Which of the following is a rational number between 5 and 5 1/4?
Square root of 26
5 1/7
5 1/3
5 2/5
The rational number between 5 and 5 1/4 is 5 1/7.
To find a rational number between 5 and 5 1/4, we need to look for a fraction that lies between those two numbers.
To compare fractions, we can convert them to a common denominator. In this case, we can convert 5 to a fraction with the common denominator of 4, which gives us 20/4.
Now, we can compare the fractions:
20/4 is equivalent to 5, 5 1/4 is equivalent to 21/4.
To find a rational number between 5 and 5 1/4, we need to find a fraction that is greater than 5 and less than 5 1/4.
Option 5 1/7 is greater than both 5 and 5 1/4, so it is not the answer.
Option 5 1/3 is also greater than both 5 and 5 1/4, so it is not the answer.
Option 5 2/5 is less than both 5 and 5 1/4, so it is not the answer.
Therefore, the rational number between 5 and 5 1/4 is the square root of 26.
To find a rational number between 5 and 5 1/4, we need to find a number with a denominator larger than 4 that lies between 5 and 5 1/4.
Let's start by converting 5 1/4 to an improper fraction.
5 1/4 = (5 * 4 + 1) / 4 = 21/4
Now, let's find a rational number between 5 and 21/4 by comparing the numerators and denominators of the given options:
Option 1: Square root of 26
The square root of 26 is an irrational number, so it is not a rational number.
Option 2: 5 1/7
To compare this option, we need to convert it to an improper fraction:
5 1/7 = (5 * 7 + 1) / 7 = 36/7
36/7 is larger than 21/4, so it is not between 5 and 5 1/4.
Option 3: 5 1/3
To compare this option, we need to convert it to an improper fraction:
5 1/3 = (5 * 3 + 1) / 3 = 16/3
16/3 is larger than 21/4, so it is not between 5 and 5 1/4.
Option 4: 5 2/5
To compare this option, we need to convert it to an improper fraction:
5 2/5 = (5 * 5 + 2) / 5 = 27/5
27/5 is smaller than 21/4 and larger than 5, so it lies between 5 and 5 1/4.
Therefore, the rational number between 5 and 5 1/4 is 5 2/5.