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

explain how 5 1/7 is the correct answer

3 answers

To determine a rational number between 5 and 5 1/4, we need to find a number that lies between these two values and can be expressed as a fraction.

To do this, we can convert 5 into a fraction with a common denominator. The number 5 is equivalent to 5/1. Now, since the denominators are the same, we can compare the numerators.

The fraction 5 1/4 can be rewritten as 5/1 and 5/4. To find a rational number between these two fractions, we can add them and divide the sum by 2.

(5/1 + 5/4)/2 = (20/4 + 5/4)/2 = 25/4/2 = 25/8

So, 25/8 is a rational number between 5 and 5 1/4.

However, the given answer of 5 1/7 is incorrect as it is greater than 5 1/4, which contradicts the requirement of finding a number between these two values.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.

explain how 8/11 is the correct answer
To convert the repeating decimal 0.72¯¯¯¯¯¯ to a rational number, we can call it x and use algebraic manipulation to solve for x.

Let's represent 0.72¯¯¯¯¯¯ as x:
x = 0.72¯¯¯¯¯¯

Now, we multiply both sides of the equation by 100 to remove the repeating decimal:
100x = 72.72¯¯¯¯¯¯

Next, we subtract the original equation from the multiplied equation to eliminate the repeating decimal:
100x - x = 72.72¯¯¯¯¯¯ - 0.72¯¯¯¯¯¯
99x = 72

Dividing both sides of the equation by 99, we find:
x = 72/99

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 9:

72 ÷ 9 = 8
99 ÷ 9 = 11

Therefore, 0.72¯¯¯¯¯¯ is equivalent to the rational number 8/11 in simplest form.