You probably know that guide dogs are used to lead blind people. Did you know that a few blind people have guide horses? These are miniature horses trained much as guide dogs are. The small horses respond to more than 25 commands. They can see well in the dark. They are also trained to tap with a hoof on the door if they need to go out. One man has even taken his guide horse on an airplane!

The main idea of this paragraph is

A. How guide dogs are trained

B. A guide horse on an airplane

C. The use of small horses as guides

D. Why blind people like animals

C. The use of small horses as guides

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Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.

Rational numbers and whole numbers are related to each other, but they are not the same.

A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers (whole numbers), and the denominator is not zero. This includes numbers like 1/2, 3/4, and -5/6.

On the other hand, whole numbers are a set of numbers that include all the natural numbers (positive integers) and zero (0). These include numbers like 0, 1, 2, 3, and so on.

It is important to note that while all whole numbers can be expressed as fractions by placing them over 1 (e.g., 5 can be written as 5/1), not all rational numbers are whole numbers. For example, 3/2 is a rational number, but it is not a whole number since it is not an integer.

On the other hand, all whole numbers can be considered rational numbers because they can be expressed as fractions with a denominator of 1 (e.g., 5 = 5/1).

To summarize, all whole numbers can be considered rational numbers, but not all rational numbers are whole numbers.

So are all whole numbers also rational numbers?

Yes, all whole numbers can be considered rational numbers. This is because a rational number is any number that can be expressed as a fraction, and whole numbers can be expressed as fractions by placing them over 1. For example, 5 can be written as 5/1, and 0 can be written as 0/1. Since these can be expressed as fractions with integer numerators and denominators, they are rational numbers.

but are all rational numbers whole numbers?

No, not all rational numbers are whole numbers. While whole numbers can be expressed as fractions with a denominator of 1, not all rational numbers can be represented in this form. For example, the rational number 3/2 is not a whole number because it is not an integer. Similarly, -4/3 is a rational number, but it is not a whole number since it is not a non-negative integer or zero. Therefore, while all whole numbers can be considered rational numbers, not all rational numbers can be considered whole numbers.

wow, that's neat