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
11 answers
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.
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.
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.
√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.
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.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.
Rational numbers and whole numbers are related, but they are not the same.
All whole numbers are rational numbers because they can be expressed as a fraction with a denominator of 1. For example, 5 can be written as 5/1, which is a fraction.
However, not all rational numbers are whole numbers. Rational numbers are any numbers that can be expressed as a fraction, where the numerator and denominator are both integers. This includes fractions such as 2/3 and -4/5, as well as decimals like 0.75.
Examples of rational numbers that are not whole numbers are 2/3 and -4/5. These fractions are rational numbers because they can be expressed as the ratio of two integers. However, they are not whole numbers because they are not integers themselves.
To summarize, all whole numbers are rational numbers, but not all rational numbers are whole numbers. Whole numbers are a subset of rational numbers.
All whole numbers are rational numbers because they can be expressed as a fraction with a denominator of 1. For example, 5 can be written as 5/1, which is a fraction.
However, not all rational numbers are whole numbers. Rational numbers are any numbers that can be expressed as a fraction, where the numerator and denominator are both integers. This includes fractions such as 2/3 and -4/5, as well as decimals like 0.75.
Examples of rational numbers that are not whole numbers are 2/3 and -4/5. These fractions are rational numbers because they can be expressed as the ratio of two integers. However, they are not whole numbers because they are not integers themselves.
To summarize, all whole numbers are rational numbers, but not all rational numbers are whole numbers. Whole numbers are a subset of rational numbers.
20 answers