Question

1. $5\frac{1}{2} = b - 12\frac{1}{4}$

Explanation:

Step1: Isolate the variable \( b \)

To solve for \( b \), we need to isolate it. We can do this by adding \( 12\frac{1}{4} \) to both sides of the equation \( 5\frac{1}{2}=b - 12\frac{1}{4} \).
So the equation becomes \( b=5\frac{1}{2}+ 12\frac{1}{4} \)

Step2: Convert mixed numbers to improper fractions

First, convert \( 5\frac{1}{2} \) to an improper fraction. \( 5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2} \)
Then, convert \( 12\frac{1}{4} \) to an improper fraction. \( 12\frac{1}{4}=\frac{12\times4+ 1}{4}=\frac{49}{4} \)

Step3: Find a common denominator and add the fractions

The common denominator of 2 and 4 is 4. So we rewrite \( \frac{11}{2} \) with a denominator of 4: \( \frac{11}{2}=\frac{11\times2}{2\times2}=\frac{22}{4} \)
Now we add \( \frac{22}{4}+\frac{49}{4}=\frac{22 + 49}{4}=\frac{71}{4} \)

Step4: Convert the improper fraction back to a mixed number

\( \frac{71}{4}=17\frac{3}{4} \) (since \( 71\div4 = 17\) with a remainder of 3)

Answer:

\( b = 17\frac{3}{4} \)