Choose which group of sets the following number belongs to. Be sure to account for ALL sets.
-6/7
Part 1
A.
real numbers, rational numbers
B.
real numbers, irrational numbers
C.
real numbers, rational numbers, natural numbers
D.
rational numbers, natural numbers, integers
E.
irrational numbers, natural numbers
The number -6/7 belongs to the following group of sets:
A. real numbers, rational numbers
The number -6/7 belongs to the group of sets: A. real numbers, rational numbers.
To determine which group of sets the number -6/7 belongs to, we need to understand the definitions of these sets.
1. Real numbers: Real numbers include all rational numbers and irrational numbers. Real numbers can be represented on a number line.
2. Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They can be positive, negative, or zero. Examples include integers, fractions, and terminating or repeating decimals.
3. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They cannot be written as a terminating or repeating decimal. Examples include the square root of 2 (√2) and pi (π).
4. Natural numbers: Natural numbers are positive whole numbers starting from 1 and excluding zero. They do not include fractions or decimals.
5. Integers: Integers include all natural numbers (positive whole numbers), their negatives, and zero. They can be represented on a number line.
Now, let's analyze the given number, -6/7.
-6/7 is a fraction where both the numerator and denominator are integers. It can be expressed as a ratio of two integers.
Since it can be expressed as a fraction and satisfies the definition of a rational number, we can conclude that -6/7 belongs to the set of rational numbers.
Therefore, the correct answer is option A: real numbers, rational numbers.