Problem 38
Question
Add. Do not use the number line except as a check. \(40+(-8)\)
Step-by-Step Solution
Verified Answer
32
1Step 1: Identify the Numbers
First, identify the numbers involved in the addition. The numbers are 40 and -8.
2Step 2: Understand the Operation
Understand that you are adding a positive number (40) and a negative number (-8).
3Step 3: Subtract the Numbers
When adding a positive number and a negative number, subtract the smaller absolute value from the larger absolute value. Here, you subtract 8 from 40, which is 32.
4Step 4: Determine the Sign
Since the larger absolute value is 40 and it is positive, the result will be positive. Thus, the result is 32.
Key Concepts
Positive and Negative NumbersAbsolute ValueArithmetic Operations
Positive and Negative Numbers
When dealing with integer addition, it is important to understand positive and negative numbers. Positive numbers are those greater than zero, such as 1, 2, 3, etc. Negative numbers are less than zero and have a minus sign in front, such as -1, -2, -3, etc.
Negative numbers can seem tricky, but they simply represent values below zero. Imagine temperatures dropping below freezing. Just as you might say it's -5 degrees outside, in math, you might see calculations like -5.
Understanding these will help you master integer addition.
Negative numbers can seem tricky, but they simply represent values below zero. Imagine temperatures dropping below freezing. Just as you might say it's -5 degrees outside, in math, you might see calculations like -5.
Understanding these will help you master integer addition.
Absolute Value
Absolute value is the distance of a number from zero on the number line, regardless of direction. It’s always positive. For example, the absolute value of -8 is written as \(|-8|\) and is equal to 8. Similarly, \(|40|\) is just 40.
Recognizing the absolute value is vital when performing operations involving both positive and negative numbers. In the exercise of adding \( 40 + (-8) \), understanding that the absolute value of -8 is 8 helps you determine how to subtract the smaller value from the larger one.
This concept ensures you approach these problems systematically.
Recognizing the absolute value is vital when performing operations involving both positive and negative numbers. In the exercise of adding \( 40 + (-8) \), understanding that the absolute value of -8 is 8 helps you determine how to subtract the smaller value from the larger one.
This concept ensures you approach these problems systematically.
Arithmetic Operations
Arithmetic operations involve addition, subtraction, multiplication, and division.
When performing addition with integers, if both numbers have the same sign, simply add their absolute values. For example, \(5 + 3 = 8\) or \(-5 + (-3) = -8\).
If the numbers have different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value. Like in the exercise, \(40 + (-8)\). Here you subtract 8 from 40, resulting in 32.
Understanding these operations is crucial for solving math problems efficiently.
When performing addition with integers, if both numbers have the same sign, simply add their absolute values. For example, \(5 + 3 = 8\) or \(-5 + (-3) = -8\).
If the numbers have different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value. Like in the exercise, \(40 + (-8)\). Here you subtract 8 from 40, resulting in 32.
Understanding these operations is crucial for solving math problems efficiently.