How do I figure out -144/4 to find out if it is a natural number,a whole number, an interger, if it is a rational or irrational number,or a real number? I don't want direct answers i would like to understand how I would go about solving to figure it out on my own. I just don't understand it?
Thank you very much, that has helped me so much. :-)
divide -144 by 4.
If there is no remainder, it is an integer
if it is also positive, it is a natural number
I've seen various definitions for whole numbers. Using yours, just recall that it must first be an integer, then check to see whether it also matches your definition of a whole number.
If there is a remainder, it is still a rational number. Because it is the ratio of two integers.
If not rational, it is irrational.
In any case, the answer will always be a real number. Real numbers include all of the other categories.
Better review your class notes on these definitions.
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To determine the nature of the number -144/4, you would need to evaluate it step by step. Here is how you can go about it:
1. Simplify the fraction:
-144/4 can be simplified by dividing both the numerator (-144) and the denominator (4) by their common factor, 4:
-144 ÷ 4 = -36
2. Determine if it is a natural number:
Natural numbers are positive counting numbers (1, 2, 3, 4, ...). Since -36 is a negative number, it is not a natural number.
3. Determine if it is a whole number:
Whole numbers include all natural numbers (0, 1, 2, 3, 4, ...). Since -36 is an integer but not a positive number, it is not a whole number.
4. Determine if it is an integer:
Integers include all positive and negative whole numbers (-3, -2, -1, 0, 1, 2, 3, ...). As -36 is a negative number and a whole number, it is indeed an integer.
5. Determine if it is a rational or irrational number:
Rational numbers can be expressed as a fraction (where the numerator and denominator are integers) or as a terminating or repeating decimal. Since -36 can be expressed as the fraction -36/1 (where both the numerator and denominator are integers), it is a rational number.
6. Determine if it is a real number:
All rational numbers, along with irrational numbers (numbers that cannot be expressed as a fraction or as a decimal that terminates or repeats), fall under the category of real numbers. As -36 is a rational number, it is also classified as a real number.
By following these steps, you can analyze any given number to determine its nature.