Answer:
C. 7
This is the correct answer. How do we got this? Let's take a look at the solution below.
The starting fraction, the main fraction being added, in the given problem is [tex]\bold{\dfrac{5}{7}}[/tex]. However when a certain number, let's call it as [tex]\bold{x}[/tex], is added, the resulting fraction is [tex]\bold{\dfrac{6}{7}}[/tex].
[Sol]
[tex]\text{Let}\ x\ \text{be the "number" added to both numerator and denominator,}\\\text{Let}\ \dfrac{5}{7}\ \text{be the starting fraction, and}\\\text{Let}\ \dfrac{6}{7}\ \text{be the resulting fraction.}[/tex]
[tex]\text{Equation:}\\\\\dfrac{5+x}{7+x}=\dfrac{6}{7}\\\\\text{Do cross multiplication.}\\\\6(7+x)=7(5+x)\\42+6x=35+7x\\42-35=7x-6x\ \ \ \ \ \ \ \ \leftarrow\ \text{Interchange both sides for clearer solving.}\\7x-6x=42-35\\\boxed{\bold{x=7}}[/tex]
The number added to both parts of the starting fraction is 7.
To check if this number is true for the given problem, substitute 7 to [tex]x[/tex] in the equation.
[tex]\dfrac{5+\bold{7}}{7+\bold{7}}=\dfrac{6}{7}\\\dfrac{12}{14}=\dfrac{6}{7}\\\bold{\dfrac{6}{7}=\dfrac{6}{7}}\ \ \ \ \ \ \ \text{It's correct!}[/tex]
One of the previous answerer in this question quoted that "the resulting fraction is closer to 1 than that of the starting fraction." That is the case if we put them in a number line. See the number line below (Isipin nyo na lang na solid line sya. Hehe)
[tex]0\bullet------------\bullet \dfrac{5}{7}---\bullet \dfrac{6}{7}---\bullet1[/tex]
Any fraction when added the same natural number (i.e. positive integers) will have their resulting fraction closer 1 than the former. This is the RELATIONSHIP between the starting fraction and resulting fraction in this problem. So when you are asked what is the relationship in this problem, write down the bolded and underlined sentence in this paragraph.
However, if we add negative integers, the opposite willbe observed. I tried to solve some and the result is this. The relationship will be any fraction added with a certain negative integer in its numerator and denominator will result to the resulting fraction closer to 0 (zero) than that of starting fraction.
You can check out the answer in the similar problem here: https://brainly.in/question/7263500
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