Flashback #39 (Mixed Review)

Front

What are rational numbers?

Back

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Examples include \( \frac{1}{2}, 3, -4.5 \).

Front

What is a tree diagram in set theory?

Back

A tree diagram is a visual representation that shows the relationships between sets and subsets, illustrating how elements are grouped.

Front

Identify the set of rational numbers from the following: \( \{ 4, 8, 0, -2 \} \)

Back

All numbers in this set are rational numbers because they can be expressed as fractions.

Front

Which of the following is not a rational number: \( \sqrt{11}, 3, 0, \sqrt{4} \)?

Back

\( \sqrt{11} \) is not a rational number because it cannot be expressed as a fraction of two integers.

Front

What is the square root of 81?

Back

The square root of 81 is 9, since \( 9 \times 9 = 81 \).

Front

How do you determine if a number is rational?

Back

A number is rational if it can be written as \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

Front

What is the relationship between integers and rational numbers?

Back

All integers are rational numbers because any integer \( n \) can be expressed as \( \frac{n}{1} \).

Front

Provide an example of a rational number that is negative.

Back

An example of a negative rational number is -3, which can be expressed as \( \frac{-3}{1} \).

Front

What is the decimal representation of \( \frac{1}{4} \)?

Back

The decimal representation of \( \frac{1}{4} \) is 0.25.

Front

List the rational numbers from the set: \( \{ \sqrt{4}, 5.2, 7, \frac{1}{2} \} \).

Back

The rational numbers in this set are \( \sqrt{4} = 2, 5.2, 7, \frac{1}{2} \).