Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
start root 26 end root
5 2/5
5 Start Fraction 2 over 5 end fraction
5 1/7
5 Start Fraction 1 over 7 end fraction
5 1/3
5 2/5
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 between √7 and √8 with a denominator of 7, we need to calculate the square roots and find a value that lies between them.
The square root of 7 is approximately 2.65, and the square root of 8 is approximately 2.83.
To find a rational number between these two values, we can use the average:
(2.65 + 2.83)/2 = 2.74
So, one rational number with a denominator of 7 between √7 and √8 is 2.74.
To write this as an improper fraction, we can multiply both the numerator and denominator by 7 to get rid of the decimal:
2.74 * 7 = 19.18 (approximately)
The improper fraction for the rational number 19.18 with a denominator of 7 is 191/7.
To determine which of the options is a rational number between 5 and 514, we need to determine if each option can be written as a fraction.
Option 1: √26
This is an irrational number since it involves the square root of a non-perfect square.
Option 2: 5 2/5
This is a mixed number and can be written as a fraction.
Option 3: 5 1/7
This is also a mixed number and can be written as a fraction.
Option 4: 5 1/3
This is also a mixed number and can be written as a fraction.
Since options 2, 3, and 4 can be written as fractions, they are rational numbers. Now we need to check if they lie between 5 and 514.
Option 2: 5 2/5
To convert this mixed number to an improper fraction, we can multiply the whole number (5) by the denominator of the fraction (5) and then add the numerator (2), giving us 27/5.
Option 3: 5 1/7
To convert this mixed number to an improper fraction, we can multiply the whole number (5) by the denominator of the fraction (7) and then add the numerator (1), giving us 36/7.
Option 4: 5 1/3
To convert this mixed number to an improper fraction, we can multiply the whole number (5) by the denominator of the fraction (3) and then add the numerator (1), giving us 16/3.
Now we can compare these fractions to see if they lie between 5 and 514.
27/5 is approximately 5.4, which lies between 5 and 514.
36/7 is approximately 5.14, which also lies between 5 and 514.
16/3 is approximately 5.33, which also lies between 5 and 514.
Therefore, the rational numbers between 5 and 514 are the following options:
- Option 2: 5 2/5
- Option 3: 5 1/7
- Option 4: 5 1/3
To find a rational number between 5 and 514, we need to look for a number that lies between these two values.
Let's evaluate the given options:
1. √26 is irrational because it involves taking the square root of a non-perfect square, so we can eliminate this option.
2. 5 2/5 is a rational number, but it is equal to 5.4, which is less than 514.
3. 5 1/7 is a rational number, but it is equal to 5.14285714..., which is also less than 514.
4. 5 1/3 is a rational number, and it is equal to 5.3333..., which is between 5 and 514.
Therefore, the rational number between 5 and 514 is 5 1/3.