Nine times the reciprocal of a rational number equals 6 times the reciprocal of 17.Find the rational number
9(1/x) = 6(1/17)
9/x = 6/17
6x = 153
x = 153/6
= 51/2
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Let's call the rational number "x." So, nine times the reciprocal of x can be written as 9 * (1/x). Similarly, six times the reciprocal of 17 can be written as 6 * (1/17).
Now, according to the problem, we have the equation:
9 * (1/x) = 6 * (1/17)
To make things easier, let's find the common denominator between x and 17. And, since we're dealing with fractions, let's imagine they're at a party. So, x and 17 walk up to the DJ and request the common denominator song! 🎵
The common denominator for x and 17 is 17x. So, the equation becomes:
(9 * 17) / x = (6 * x) / 17
Now, we'll cross-multiply and get:
9 * 17 = 6 * x^2
Simplifying this, we have:
153 = 6 * x^2
Dividing both sides by 6, we get:
25.5 = x^2
Taking the square root of both sides, we find that:
x = ±√25.5
Therefore, the rational number can be written as either x = √25.5 or x = -√25.5.
So, the rational number could be a positive or negative square root of 25.5.
Let's solve the problem step by step:
Step 1: Let's assume the rational number we need to find as "x".
Step 2: The reciprocal of "x" is denoted as 1/x.
Step 3: The statement "Nine times the reciprocal of a rational number" can be written as 9 * (1/x).
Step 4: The statement "equals" can be represented as an equal sign "=".
Step 5: The statement "6 times the reciprocal of 17" can be written as 6 * (1/17).
Putting it all together, we have the equation:
9 * (1/x) = 6 * (1/17)
Step 6: To solve for "x", we can cross-multiply. This means multiplying both sides of the equation by the denominators:
9 * 17 * (1/x) = 6 * 1
Step 7: Simplifying the equation:
(9 * 17) / x = 6
Step 8: Further simplifying:
153 / x = 6
Step 9: To isolate "x" on one side of the equation, we can multiply both sides by "x":
(153 / x) * x = 6 * x
Step 10: Simplifying the equation:
153 = 6x
Step 11: Divide both sides of the equation by 6 to solve for "x":
153 / 6 = (6x) / 6
25.5 = x
Therefore, the rational number we are looking for is 25.5.
To find the rational number described in the problem, we can follow these steps:
Step 1: Let's assume the rational number we are looking for is represented by 'x'.
Step 2: The reciprocal of a number is obtained by taking the inverse of the number, which means dividing 1 by that number. So, the reciprocal of 'x' is 1/x.
Step 3: According to the problem, "Nine times the reciprocal of a rational number equals 6 times the reciprocal of 17." Mathematically, this can be represented as:
9 * (1/x) = 6 * (1/17)
Step 4: We can simplify this equation by multiplying both sides by 'x' and 17 to eliminate the fractions:
9 * (1/x) * x * 17 = 6 * (1/17) * x * 17
9 * 17 = 6 * x
Step 5: Now we can solve for 'x' by dividing both sides of the equation by 6:
(9 * 17) / 6 = x
153 / 6 = x
x = 25.5
Therefore, the rational number that satisfies the given equation is 25.5.