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Chapter 1: Problem 18

Find each sum. $$ 3+(-7) $$

Short Answer

Expert verified
-4

Step by step solution

01

Understand Addition with Negative Numbers

When adding a negative number, it is the same as subtracting the absolute value of that number. For the expression 3 + (-7), this means we need to subtract 7 from 3.
02

Perform the Subtraction

Subtract 7 from 3: 3 - 7 = -4
03

Write the Final Answer

The result of 3 + (-7) is -4.

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Key Concepts

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

addition
Addition is one of the basic operations in mathematics, often symbolized by the plus sign (+). It involves combining two or more numbers to form a total or sum. For example, in the expression 3 + (-7), we are combining the number 3 with the number -7. This activity might seem straightforward when dealing with positive numbers, but it gets slightly intricate when negative numbers are involved.
negative numbers
Negative numbers are numbers less than zero, represented with a minus sign (-) in front of them. They are used to represent values below zero, such as debts or temperatures in certain conditions. For instance, -7 is a negative number, meaning it鈥檚 7 units to the left of zero on the number line. When performing arithmetic operations involving negative numbers, it's crucial to keep track of the signs to ensure accuracy. In the expression 3 + (-7), -7 indicates a movement seven units leftwards from zero.
absolute value
The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, the absolute value of -7 is 7, as it is 7 units away from zero. In mathematical terms, it鈥檚 denoted as \(|-7| = 7\). When dealing with addition involving a negative number, you can think of subtracting the absolute value of the negative number from the other number. This mindset helps in simplifying and solving the expression, just like in the example of 3 + (-7). Here, we're essentially subtracting the absolute value of -7 (which is 7) from 3.
subtraction
Subtraction is another fundamental mathematical operation, represented by the minus sign (-). It involves finding the difference between two numbers. Subtraction can also be interpreted as adding a negative number. For example, in the equation 3 - 7, we're seeking the difference between 3 and 7. Subtracting a larger number from a smaller one results in a negative number. This concept is directly applied in the expression 3 + (-7), which transforms into 3 - 7. Performing this operation, we get -4, illustrating how addition and subtraction intertwine, especially when negative numbers are involved.

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Most popular questions from this chapter

Solve each problem. In \(1998,\) undergraduate college students had an average (mean) credit card balance of 1879. The average balance increased \(\$ 869\) by 2000 , then dropped \(\$ 579\) by \(2004,\) and then increased \(\$ 1004\) by \(2008 .\) What was the average credit card balance of undergraduate college students in \(2008 ?\)

Write a numerical expression for each phrase and simplify. 19 less than the difference between 9 and \(-2\)

Write a numerical expression for each phrase and simplify. See Examples 7 and \(8 .\) The product of 12 and the difference between 9 and \(-8\)

Write a numerical expression for each phrase and simplify. 8 less than \(-2\)

Write a numerical expression for each phrase and simplify. \(\frac{2}{7}\) more than the sum of \(\frac{5}{7}\) and \(-\frac{9}{7}\)
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