Rational Numbers

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What is a rational number?

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where the numerator p is an integer, and the denominator q is a non-zero integer.

Can a whole number be considered a rational number? Why or why not?

Yes, a whole number is a rational number because it can be expressed as a fraction with the whole number as the numerator and 1 as the denominator.

Is the number 0 a rational number?

Yes, 0 is a rational number because it can be represented as 0/1.

Are all integers rational numbers?

Yes, all integers are rational because any integer z can be written as z/1.

Give an example of a negative rational number.

Examples of negative rational numbers include -3/4 or -2.

Explain how to determine if a number is rational.

A number is rational if it can be written as a fraction a/b where a and b are integers, and b is not zero.

Is the number π (pi) a rational number? Why or why not?

No, pi is not a rational number because it is an irrational number; it cannot be expressed as a simple fraction or decimal.

What is the decimal representation of every rational number like?

The decimal representation of every rational number either terminates or repeats.

Explain whether 1.25 is a rational number and why.

Yes, 1.25 is a rational number because it can be expressed as a fraction 5/4.

Are fractions like 2/3 considered rational numbers?

Yes, fractions like 2/3 are considered rational numbers as both the numerator and denominator are integers, and the denominator is not zero.

Is the square root of 4 a rational number? Explain.

Yes, the square root of 4 is rational because it equals 2, which can be expressed as 2/1.

How do rational numbers behave with addition and subtraction?

Rational numbers are closed under addition and subtraction, meaning if you add or subtract two rational numbers, the result is also a rational number.

Explain how multiplication affects rational numbers.

Rational numbers are closed under multiplication; multiplying two rational numbers always results in another rational number.

What is the result of dividing two rational numbers?

The result of dividing one rational number by another (except division by zero) is also a rational number.

Describe how to convert a repeating decimal into a fraction.

To convert a repeating decimal to a fraction, set the repeating decimal to a variable, then multiply by a power of 10 that moves the repeating part next to the decimal point, subtract, and solve for the fraction.





Test Your Knowledge

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1. What is a rational number?

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where the numerator p is an integer, and the denominator q is a non-zero integer.

A number that cannot be expressed as a simple fraction.

A number that is greater than zero.

A number that is a multiple of an integer.

2. Can a whole number be considered a rational number? Why or why not?

Yes, a whole number is a rational number because it can be expressed as a fraction with the whole number as the numerator and 1 as the denominator.

No, because whole numbers cannot be expressed as fractions.

Yes, but only if the whole number is negative.

No, because rational numbers must include decimals.

3. Is the number 0 a rational number?

No, 0 cannot be a rational number as it is neither positive nor negative.

Yes, 0 is a rational number because it can be represented as 0/1.

Yes, because 0 is an integer and integers are irrational.

No, because it cannot be expressed as a non-zero fraction.

4. Are all integers rational numbers?

Yes, all integers are rational because any integer z can be written as z/1.

No, only positive integers are rational numbers.

Yes, but only even integers.

No, integers are not usually considered rational.

5. Give an example of a negative rational number.

47/3

-3/4

0.25

2/1

6. Explain how to determine if a number is rational.

A number is rational if it can be written as a fraction a/b where a and b are integers, and b is not zero.

A number is rational if it can be expressed as a whole number.

A number is rational if it repeats forever.

A number is rational only if both a and b are even numbers.

7. Is the number π (pi) a rational number? Why or why not?

Yes, pi can be approximated as 22/7, a rational number.

Yes, because pi is used in rational calculations.

No, pi is not a rational number because it is an irrational number; it cannot be expressed as a simple fraction or decimal.

No, pi is rational because it is a constant.

8. What is the decimal representation of every rational number like?

The decimal representation of every rational number either terminates or repeats.

The decimal representation of a rational number is always non-repeating.

It never terminates nor repeats.

It terminates but never repeats.

9. Explain whether 1.25 is a rational number and why.

Yes, 1.25 is a rational number because it can be expressed as a fraction 5/4.

Yes, 1.25 is a rational number because it is a whole number.

No, 1.25 is not a rational number because it is a decimal.

No, because 1.25 is less than 2.

10. Are fractions like 2/3 considered rational numbers?

Yes, fractions like 2/3 are considered rational numbers as both the numerator and denominator are integers, and the denominator is not zero.

No, fractions are not considered rational numbers.

Yes, but only if the numerator is less than the denominator.

Only if the fraction simplifies to a whole number.

11. Is the square root of 4 a rational number? Explain.

No, square roots are never rational numbers.

Yes, the square root of 4 is rational because it equals 2, which can be expressed as 2/1.

Yes, because it is an even number.

No, because 4 is not a prime number.

12. How do rational numbers behave with addition and subtraction?

Rational numbers change form with operations.

Rational numbers are closed under addition and subtraction, meaning if you add or subtract two rational numbers, the result is also a rational number.

Addition and subtraction of rational numbers result in irrational numbers.

They cannot be added or subtracted.

13. Explain how multiplication affects rational numbers.

Rational numbers are closed under multiplication; multiplying two rational numbers always results in another rational number.

Multiplying rational numbers can sometimes result in irrational numbers.

Multiplying two rational numbers results in a greater non-rational number.

It results in a decimal format.

14. What is the result of dividing two rational numbers?

Dividing two rational numbers always results in an irrational number.

It results in zero.

The result of dividing one rational number by another (except division by zero) is also a rational number.

It is not defined.

15. Describe how to convert a repeating decimal into a fraction.

By guessing the fraction that matches the decimal best.

Converting involves only knowing the decimal and moving it two places.

To convert a repeating decimal to a fraction, set the repeating decimal to a variable, then multiply by a power of 10 that moves the repeating part next to the decimal point, subtract, and solve for the fraction.

Repeating decimals cannot be converted to fractions.