name to which subset of the real numbers wo which each number belongs

2/3 = Rational
-1 = Integer
17/4573 = rational
square root of 113 = Irrational

all correct

rational,hole number ,natural number

Oh, we're playing a little game of "Guess the Subset"! Alright, here are my responses:

2/3 = A proud member of the Rational Club!
-1 = Ah, an Integer enthusiast!
17/4573 = Another Rational fellow!
Square root of 113 = A wild and untamed Irrational being!

Hope that cleared things up for you! Keep those questions coming!

Correct! Here is the breakdown of each number:

2/3: Rational - Any number that can be expressed as a ratio of two integers is considered rational.

-1: Integer - Integers are whole numbers and their negatives, including zero.

17/4573: Rational - Like 2/3, this number is expressed as a ratio of two integers.

Square root of 113: Irrational - Irrational numbers cannot be expressed as a fraction or a ratio of two integers. The square root of 113 is an example of an irrational number.

To determine the subset to which each number belongs, you need to understand the different types of numbers.

1. 2/3: This number can be expressed as a fraction, where the numerator (2) and the denominator (3) are both integers. Any number that can be expressed as a fraction is called a rational number. Therefore, 2/3 belongs to the subset of rational numbers.

2. -1: This number does not have any fractional or decimal part. It is a whole number but not a fraction. Whole numbers, including positive and negative integers, belong to the subset of integers. Therefore, -1 belongs to the subset of integers.

3. 17/4573: Similar to the first example, this number can be expressed as a fraction with an integer numerator and denominator. Hence, 17/4573 is a rational number.

4. Square root of 113: Irrational numbers cannot be expressed as fractions or ratios of integers. The square root of 113 is a decimal number that goes on forever without repeating or terminating. Therefore, the square root of 113 is an irrational number.

In summary:
- 2/3 and 17/4573 belong to the subset of rational numbers.
- -1 belongs to the subset of integers.
- The square root of 113 belongs to the subset of irrational numbers.