)$$ as an equivalent addition, we remove the subtraction followed by the negative number and replace it with the addition of the positive version of that number. So, the expression becomes: $$-19+24$$
02

Evaluate the expression

Now, we can simply add the numbers together: $$-19+24=5$$ So, the equivalent addition of the given expression is 5.

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Key Concepts

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

Addition of Integers
When dealing with integers, addition is a fundamental operation. It allows you to combine numbers to find their total or sum.
Integer addition may involve positive numbers, negative numbers, or a combination of both. Here's how it works:
  • Adding two positive integers results in a positive sum (e.g., 5 + 7 = 12).
  • Adding two negative integers yields a larger negative number (e.g., -3 + (-4) = -7).
  • Adding a positive integer to a negative integer requires determining which number has a larger absolute value, and the result will take the sign of that larger value (e.g., -8 + 5 = -3 because |-8| > |5|).
In the context of our example, rewrite subtraction as addition to simplify and solve expressions.
Subtraction of Integers
Subtraction can seem tricky, especially with negative numbers involved. But once you remember that subtraction is simply adding the opposite, things become simpler.
Consider this: when you have an expression like \(-19 - (-24)\), you can rewrite it as an addition problem. The rule is to convert the subtraction of a negative number into the addition of a positive number.
You do this by changing the subtraction sign to an addition, and the negative number to its positive counterpart.
In our example:
  • Start with \(-19 - (-24)\).
  • Rewrite it as \(-19 + 24\).
  • This transformed expression is much easier to evaluate.
Remember, when subtracting integers, find the opposite number to add!
Negative Numbers
Negative numbers represent values less than zero and can be tricky at first glance.
They appear in various scenarios, such as debts or temperatures below freezing. Working with negative numbers requires attention to rules for addition and subtraction.
Here's what to keep in mind:
  • Negative numbers become positive when you take their opposite (the opposite of -5 is 5).
  • When adding negative numbers, you move further left on the number line.
  • To subtract a negative number, rewrite the expression as the addition of a positive number.
Understanding how to manipulate negative numbers is crucial for solving expressions like \(-19 - (-24)\).
This concept underpins all integer operations and is a valuable skill in mathematics.
Evaluate Expressions
Evaluating expressions involves simplifying them down to a single number or value.
To evaluate means to perform the operations in the expression step-by-step, following mathematical rules. Here's how you can approach it:
  • Simplify any complex operations, such as turning subtraction into addition.
  • Work sequentially from left to right unless grouped by parentheses.
  • Always be mindful of signs, especially when they involve negative numbers.
In our example, you start by rewriting \(-19 - (-24)\) as \(-19 + 24\), then simply add.
These steps ensure accurate results and enhance problem-solving confidence in mathematics.

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Most popular questions from this chapter

Prep Exercise 9 Every positive integer has two square roots, a ____ square root and a ____ square root. Prep Exercise 10 A negative number has ____ real square roots. find all square roots of each number. $$36$$

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