Question

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

Explanation:

Step1: Add \(12\frac{1}{4}\) to both sides

To solve for \(b\), we add \(12\frac{1}{4}\) to both sides of the equation \(5\frac{1}{2}=b - 12\frac{1}{4}\). This gives us \(b=5\frac{1}{2}+12\frac{1}{4}\).

Step2: Convert mixed numbers to improper fractions

Convert \(5\frac{1}{2}\) to an improper fraction: \(5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2}\). Convert \(12\frac{1}{4}\) to an improper fraction: \(12\frac{1}{4}=\frac{12\times4+1}{4}=\frac{49}{4}\). Now the equation is \(b = \frac{11}{2}+\frac{49}{4}\).

Step3: Find a common denominator and add

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

Step4: Convert back to a mixed number

Convert \(\frac{71}{4}\) to a mixed number: \(71\div4 = 17\) with a remainder of 3, so \(\frac{71}{4}=17\frac{3}{4}\).

Answer:

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