Let the numerator be \( x \). According to Roberto's statement, the denominator will be \( x + 2 \).
So, the fraction can be expressed as:
\[ \frac{x}{x + 2} \]
We know this fraction is equivalent to \( \frac{39}{1} \).
Setting the two fractions equal gives us:
\[ \frac{x}{x + 2} = \frac{39}{1} \]
Cross-multiplying yields:
\[ x \cdot 1 = 39 \cdot (x + 2) \]
This simplifies to:
\[ x = 39x + 78 \]
Rearranging the equation by getting all terms involving \( x \) on one side gives us:
\[ x - 39x = 78 \]
Which simplifies to:
\[ -38x = 78 \]
Dividing both sides by -38:
\[ x = -\frac{78}{38} = -\frac{39}{19} \]
Now we can find the denominator:
\[ x + 2 = -\frac{39}{19} + 2 = -\frac{39}{19} + \frac{38}{19} = -\frac{1}{19} \]
So the fraction Roberto is thinking of is:
\[ \frac{-\frac{39}{19}}{-\frac{1}{19}} = \frac{39}{1} \]
Thus, the numerator and denominator of the fraction Roberto is thinking of are:
Numerator: \( 39 \)
Denominator: \( 1 \)
So, placing this into the provided blanks:
39
1
1 answer