Problem 66
Question
What are consecutive even integers? Name three consecutive even integers between -50 and -40 .
Step-by-Step Solution
Verified Answer
The three consecutive even integers between -50 and -40 are -48, -46, and -44.
1Step 1: Understand Consecutive Even Integers
Consecutive even integers are even numbers that follow each other in order. For example, if the first even integer is represented by x, the next consecutive even integer will be x+2, and the one after that will be x+4.
2Step 2: Set the Range
Identify that the three consecutive even integers need to be between -50 and -40. Make sure they are within this specified range.
3Step 3: Choose the First Even Integer
Select the smallest even integer within the given range. In this case, start with -48.
4Step 4: Find the Next Two Consecutive Even Integers
Add 2 to -48 to find the next consecutive even integer: -48 + 2 = -46. Then add another 2 to -46 to get the next even integer: -46 + 2 = -44.
Key Concepts
Understanding Even NumbersConsecutive Even NumbersBasics of Integer Operations
Understanding Even Numbers
Even numbers are integers that can be divided evenly by 2. This means there is no remainder when an even number is divided by 2.
Examples of even numbers include -10, 0, 6, and 24.
It's important to note that these numbers are spaced at a regular interval of 2.
Recognizing even numbers helps in solving problems involving sequences and arithmetic operations.
In arithmetic, even numbers play a crucial role, especially when dealing with sequences like consecutive even numbers.
Examples of even numbers include -10, 0, 6, and 24.
It's important to note that these numbers are spaced at a regular interval of 2.
Recognizing even numbers helps in solving problems involving sequences and arithmetic operations.
In arithmetic, even numbers play a crucial role, especially when dealing with sequences like consecutive even numbers.
Consecutive Even Numbers
Consecutive even numbers are even numbers placed one after another with a difference of 2 between each pair.
For instance, if you start with an even number such as x, the next consecutive even number will be x+2, followed by x+4, and so on.
This pattern keeps repeating, making it simpler to identify and work with these numbers. For instance, based on the exercise, the three consecutive even integers starting from -48 would be:
For instance, if you start with an even number such as x, the next consecutive even number will be x+2, followed by x+4, and so on.
This pattern keeps repeating, making it simpler to identify and work with these numbers. For instance, based on the exercise, the three consecutive even integers starting from -48 would be:
- -48
- -46
- -44
Basics of Integer Operations
Integer operations involve basic mathematical procedures applied to integers, which include addition, subtraction, multiplication, and division. Working with integers often requires understanding how these operations affect positive and negative numbers.
For example, adding two negative integers results in a more negative number, whereas the sum of two integers with opposite signs will depend on which has the larger absolute value, determining the sign of the result.
When dealing with consecutive even integers, mostly addition and sometimes subtraction are used to find the next or previous number in the series.
Adding 2, as often done with consecutive even numbers, is a fundamental operation that must be clearly understood. For instance, starting from -48 and adding 2 gives -46, and adding another 2 results in -44, and so on.
Practicing these operations will boost your confidence and accuracy in working with number sequences.
For example, adding two negative integers results in a more negative number, whereas the sum of two integers with opposite signs will depend on which has the larger absolute value, determining the sign of the result.
When dealing with consecutive even integers, mostly addition and sometimes subtraction are used to find the next or previous number in the series.
Adding 2, as often done with consecutive even numbers, is a fundamental operation that must be clearly understood. For instance, starting from -48 and adding 2 gives -46, and adding another 2 results in -44, and so on.
Practicing these operations will boost your confidence and accuracy in working with number sequences.
Other exercises in this chapter
Problem 62
In the following exercises, solve each number word problem. Price before Sales Tax Kenji paid \(\$ 2,279\) for a new living room set, including \(\$ 129\) tax.
View solution Problem 65
What are consecutive odd integers? Name three consecutive odd integers between 50 and 60 .
View solution Problem 67
In the following exercises, translate and solve. What number is \(45 \%\) of \(120 ?\)
View solution Problem 68
In the following exercises, translate and solve. What number is \(65 \%\) of \(100 ?\)
View solution