Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
start root 26 end root
517
5 Start Fraction 1 over 7 end fraction
525
5 Start Fraction 2 over 5 end fraction
513
5 Start Fraction 26 over 5 end fraction
Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
start root 26 end root
517
5 Start Fraction 1 over 7 end fraction
525
5 Start Fraction 2 over 5 end fraction
513
5 Start Fraction 1 over 3 end fraction
In this case, the rational number between 5 and 514 is 5 Start Fraction 1 over 3 end fraction.
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)
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To find a rational number with a denominator of 7 between 7–√ and 8–√, we take the average of these two numbers.
The average of 7–√ and 8–√ can be calculated as follows:
(7–√ + 8–√) / 2 = (15 – 2√) / 2
To get a denominator of 7, we multiply both the numerator and denominator by 7:
[(15 – 2√) / 2] * (7/7) = (105 – 14√) / 14
Therefore, the rational number with a denominator of 7 between 7–√ and 8–√ is (105 – 14√) / 14.
i don't understand
I apologize for the confusion. Let's break down the steps:
1. We have two numbers, 7−√ and 8−√. These are both irrational numbers because they have a square root in them.
2. To find a rational number between these two, we want to find the average of these two numbers. The average can be calculated by adding these two numbers and then dividing the sum by 2.
(7−√ + 8−√) / 2 = (15−2√) / 2
3. However, we want the denominator to be 7. To accomplish this, we can multiply the numerator and denominator by 7.
[(15−2√) / 2] * (7/7) = (105−14√) / 14
Therefore, the rational number with a denominator of 7 that lies between 7−√ and 8−√ is (105−14√) / 14.
Please let me know if you still have any questions or need further clarification.
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.(4 points)
The relationship between rational numbers and whole numbers is that every whole number is a rational number, but not every rational number is a whole number.
A whole number is an integer that does not have a fraction or decimal part. Examples of whole numbers include 0, 1, 2, 3, and so on. Whole numbers can also be negative, such as -1, -2, -3, etc.
Rational numbers, on the other hand, include all numbers that can be expressed as a ratio of two integers (where the denominator is not zero). This means that rational numbers include both whole numbers and fractions. For example, 2/3, -1/2, and 4 are all rational numbers.
So, while all whole numbers are rational numbers because they can be expressed as a ratio of themselves over 1, not all rational numbers are whole numbers. The distinction lies in the presence of a fractional or decimal component in rational numbers that are not whole numbers. For instance, 3/5 and 1.2 are rational numbers, but they are not whole numbers.
In summary, all whole numbers are rational numbers, but not all rational numbers are whole numbers.