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Chapter 2: Problem 17

Adding integers with different signs is similar to reconciling assets and debts. $$35+(-53)$$

Short Answer

Expert verified
Answer: The sum of the integers 35 and -53 is -18.

Step by step solution

01

Identify the larger number and its sign

Compare the absolute values of the integers: \(|-53|=53\) is greater than \(|35|=35\). Hence, the larger number is -53, and its sign is negative.
02

Subtract the smaller number from the larger number

Since we identified the larger number as -53, we subtract the smaller number, 35, from it: $$53 - 35 = 18$$
03

Assign the larger number's sign to the result

We previously identified that the larger number has a negative sign. So, the result should also take on this negative sign: $$-18$$ Therefore, the sum of the given integers is: $$35 + (-53) = -18$$

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Key Concepts

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

Absolute Value
Understanding the concept of absolute value is crucial when working with integers, especially when they have different signs. The absolute value of an integer is essentially its distance from zero on the number line, regardless of direction. This means it's always a positive number or zero.

For example, the absolute value of -53, denoted as \(|-53|\), is 53. Similarly, the absolute value of 35 is \(|35|\), which is also 35. When we're adding integers with different signs, comparing their absolute values helps to determine the larger number in magnitude, which is a central step in determining the outcome of their addition.
Subtraction of Integers
The subtraction of integers involves finding the difference between two numbers. When adding integers with different signs, we often convert the problem into a subtraction. This is because subtracting a negative number is the same as adding its positive counterpart.

In the given example, we convert the addition problem into a subtraction one by subtracting 35 from 53, because the latter has a larger absolute value. By doing so, we determine the difference between their magnitudes, which gives us the absolute value of the final answer when added together.
Negative Numbers
Negative numbers represent values less than zero. They are often depicted to the left of zero on a number line. In the given problem, -53 is a negative number.

Understanding how to work with negative numbers is significant in integer operations. When a negative number is involved in addition or subtraction, it's essential to account for its sign. In our case, after determining that -53 has the larger magnitude, we also confirm that the final result should be negative, following the sign of the larger (in absolute value) integer.
Integer Operations
Integer operations include addition, subtraction, multiplication, and division. When performing operations with integers, it is particularly important to pay attention to signs, as they can change the result significantly.

In the given exercise, combining the concepts of absolute value, subtraction, and the understanding of negative numbers, we are able to correctly navigate through adding integers with different signs. Remember that when the signs are different, the operation essentially becomes a subtraction, and the result takes the sign of the number with the larger absolute value.

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Most popular questions from this chapter

Prep Exercise 8 For the following equation, complete the related division equation used to solve the equation. \(3 x=-15\) \(x=\) ____ solve and check. $$(-9)(-1)(2) w=-90$$

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