What type of number is 12/3? Choose all the answers that apply. A. whole number B. integer C. rational D. irrational
The Correct Answer and Explanation is:
Correct answers: A. whole number, B. integer, C. rational
The number 12 ÷ 3 = 4, which is the simplified form of the fraction 12/3.
To determine the types of numbers this result belongs to, it helps to analyze the definitions of each category:
- Whole number: This set includes all non-negative numbers without fractions or decimals. These numbers begin at 0 and increase by 1, such as 0, 1, 2, 3, 4, etc. Since 4 fits this description, it qualifies as a whole number.
- Integer: Integers include all whole numbers and their negative counterparts. This set includes …, -3, -2, -1, 0, 1, 2, 3, 4, etc. The number 4, being a positive whole number, is also an integer.
- Rational number: A rational number is any number that can be expressed as a ratio or fraction of two integers, where the denominator is not zero. The original form, 12/3, is already a fraction, which makes it a rational number. Also, the result 4 can be expressed as 4/1, confirming its rational status.
- Irrational number: This category includes numbers that cannot be written as a fraction of two integers. Their decimal representations are non-repeating and non-terminating. Examples include π and √2. The number 4 is a terminating decimal and can be written as a fraction, so it does not meet the criteria for being irrational.
Therefore, 12/3 simplifies to 4, which fits into the categories of whole number, integer, and rational number, but not irrational number. The correct answers are A, B, and C.
