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Since it is a ratio of two integers, 5/15 is rational.

Since it is a terminating decimal, 3.8 is irrational
Which is all the true statements?"
Option 1: Statement 1
Option 2: Statement 2
Option 3: Both statements
Option 4: Neither statement

User GGAnderson
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1 Answer

5 votes

Final Answer:

Option 1: Statement 1 - This option is true.
Option 2: Statement 2 - This option is false.
Option 3: Both statements - This option is not correct because Statement 2 is false.
Option 4: Neither statement - This option is not correct because Statement 1 is true.

Step-by-step explanation:

Statement 1: "5/15 is rational"
To determine whether this statement is true, we need to understand what a rational number is. A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero.

The fraction 5/15 is equivalent to 1/3 after simplification (because both the numerator and denominator can be divided by 5).

Since 1 and 3 are both integers and 3 is not zero, 5/15 (or 1/3) can indeed be expressed as the ratio of two integers.

Therefore, 5/15 is a rational number, and Statement 1 is true.

Statement 2: "3.8 is irrational"
To evaluate this statement, we again need to refer to the definitions. A number is irrational if it cannot be expressed as a ratio of two integers.

However, 3.8 can be expressed as the fraction 38/10, which simplifies further to 19/5 (by dividing both numerator and denominator by 2). 19 and 5 are both integers, and 5 is not zero, which means that 3.8 is the ratio of two integers.

As a result, 3.8 is a rational number, not an irrational one, so Statement 2 is false.

Therefore, the correct answer to the question is Option 1: Statement 1.

User Sph
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