Problem 13 - Elementary Algebra

Question

Add and subtract. $$ -5+(-3)-(-7) $$

Step-by-Step Solution

Answer

The result is -1.

Step 1: Simplify the First Two Terms

Start by adding the first two numbers. We have \[-5 + (-3) = -5 - 3\]Adding a negative number is the same as subtracting the absolute value, so:\[-5 - 3 = -8\]

Step 2: Handle the Subtraction of a Negative Number

Now we take the result from Step 1 and subtract the negative seven:\[-8 - (-7)\]Subtracting a negative number is equivalent to adding its absolute value, so:\[-8 + 7\]

Step 3: Complete the Addition

Finally, add the numbers:\[-8 + 7 = -1\]

Step 4: Conclusion

After performing the steps, the expression evaluates to -1.

Key Concepts

Addition

Adding integers is a fundamental skill in math. When dealing with positive numbers, it's straightforward: just combine the numbers to get a larger total. However, things can be a bit trickier with negative numbers. If you add a negative number, it's like taking away from your total. Instead of the number getting larger, it decreases by the amount of the negative number.

For example, in the expression \[-5 + (-3)\], instead of thinking as adding -3, imagine subtracting 3 because \[+(-3)\] is the same as \[-3\].

• This way, \[-5 + (-3) = -8\].
• Be sure to always pay attention to the signs. Adding two negative numbers will yield a more negative result.

Understanding these basics helps you confidently tackle any addition problem with integers.

Subtraction

Subtraction can be thought of as removing quantities from a total. When it involves negative numbers, it can initially seem confusing. However, remember this simple rule: subtracting a negative number is the same as adding its positive counterpart.

In the expression \[-8 - (-7)\], you can transform it by changing the double negatives into a positive:

• Subtracting \[(-7)\] is the same as adding \[7\], thus this step becomes \[-8 + 7\].
• This transformation simplifies the problem and guides you toward a more intuitive calculation.

This technique is particularly useful and is a handy tool for any subtraction involving negative numbers.

Negative Numbers

Negative numbers are less than zero and often represent a deficit or loss in real-world scenarios. When working with these numbers in calculations, understanding their properties is crucial.

Some key points to consider:

• Adding two negative numbers results in a more negative number.
• Subtracting a negative number is the same as adding its absolute positive value.
• Negative numbers on a number line are located to the left of zero.

Handling negative numbers successfully involves recognizing when to switch subtraction into addition and being mindful of the direction and magnitude on the number line.