Which of the following is a rational number between 5 and 5 1/4?
explain how 5 1/7 is the correct answer
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.
To find a rational number between 5 and 5 1/4, we need to look for a fraction that lies between these two numbers.
We can start by converting both 5 and 5 1/4 to fractions with the same denominator. The denominator will be 4 because it is the least common multiple of 1 and 4.
- 5 can be written as 20/4, since 5 multiplied by 4 is 20.
- 5 1/4 is already in fraction form with the same denominator, so it is 21/4.
Now, we need to find a fraction between 20/4 and 21/4. One way to do this is by taking the average of the two fractions. To find the average, we add the two fractions and divide the result by 2:
(20/4 + 21/4) / 2
Combining the fractions, we get:
(41/4) / 2
To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number. In this case, we want to divide by 2, so we multiply by 1/2:
41/4 * 1/2
Multiplying the numerators gives us 41, and multiplying the denominators gives us 8:
41/8
Therefore, the rational number between 5 and 5 1/4 is 41/8.
However, this does not match the answer you provided in your question. If you believe that 5 1/7 is the correct answer, please double-check your work or provide additional information on how you arrived at that answer.