Problem 26 Find each difference. $$-9-(-7... [FREE SOLUTION]

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Chapter 2: Problem 26

Find each difference. $$-9-(-7)$$

Short Answer

Expert verified

The difference is -2.

Step by step solution

Identify the Original Expression

The original expression given is $-9 - (-7)$.Notice that we have a subtraction of a negative number.

Understand Minus and Negative Signs

Subtracting a negative number is the same as adding its positive counterpart. So, we need to remember that $-(-7) = +7$.

Simplify the Expression

Replace the subtraction of the negative with the addition of the positive: $-9 + 7$.

Calculate the Result

Now, compute $-9 + 7$. Begin by thinking of a number line: move 9 units left for the -9, then 7 units right for the +7. You land at -2.

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Key Concepts

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

Subtracting Negatives

When you encounter a mathematical expression where you need to subtract a negative number, it can initially seem confusing. However, there is an important rule that can simplify the process:

Subtracting a negative is the same as adding the positive of that number.

So, in the context of the given exercise $-9 - (-7)$, the subtraction of $-7$ becomes an addition $+7$. This rule comes from the idea that two negative signs back to back cancel each other out, effectively switching to a positive sign.

Thinking this way can greatly simplify calculations and help avoid errors.

Integer Operations

Integer operations refer to basic math operations (such as addition, subtraction, multiplication, and division) performed on whole numbers. When working with integers:

Positive numbers are numbers greater than zero.
Negative numbers are numbers less than zero.
Zero itself is neutral - neither positive nor negative.

Understanding how to perform operations involving negative numbers is essential. When you have a problem like $-9 + 7$, start by identifying the biggest number and its sign. In this case, $-9$ is bigger than $+7$, so the answer will be negative.

Subtract the smaller absolute value from the larger: $9 - 7 = 2$. Then, because the larger number (9) was negative, the result is -2. This keeps the calculation straightforward and logical.

Number Line

Visualizing numbers and their operations on a number line can make understanding integer operations much easier. A number line is a straight line where we can represent integers:

Moving right indicates increasing or adding positive numbers.
Moving left indicates decreasing or adding negative numbers.

If we take the problem $-9 + 7$, start at $0$ and move 9 steps left to reach $-9$. Then, move 7 steps to the right because we are adding 7. You'll find yourself at $-2$ on the number line.

This visual approach can help solidify the understanding of how integer operations work in practical terms.

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91影视

Find each difference. $$-9-(-7)$$

Short Answer

Step by step solution

Identify the Original Expression

Understand Minus and Negative Signs

Simplify the Expression

Calculate the Result

Key Concepts

Subtracting Negatives

Integer Operations

Number Line

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