Question

1. $9\frac{1}{2} = b + 2\frac{1}{4}$

Explanation:

Step1: Isolate the variable \( b \)

To solve for \( b \), we subtract \( 2\frac{1}{4} \) from both sides of the equation \( 9\frac{1}{2}=b + 2\frac{1}{4} \). So, \( b=9\frac{1}{2}-2\frac{1}{4} \).

Step2: Convert mixed numbers to improper fractions

Convert \( 9\frac{1}{2} \) to an improper fraction: \( 9\frac{1}{2}=\frac{9\times2 + 1}{2}=\frac{19}{2} \). Convert \( 2\frac{1}{4} \) to an improper fraction: \( 2\frac{1}{4}=\frac{2\times4+1}{4}=\frac{9}{4} \). Now the equation becomes \( b = \frac{19}{2}-\frac{9}{4} \).

Step3: Find a common denominator and subtract

The common denominator of 2 and 4 is 4. Rewrite \( \frac{19}{2} \) with denominator 4: \( \frac{19}{2}=\frac{19\times2}{2\times2}=\frac{38}{4} \). Now subtract: \( b=\frac{38}{4}-\frac{9}{4}=\frac{38 - 9}{4}=\frac{29}{4} \).

Step4: Convert back to a mixed number (optional)

\( \frac{29}{4}=7\frac{1}{4} \) since \( 29\div4 = 7 \) with a remainder of 1.

Answer:

\( b = 7\frac{1}{4} \) (or \( b=\frac{29}{4} \))