what other way can –4 be represented as a rational number?
1) -24/6
2) -v12/3
3) 1/4
4) v144/3
Option 1) -24/6 is equivalent to -4, so it is another way to represent -4 as a rational number.
Option 2) -v12/3 can be simplified to -2v3, which is not equal to -4.
Option 3) 1/4 is not equal to -4.
Option 4) v144/3 can be simplified to 12v3, which is not equal to -4.
Therefore, the only other way to represent -4 as a rational number is option 1) -24/6.
To represent -4 as a rational number, we need to find an equivalent fraction where the numerator and denominator are integers and have no common factors other than 1. Let's examine each option:
1) -24/6: We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 6. This simplifies the fraction to -4/1, which is the same as -4.
2) -√12/3: The square root (√) in the numerator indicates an irrational number, as the square root of 12 is not a rational number. Therefore, this option does not represent -4 as a rational number.
3) 1/4: This fraction does not represent -4, as it is equal to 0.25.
4) √144/3: Similar to option 2, the square root (√) in the numerator indicates an irrational number. The square root of 144 is a rational number, which is 12. Therefore, this option does not represent -4 as a rational number.
From the given options, only option 1 (-24/6) represents -4 as a rational number.
In order to find the other way that -4 can be represented as a rational number, we need to first understand what a rational number is. A rational number can be expressed as the ratio of two integers, where the denominator is not zero.
To find the other way -4 can be represented as a rational number, let's evaluate the options given:
1) -24/6: Let's simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which in this case is 6. By dividing -24 by 6, we get -4. Therefore, -24/6 is equal to -4.
2) -√12/3: The square root of 12 is equal to √(4 × 3), and simplifying it further, we get √4 × √3, which is 2√3. Therefore, -√12/3 is not equal to -4.
3) 1/4: This fraction represents the number 0.25, which is not equal to -4.
4) √144/3: The square root of 144 is equal to √(12 × 12), which simplifies to 12. Therefore, √144/3 is equal to 12/3, which is 4 and not -4.
So, out of the given options, the only accurate representation of -4 as a rational number is -24/6 (option 1).