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Which elements in the set below are integers? Choose the most complete answer.
[tex]$12,-3 / 4,5,-7,2.24,14 / 7,9$[/tex]
A) [tex]$-3 / 4,5,2.24,14 / 7$[/tex]
B) [tex]$12,-7,9$[/tex]
C) [tex]$12,5,-7,14 / 7,9$[/tex]
D) [tex]$12,5,-7,9$[/tex]
Answer (2)
An integer is a whole number (positive, negative, or zero).
Examine each number in the set: 12 , − 3/4 , 5 , − 7 , 2.24 , 14/7 , 9 .
Identify the integers: 12 , 5 , − 7 , 14/7 = 2 , 9 .
The correct answer is 12 , 5 , − 7 , 14/7 , 9 .
Explanation
Understanding the Problem We are given the set of numbers 12 , − 3/4 , 5 , − 7 , 2.24 , 14/7 , 9 and asked to identify which of these are integers. An integer is a whole number (not a fraction) that can be positive, negative, or zero.
Identifying Integers Let's examine each element of the set:
12 is an integer.
− 3/4 is a fraction and not an integer.
5 is an integer.
− 7 is an integer.
2.24 is a decimal and not an integer.
14/7 = 2 , which is an integer.
9 is an integer.
Listing the Integers Therefore, the integers in the set are 12 , 5 , − 7 , 14/7 , and 9 .
Selecting the Correct Option Comparing our list to the multiple-choice options, we see that option C, 12 , 5 , − 7 , 14/7 , 9 , matches our result.
Final Answer The elements in the set that are integers are 12 , 5 , − 7 , 14/7 , and 9 . Therefore, the most complete answer is C.
Examples
Understanding integers is crucial in many real-life situations. For example, when counting the number of items, like the number of apples in a basket, you can only have a whole number of apples (integers). You can't have 2.5 apples. Similarly, when dealing with money, you might have a whole number of dollars, but not necessarily a fraction of a dollar unless you're considering cents. Integers also come into play when measuring temperature, where you can have temperatures below zero, represented by negative integers.
The integers in the set are 12, 5, -7, 2 (from 14/7), and 9. The most complete answer that includes all the integers is option C: 12 , 5 , − 7 , 14/7 , 9 . This means option C accurately reflects all the integers from the provided list.
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