Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). Examples include \( \frac{1}{2}, 3, -4.5 \).

Tags

CCSS.5.NBT.A.2

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction. It cannot be written as \( \frac{a}{b} \) where \( a \) and \( b \) are integers. Examples include \( \sqrt{2}, \pi, e \).

Tags

CCSS.8.NS.A.1

Front

Is the sum of a rational number and an irrational number rational or irrational?

Back

The sum of a rational number and an irrational number is always irrational.

Tags

CCSS.7.NS.A.1D

Front

Is the product of two irrational numbers always irrational?

Back

No, the product of two irrational numbers can be rational. For example, \( \sqrt{2} \times \sqrt{2} = 2 \), which is rational.

Tags

CCSS.HSN.RN.B.3

Front

What is the result of adding two irrational numbers?

Back

The sum of two irrational numbers can be either rational or irrational. For example, \( \sqrt{2} + (-\sqrt{2}) = 0 \) (rational), but \( \sqrt{2} + \sqrt{3} \) is irrational.

Tags

CCSS.7.NS.A.1D

Front

What is the definition of a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are polynomials. For example, \( \frac{x^2 + 1}{x - 3} \) is a rational expression.

Tags

CCSS.HSA.APR.D.7

Front

Can a rational number be expressed as a decimal?

Back

Yes, a rational number can be expressed as a decimal that either terminates (e.g., 0.75) or repeats (e.g., 0.333...).

Tags

CCSS.7.NS.A.2D

CCSS.8.NS.A.1

Front

What is the significance of the square root of a non-perfect square?

Back

The square root of a non-perfect square is an irrational number. For example, \( \sqrt{3} \) is irrational.

Tags

CCSS.8.NS.A.1

Front

Is the number 0 a rational number?

Back

Yes, 0 is a rational number because it can be expressed as \( \frac{0}{1} \).

Tags

CCSS.HSN.RN.B.3

Front

What is the product of a rational number and an irrational number?

Back

The product of a rational number and an irrational number is always irrational. For example, \( 2 \times \sqrt{3} = 2\sqrt{3} \) is irrational.

Tags

CCSS.HSN.RN.B.3