Problem 238 Simplify each expression. $$ ... [FREE SOLUTION]

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Chapter 1: Problem 238

Simplify each expression. $$ -58-(-67) $$

Short Answer

Expert verified

-58 - (-67) = 9

Step by step solution

Identify the Expression

The given expression is $-58 - (-67)$

Simplify the Double Negative

When you subtract a negative number, it is equivalent to adding the positive version of that number. Therefore, $-58 - (-67) = -58 + 67$.

Perform the Addition

Now, add $-58 + 67$. When adding a negative number and a positive number, subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value. In this case, $67$ is larger than $58$. Thus, $67 - 58 = 9$.

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Key Concepts

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

Subtracting Negative Numbers

Subtracting negative numbers might seem tricky at first, but it is quite straightforward once you understand the concept. When you see an expression like $-a - (-b)$, remember that subtracting a negative number is the same as adding its positive counterpart. This means: $-a - (-b) = -a + b$. Let's see why this is true:

Consider a number line. Moving left means subtracting, and moving right means adding.
If you subtract -10, you move to the right by 10 units, which is the same as adding 10.

Just remember: Subtracting a negative number flips the sign and turns it into a positive addition!

Absolute Value

Understanding absolute value is key to simplifying expressions involving integers. The absolute value of a number is its distance from zero on the number line, without considering direction. It's always positive or zero.

For example, the absolute value of -5 is 5, denoted as $|-5| = 5$.
Similarly, the absolute value of 5 is also 5, denoted as $|5| = 5$.

Using absolute values can help in comparing the magnitudes of numbers without worrying about their signs. For instance, when dealing with the expression $-58 + 67$, think in terms of absolute values to determine which number has a larger magnitude.

Integers Addition and Subtraction

Adding and subtracting integers often cause confusion, but it's simpler with some basic rules:

When adding integers with the same sign, add their absolute values and keep the sign. For example, $-3 + (-4) = -(3 + 4) = -7$.
When adding integers with different signs, subtract the smaller absolute value from the larger absolute value, and use the sign of the larger absolute value. For instance, $-58 + 67$ involves subtracting 58 from 67, resulting in 9, and since 67 is positive, the result is positive 9.
Subtracting is just adding the opposite. For example, $-58 - 67$ is the same as $-58 + (-67)$.

Practicing these rules will help you effortlessly handle any problem involving addition or subtraction of integers.

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91影视

Simplify each expression. $$ -58-(-67) $$

Short Answer

Step by step solution

Identify the Expression

Simplify the Double Negative

Perform the Addition

Key Concepts

Subtracting Negative Numbers

Absolute Value

Integers Addition and Subtraction

One App. One Place for Learning.

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