Which of the following is a rational number between 5 and 5 1/4?
√26, 5 1/7, 5 2/5, or 5 1/3?
To find a rational number between 5 and 5 1/4, we need to find a fraction greater than 5 and less than 5 1/4.
The fraction 5 1/3 is greater than 5 and less than 5 1/4. Therefore, the rational number between 5 and 5 1/4 is 5 1/3.
To find a rational number between 5 and 5 1/4, we need to look for a number that falls within this range and can be expressed as a ratio of two integers.
Let's examine the given options:
√26: The square root of 26 is an irrational number, as it cannot be expressed as a fraction.
5 1/7: This is a mixed fraction. To convert it to an improper fraction, we multiply the whole number (5) by the denominator (7) and add the numerator (1). That gives us (5 * 7) + 1 = 36/7.
This number is larger than 5 1/4.
5 2/5: Similar to the previous fraction, we convert this mixed fraction to an improper fraction. (5 * 5) + 2 = 25/5 + 2 = 27/5.
This number is larger than 5 1/4.
5 1/3: Again, we convert this mixed fraction to an improper fraction. (5 * 3) + 1 = 15/3 + 1 = 16/3.
This number is smaller than 5 1/4.
From the provided options, the rational number between 5 and 5 1/4 is 5 1/3, or 16/3.