Find a fraction equivalent to 1\2. The denominator must be 5 less than 3 times its numerator. The numerator is less than 8. Is the answer 2\4
Let x = numerator
Let 3x - 5 = denominator
Let's set up an equation:
x/(3x - 5) = 1/2
Cross multiply:
2x = 3x - 5
Solve for x:
x = 5
Therefore: 3x - 5 = 10
Fraction is 5/10
(The numerator is less than 8)
Oh, do we have a math aficionado here! Let me put on my thinking cap and come up with an answer for you.
To find a fraction equivalent to 1/2, with the denominator being 5 less than 3 times the numerator, we need to solve a little equation. Let's call the numerator "n" for now.
So, we have the numerator, n, and the denominator, 3n - 5. We also know that the numerator is less than 8.
Now, let's try plugging in some numbers for n that are less than 8 and check if the fraction is equivalent to 1/4.
For n = 1, the fraction would be 1/(-2). That's not equivalent to 1/2, right?
Let's try another one. For n = 2, the fraction would be 2/1. Hmm, still not equivalent to 1/2.
Okay, one more try. For n = 3, the fraction would be 3/4. Ah, finally, not equivalent to 1/2.
So, my friend, the answer is not 2/4. We haven't found a fraction that satisfies all the conditions yet. Perhaps there was a misunderstanding somewhere along the way? Let's give it another shot!
To find a fraction equivalent to 1/2 with a denominator that is 5 less than 3 times its numerator, we need to solve the given conditions.
Let's denote the numerator by "x". We know that the denominator is 5 less than 3 times the numerator, which can be written as 3x - 5.
We are also given that the numerator is less than 8, so we have the inequality x < 8.
To find the equivalent fraction, we need to determine values of x that satisfy the given conditions.
Let's try different possible values of x:
For x = 1, the denominator would be 3(1) - 5 = 3 - 5 = -2, which is not a valid denominator.
For x = 2, the denominator would be 3(2) - 5 = 6 - 5 = 1, which is a valid denominator.
For x = 3, the denominator would be 3(3) - 5 = 9 - 5 = 4, which is a valid denominator.
So, the possible fractions are 1/2, 2/1, and 3/4.
The fraction 2/4 is equivalent to 1/2, but it does not satisfy the condition that the denominator is 5 less than 3 times the numerator. Therefore, the answer is not 2/4.
To find a fraction equivalent to 1/2, with the denominator being 5 less than 3 times its numerator, and the numerator being less than 8, we need to follow a logical process.
Let's start by assuming the numerator of the fraction is "x." According to the given condition, the denominator will be 3x - 5.
Now, we can set up an equation to find the specific value for "x":
3x - 5 = 2
By adding 5 to both sides of the equation, we get:
3x = 7
Dividing both sides of the equation by 3, we find:
x = 7/3
However, the problem specifies that the numerator should be less than 8. Since 7/3 is greater than 8, we need to find an alternative value for the numerator.
Let's try substituting x = 2. Plugging in this value, we find that the denominator is:
3(2) - 5 = 1
Thus, the fraction equivalent to 1/2, with the denominator being 5 less than 3 times its numerator, and the numerator being less than 8, is indeed 2/1 or simply 2.
So, the answer is not 2/4 but rather 2/1.