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 the fraction that is equivalent to 2/5 and has a numerator that is 18 less than the denominator, we first need to determine the value of the denominator.
Let's assume the denominator of Eric's fraction is "x".
According to the information given, the numerator is 18 less than the denominator, which means it is x - 18.
Now, we can set up an equation to find the value of x:
x - 18 = 2/5
To solve this equation, we can cross-multiply:
5(x - 18) = 2
Expand and simplify the equation:
5x - 90 = 2
Add 90 to both sides of the equation:
5x = 2 + 90
5x = 92
Divide both sides by 5:
x = 92/5
So, the denominator of Eric's fraction is 92/5. Now, to find the numerator, we subtract 18 from the denominator:
Numerator = (92/5) - 18
To perform this subtraction, we need to convert 18 into a fraction with the same denominator:
Numerator = (92/5) - (18/1)
To subtract these fractions, we need a common denominator:
Numerator = (92 - 18*5)/5
Simplify the numerator:
Numerator = (92 - 90)/5
Numerator = 2/5
Therefore, Eric's fraction is also 2/5.