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Chapter 1: Problem 17

Evaluate each of the following a. \(20-(-10)=\) b. \(-6+(-38)=\) c. \(2 \times(-7)+14=\)

Short Answer

Expert verified
a. 30, b. -44, c. 0

Step by step solution

01

Evaluate Part a

First, calculate the expression: \(20 - (-10)\). Subtracting a negative number is the same as adding the positive counterpart of that number. Therefore, the expression becomes: \(20 + 10\). Adding these values together gives: \(20 + 10 = 30\).
02

Evaluate Part b

Next, evaluate the expression: \(-6 + (-38)\). Adding a negative number is the same as subtracting its positive counterpart: \(-6 - 38\). Subtracting these values gives: \(-6 - 38 = -44\).
03

Evaluate Part c

Finally, evaluate the expression: \(2 \times (-7) + 14\). First, perform the multiplication: \(2 \times (-7) = -14\). Next, add 14 to the result: \(-14 + 14 = 0\).

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Key Concepts

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

subtraction of negative numbers
Understanding the subtraction of negative numbers can sometimes be tricky but is very important. Remember, when you subtract a negative number, it is the same as adding its positive counterpart.
For example, in the exercise above:
\(20 - (-10)\) might look confusing at first. However, you can simplify it by converting the subtraction of a negative number into addition:
\(20 - (-10)\) becomes \(20 + 10\. = 30\).
This is because subtracting a negative value can be thought of as removing debt - you're essentially adding to your total.
So, the key rule here is: Subtracting a negative is the same as adding a positive.
addition of negative numbers
Adding negative numbers can sometimes seem daunting, but it's easier when you understand that adding a negative number is just like subtracting a positive number.
In our exercise, we had the expression \(-6 + (-38)\).
First, recognize that adding a negative is the same as subtraction:
\(-6 + (-38)\) is equivalent to \(-6 - 38\). This process changes the addition into subtraction:
\(-6 - 38 = -44\).
So, the key rule here is: Adding a negative number is the same as subtracting a positive number.
multiplication with negative numbers
Multiplication with negative numbers follows straightforward rules. Knowing these rules helps in simplifying expressions quickly.
In our problem, we had to evaluate \(2 \times (-7) + 14\).
First, let's focus on the multiplication part:\(2 \times (-7) = -14\). Remember, a positive number multiplied by a negative number is always negative. Next, we add the result with 14:
\(-14 + 14 = 0\).
So here, after the multiplication step, we treated the resulting negative product just as any other integer when performing addition or subtraction.
The key rules for multiplication are:
  • Positive \(\times\) Positive = Positive
  • Positive \(\times\) Negative = Negative
  • Negative \(\times\) Negative = Positive

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