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Chapter 2: Problem 34

Add the numbers with different signs. $$-3+9$$

Short Answer

Expert verified
The result of (-3) + 9 is 6.

Step by step solution

01

Determine the Signs of Both Numbers

Identify the signs of the two numbers involved. In this case, (-3) is negative and (9) is positive.
02

Subtract the Smaller Number from the Larger Number

Since the numbers have different signs, subtract the smaller magnitude from the larger magnitude. Calculate ewline |9 - 3| = 6.
03

Determine the Sign of the Result

Since the larger number was positive (9), the result will inherit its sign. Therefore, the final answer is +6.

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Key Concepts

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

integer addition
Adding integers involves combining two numbers to get a single sum. When the integers have different signs, you don't simply add them as you would with numbers of the same sign. Instead, you are effectively subtracting their absolute values. This means you take the absolute value of each integer鈥攊gnoring their signs at first鈥攖o find the magnitudes and then subtract the smaller one from the larger one. This method ensures you get the correct result and helps avoid confusion.
absolute value
Absolute value refers to the distance of a number from zero on the number line, regardless of direction. It is always a positive number or zero. For example, the absolute value of both -3 and 3 is 3, noted as \(|-3| = 3\) and \(|3| = 3\). When dealing with integers of different signs, absolute values make it easier to compare their magnitudes. You subtract the smaller absolute value from the larger one to simplify the process.
determining sign of result
Once you have subtracted the smaller magnitude from the larger magnitude, the next step is to determine the sign of your result. This is crucial because the final answer must carry the sign of the larger number. In our example, 9 is larger than -3. Since 9 is positive, the final result will also be positive. Therefore, after performing the subtraction \( |9 - 3| = 6 \), you assign the sign of the larger number to get +6.

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Most popular questions from this chapter

Divide the real numbers, if possible. $$\frac{-56}{-8}$$

Find the range. The range of a set of numbers is the difference between the highest value and the lowest value. That is, range = highest - lowest. Find two integers whose difference is \(-6 .\) Answers may vary.

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$-|b|$$

Jeff's balance in his checking account was 2036 dollar at the beginning of the week. During the week, he wrote two checks, made two deposits, and made one ATM withdrawal. What is his ending balance? $$\begin{array}{l|r} \hline \text { Check } & -\$ 150 \\ \hline \text { Check } & -\$ 25 \\ \hline \text { Paycheck (deposit) } & \$ 480 \\ \hline \text { ATM } & -\$ 200 \\ \hline \text { Cash (deposit) } & \$ 80 \\ \hline \end{array}$$

Translate each English phrase to a mathematical expression. Then simplify. 27 minus 40
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