This lesson explores the outcomes of adding and subtracting rational and irrational numbers. It begins by defining rational numbers as ratios of integers and irrational numbers as non-repeating decimals. The lesson explains that adding and subtracting require like terms, using examples to illustrate this concept. It demonstrates that the sum of two rational numbers is rational, while the sum of a rational and an irrational number is irrational. Special cases, such as adding an irrational number to itself, are also discussed. The lesson concludes by reinforcing the rules of counting and the nature of number types.

What is a characteristic of a rational number?

• It cannot be expressed as a ratio of integers.

• It can be expressed as a ratio of integers.

• It is always an integer.

• It has non-repeating decimals.

What happens when you add a rational number to an irrational number?

• The result is always irrational.

• The result is always rational.

• The result is always an integer.

• The result is always zero.

How can you prove that the sum of two rational numbers is rational?

• By converting them to decimals.

• By expressing them as ratios and finding a common denominator.

• By using a calculator.

• By showing their sum is an integer.

If X/Y is a rational number and B is irrational, what can be said about X/Y + B?

• It is always an integer.

• It is always zero.

• It is always irrational.

• It is always rational.

What is the result of adding an irrational number to itself?

• An irrational number

• An integer

• A rational number

• Zero

What is the result of adding pi to itself?

• A rational number

• An irrational number

• An integer

• Zero

What happens when you add a rational number to the inverse of an irrational number?

• The result is always rational.

• The result is always zero.

• The result is always irrational.

• The irrational parts cancel out.

What is the result of adding a rational number to its inverse?

• A rational number

• An integer

• An irrational number

• Zero

What is the result of adding two irrational numbers?

• Always irrational

• Always an integer

• Always zero

• Always rational

What is the result of adding a rational number to a rational number?

• Always irrational

• Always rational

• Always an integer

• Always zero