Certainly! Let's solve the problem step-by-step.
The problem given is to find the value of the numerator [tex]\( x \)[/tex] in the fraction [tex]\( \frac{x}{48} \)[/tex] that makes it equivalent to the fraction [tex]\( \frac{7}{8} \)[/tex].
Given fractions:
[tex]\[ \frac{7}{8} = \frac{x}{48} \][/tex]
Step 1: Understand that we are looking for [tex]\( x \)[/tex] such that the two fractions are equal.
Step 2: To solve this, we can use the method of cross-multiplication, which is a reliable way to find the unknown term in equivalent fractions.
Step 3: By cross-multiplying, we set up the equation as follows:
[tex]\[ 7 \times 48 = 8 \times x \][/tex]
Step 4: Calculate the left side of the equation:
[tex]\[ 7 \times 48 = 336 \][/tex]
Step 5: Now the equation becomes:
[tex]\[ 336 = 8 \times x \][/tex]
Step 6: Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 8:
[tex]\[ x = \frac{336}{8} \][/tex]
Step 7: Calculate the division:
[tex]\[ x = 42 \][/tex]
So, the value of [tex]\( x \)[/tex] is 42.
Therefore, the fraction [tex]\( \frac{42}{48} \)[/tex] is equivalent to [tex]\( \frac{7}{8} \)[/tex]. Hence, the best answer for the question is:
B. 42.
