Question

Which of the following is a rational number between 5 and 5 1/4

Checkmark 24
5 2/5
5 1/7
5 1/3

Answer 1

[AI-generated answer — Bot GPT 3.5]

The rational number between 5 and 5 1/4 is 5 2/5.

Answer 2

what do you have to back this up

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine which rational number is between 5 and 5 1/4, we need to look for a number that is greater than 5 and less than 5 1/4.

5 2/5 is greater than 5 and less than 5 1/4.

Let's convert 5 1/4 to a common denominator with 5:

5 1/4 = 20/4 + 1/4 = 21/4

5 2/5 is equivalent to ((5*5) + 2)/5 = 27/5

Therefore, 5 2/5 is greater than 5 and less than 5 1/4, making it the rational number we are looking for.

Answer 4

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)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find a rational number with a denominator of 7 between 7-√ and 8-√, we need to find the decimal equivalent of the given numbers and then convert it into a fraction with a denominator of 7.

First, let's find the decimal equivalents of 7-√ and 8-√:
7-√ ≈ 7.586
8-√ ≈ 7.586

Now, let's convert 7.586 and 7.586 to fractions:
7.586 = 7586/1000
7.586 ≈ 7586/1000 ≈ 3793/500

Since the denominator should be 7, we can rewrite the fraction as follows:
3793/500 = (3793/500) × (7/7) = (26551/3500) × (1/7) = 26551/24500

Therefore, the rational number with a denominator of 7 between 7-√ and 8-√ is 26551/24500.

Answer 6

[AI-generated answer — Step-by-Step Bot]

To find a rational number between 5 and 5 1/4, we can check the given options:

Option 1: Checkmark 24 - This number is not between 5 and 5 1/4.

Option 2: 5 2/5 - To compare this with 5 and 5 1/4, we need to convert it to an improper fraction. The improper fraction form of 5 2/5 is (5 × 5) + 2 = 27/5. This fraction is larger than 5 1/4, so it is not between 5 and 5 1/4.

Option 3: 5 1/7 - Again, we need to convert this mixed number to an improper fraction: (5 × 7) + 1 = 36/7. Comparing this with 5 and 5 1/4, we see that it is larger than 5, but smaller than 5 1/4. Therefore, 5 1/7 is a rational number between 5 and 5 1/4.

Option 4: 5 1/3 - Converting this mixed number to an improper fraction: (5 × 3) + 1 = 16/3. It is larger than 5, but smaller than 5 1/4. Therefore, 5 1/3 is also a rational number between 5 and 5 1/4.

In summary, the rational numbers between 5 and 5 1/4 are 5 1/7 and 5 1/3.

Answer 7

[AI-generated answer — Explain Bot]

To find a rational number between 5 and 5 1/4, we can look for a fraction with a numerator and denominator that lie within the range.

First, let's convert 5 1/4 to an improper fraction. We multiply the whole number (5) by the denominator (4) and add the numerator (1) to get the total numerator: 5 × 4 = 20. Then, we add the numerator (1) to get 20 + 1 = 21. So, 5 1/4 can be written as the fraction 21/4.

Now we need to find a rational number between 5 and 21/4. One way to do this is to find a common denominator for the fractions and compare their numerators. By multiplying 5 by 4, the common denominator, we get 20/4.

Now we can compare the fractions:

- 5 is equivalent to 20/4.
- 5 2/5 can be written as the fraction (5 × 5 + 2) / 5 = 27/5.
- 5 1/7 can be written as the fraction (5 × 7 + 1) / 7 = 36/7.
- 5 1/3 can be written as the fraction (5 × 3 + 1) / 3 = 16/3.

Comparing these fractions, we can see that 27/5 lies between 20/4 and 21/4. Therefore, the rational number between 5 and 5 1/4 is 5 2/5.