Which of the following is a rational number between 5 and 5 1/4?
Responses
√26
5 1/13
5 2/5
5 1/7
The rational number between 5 and 5 1/4 is 5 1/13.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(1 point)
To find a rational number with a denominator of 7 between 7-√ and 8-√, we can note that the rational number will have a numerator that is one less than 8-√.
So, the numerator will be 8-√ - 1 = 7-√.
Therefore, the rational number is (7-√)/7, which can be written as an improper fraction as 7/7 - √/7. Simplifying this, we get:
7/7 - √/7 = 1 - √/7 = (7 - √)/7.
So, the rational number with a denominator of 7 between 7-√ and 8-√ is (7 - √)/7 as an improper fraction.
What is a rational number with a denominator of 7 that is between √7 and √8. Write your answer as an improper fraction.
To find a rational number with a denominator of 7 between √7 and √8, we can start by rationalizing the denominators of √7 and √8.
The rationalizing factor for √7 is √7/√7, which gives us (√7)/√7 = 1.
The rationalizing factor for √8 is √8/√8, which gives us (√8)/√8 = 2.
Now, we can rewrite the inequality as follows:
√7 < rational number < √8
1 * √7 < rational number * √7 < 2 * √7
√7 < rational number * √7 < 2√7
Now, to make the denominator 7, we need the denominator of the rational number * √7 to be equal to 7. Therefore, the denominator of the rational number must be 1/√7.
So, the rational number with a denominator of 7 between √7 and √8 is (√7)/(1/√7) = √7 * √7 = 7.
Therefore, the rational number is 7/7, which can be simplified to 1.
So, the rational number with a denominator of 7 between √7 and √8 is 1 as an improper fraction.
shorter
To find a rational number with a denominator of 7 between √7 and √8, we can approximate the values of √7 and √8.
√7 is approximately equal to 2.64575.
√8 is approximately equal to 2.82843.
The rational number with a denominator of 7 that is between these approximated values is 3/7.
Therefore, a rational number with a denominator of 7 between √7 and √8 is 3/7.
what would it be as a rational number as a improper fraction
I apologize for the mistake in my previous response. To clarify, we are looking for a rational number with a denominator of 7 that lies between √7 and √8.
The square root of 7 is approximately 2.64575, and the square root of 8 is approximately 2.82843.
The rational number with a denominator of 7 that lies between these two values can be found by taking the average of the two approximations: (2.64575 + 2.82843)/2 = 2.73709.
So, a rational number with a denominator of 7 that lies between √7 and √8 is approximately 2.73709.
To write this number as an improper fraction, we can multiply it by 7/7 to get:
2.73709 * 7/7 = 19.15963/7
Therefore, the rational number with a denominator of 7 between √7 and √8 can be expressed as the improper fraction 19.15963/7.