Eric has a riddle: I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator"
What is eric's fraction? Explain how you know.
To find Eric's fraction, we need to find a fraction that is equivalent to 2/5 and has a numerator that is 18 less than the denominator.
Let's assume the denominator of the fraction is D.
According to the given information, the numerator would be D - 18.
Now, we can set up an equation to find the equivalent fraction:
(D - 18)/D = 2/5
To solve this equation, we can cross-multiply:
5(D - 18) = 2D
By expanding and simplifying the equation, we get:
5D - 90 = 2D
Bringing the "D" terms to one side and the constant terms to the other side:
5D - 2D = 90
3D = 90
Dividing both sides of the equation by 3:
D = 90/3
D = 30
Now substituting the value of D back into the numerator formula:
Numerator = D - 18 = 30 - 18 = 12
Therefore, Eric's fraction is 12/30, which simplifies to 2/5.
Make the sentences medium
To find Eric's fraction, we need to determine a fraction that is equivalent to 2/5 and has a numerator that is 18 less than the denominator.
Let's assume the denominator of the fraction is D. As per the given information, the numerator would be D - 18.
Next, we can set up an equation to find the equivalent fraction: (D - 18)/D = 2/5.
To solve this equation, we can cross-multiply: 5(D - 18) = 2D.
By expanding and simplifying the equation, we obtain: 5D - 90 = 2D.
Moving the "D" terms to one side and the constant terms to the other side, we have: 5D - 2D = 90.
Simplifying further, we find: 3D = 90.
Dividing both sides of the equation by 3, we get: D = 90/3.
Substituting the value of D back into the numerator formula, we find: Numerator = D - 18 = 30 - 18 = 12.
Hence, Eric's fraction is 12/30, which simplifies to 2/5.