Verify if (3·8+5)/(4+3·8) = 5/4: Fraction Simplification Check

In this question we are asked whether we can "reduce" in the expression on the left side (from which the arrow comes out) the multiplication factor $3\cdot 8$ from the numerator and denominator and as a result get the expression on the right side (to which the arrow points),

To do this, first, let's numerically simplify the expression on the left side and calculate the value of the fraction and see if we get the same fraction (or its equivalent) that is on the right side:

$\frac{3\cdot8+5}{4+3\cdot8} =\\ \frac{24+5}{4+24}=\\ \frac{29}{28}$

meaning we got that:

$\frac{3\cdot8+5}{4+3\cdot8}\stackrel{?}{\rightarrow }\frac{5}{4} \\ \downarrow\\ \frac{29}{28}\stackrel{?}{\rightarrow }\frac{5}{4}$

Now we need to determine if the fractions are equivalent, for this we note that the denominator of the fraction on the right side, the number 28, is a whole multiple of the denominator of the fraction on the left side, 4, this whole multiple is the number 7 since:

$4\cdot7=28$

therefore we will expand the fraction on the right side, this we will do by multiplying both numerator and denominator by 7, an operation that will not change the value of the fraction, since it is equivalent to multiplying the fraction by 1, an operation that never changes the value of the number, as will be demonstrated in the following calculation:

$\frac{5}{4} =\\ \frac{5}{4} \cdot1=\\ \frac{5}{4} \cdot\frac{7}{7}=\\ \frac{5\cdot7}{4\cdot7}=\\ \frac{35}{28}$

We got therefore that:

$\frac{29}{28}\stackrel{?}{\rightarrow }\frac{5}{4} \\ \downarrow\\ \frac{29}{28}\stackrel{?}{\rightarrow }\frac{35}{28}$

Now that the denominators of the fractions on the right and left sides are identical, we can definitely determine that the fractions are different from each other since:

$29\neq35$

and therefore the expression on the left and the expression on the right are definitely not identical,

Meaning:

$\frac{3\cdot8+5}{4+3\cdot8}=\frac{29}{30}\stackrel{!}{\not{\rightarrow} }\frac{5}{4}$

In other words - the reduction operation of the multiplication factor $3\cdot8$ is incorrect.

Therefore the correct answer is answer B.