1. Properties of Rational and Irrational Numbers=?
Properties of Rational and Irrational Numbers
1 2 − 6 = ?
36 • 36 =?
2𝜋•3𝜋 = ?
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2. The sum of two Rational Numbers…
If we add two rational numbers, what is the result?
Real Number System 1 + 4 = 5 𝟒𝝅
− 𝟑 𝟕 + 3 =
−𝟒𝟒 3 𝟑𝟐 7 +
−10 = −3
− 2 3
5 8
− 1 24 + =
which is a rational number!
0.75 + 3 =
3.75
15 4
Rational numbers can be written as a simple fraction, a ratio of two integers.
Irrational numbers can NOT be written as a simple fraction. 4 +
- 4 =
Can only be written as non-perfect square root or in decimal form. The decimal is a non-terminating (keeps going and going) and the decimal does not have a pattern then the number is irrational.
The sum of two rational is a rational value.
Does not need to be converted into a decimal but if you choose to convert to decimal form, the decimal will terminate (stops) or has a pattern (repeating decimal) then the number is rational.
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3. The Product of two Rational Numbers…
If we multiply two rational numbers, what is the result?
Real Number System 1 • 4 = 4 𝟒𝝅
− 𝟑 𝟕 • 3 =
−𝟒𝟒 7 •
−10 =
−70
− 2 3
5 8
− 5 12 • =
which is a rational number
0.75 • 3 =
2.25
9 4
Rational numbers can be written as a simple fraction, a ratio of two integers.
Irrational numbers can NOT be written as a simple fraction. 4 •
- 4 = −4
The product of two rational is a rational value.
Can only be written as non-perfect square root or in decimal form. The decimal is a non-terminating (keeps going and going) and the decimal does not have a pattern then the number is irrational.
Does not need to be converted into a decimal but if you choose to convert to decimal form, the decimal will terminate (stops) or has a pattern (repeating decimal) then the number is rational.
Medina

4. The sum of A Rational Numbers And An Irrational…
If we add a rational number with an irrational number, what is the result?
Real Number System 1 + 2 = … 𝟒𝝅
− 𝟑 𝟕
−𝟒𝟒 + 𝜋 = … 7 +
− 5 = …
− 2 3 − + =
− …
0.75 +
123 = …
which is an irrational number
Rational numbers can be written as a simple fraction, a ratio of two integers.
Irrational numbers can NOT be written as a simple fraction. 4 + 4𝜋 = …
The sum of any non-zero rational number with an irrational number is always an irrational value.
Can only be written as non-perfect square root or in decimal form. The decimal is a non-terminating (keeps going and going) and the decimal does not have a pattern then the number is irrational.
Does not need to be converted into a decimal but if you choose to convert to decimal form, the decimal will terminate (stops) or has a pattern (repeating decimal) then the number is rational.
Medina

5. The Product of A Rational Numbers And An Irrational…
If we multiply a rational number with an irrational what is the result?
Real Number System 1 • 2 = … 𝟒𝝅
− 𝟑 𝟕
−𝟒𝟒
−44 • 𝜋 =
− … 7 •
− 5 = …
− 2 3 − • = …
0.75 •
123 = …
which is an irrational number
Rational numbers can be written as a simple fraction, a ratio of two integers.
Irrational numbers can NOT be written as a simple fraction. 4 • 4𝜋 = …
The product of any non-zero rational number with an irrational is always an irrational value.
Can only be written as non-perfect square root or in decimal form. The decimal is a non-terminating (keeps going and going) and the decimal does not have a pattern then the number is irrational.
Does not need to be converted into a decimal but if you choose to convert to decimal form, the decimal will terminate (stops) or has a pattern (repeating decimal) then the number is rational.
Medina

6. The sum of two Irrational Numbers…
If we multiply two irrational numbers, what is the result?
Real Number System 4𝜋 + 𝜋 = … 𝟒𝝅
− 𝟑 𝟕 2 +
123 =
−𝟒𝟒 … 𝜋 •+
− 5 = … −
− 5 + =
− …
which is a rational number
123 + 𝜋 = …
which is an irrational number
Rational numbers can be written as a simple fraction, a ratio of two integers.
Irrational numbers can NOT be written as a simple fraction. 2 +
- 2 =
The sum of two irrational is always an irrational value EXCEPT when the sum equals zero.
Can only be written as non-perfect square root or in decimal form. The decimal is a non-terminating (keeps going and going) and the decimal does not have a pattern then the number is irrational.
Does not need to be converted into a decimal but if you choose to convert to decimal form, the decimal will terminate (stops) or has a pattern (repeating decimal) then the number is rational.
Medina

7. The Product of two Irrational Numbers…
If we multiply two irrational numbers, what is the result?
Real Number System 4𝜋 • 𝜋 = … 𝟒𝝅
− 𝟑 𝟕 2 •
123 =
−𝟒𝟒 … 𝜋 •
− 5 =
− … −
− 5 • = …
which is a rational number
123 • 𝜋 = …
which is an irrational number
Rational numbers can be written as a simple fraction, a ratio of two integers.
Irrational numbers can NOT be written as a simple fraction. 2 •
- 2 = −2
The product of two irrational is an irrational value except in special cases where the product of non perfect square roots becomes a rational value.
Can only be written as non-perfect square root or in decimal form. The decimal is a non-terminating (keeps going and going) and the decimal does not have a pattern then the number is irrational.
Does not need to be converted into a decimal but if you choose to convert to decimal form, the decimal will terminate (stops) or has a pattern (repeating decimal) then the number is rational.
Medina