Question

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

test practice

1. equation editor solve $x + 5.15 = 23.8$

Explanation:

Step1: Subtract \(2\frac{1}{4}\) from both sides

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

Step2: Convert mixed numbers to improper fractions

First, convert \(9\frac{1}{2}\) to an improper fraction: \(9\frac{1}{2}=\frac{9\times2 + 1}{2}=\frac{19}{2}\). Then convert \(2\frac{1}{4}\) to an improper fraction: \(2\frac{1}{4}=\frac{2\times4+1}{4}=\frac{9}{4}\). Now our equation is \(b = \frac{19}{2}-\frac{9}{4}\).

Step3: Find a common denominator and subtract

The common denominator of 2 and 4 is 4. So we rewrite \(\frac{19}{2}\) as \(\frac{38}{4}\) (since \(\frac{19}{2}=\frac{19\times2}{2\times2}=\frac{38}{4}\)). Now we subtract: \(\frac{38}{4}-\frac{9}{4}=\frac{38 - 9}{4}=\frac{29}{4}\).

Step4: Convert back to a mixed number

Convert \(\frac{29}{4}\) to a mixed number. Divide 29 by 4: \(4\times7 = 28\), so \(\frac{29}{4}=7\frac{1}{4}\).

Answer:

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