Question

there are two routes lucas can take to walk to school. route a is $2\frac{1}{8}$ miles and is $\frac{3}{8}$ mile longer than route b. the equation $b + \frac{3}{8} = 2\frac{1}{8}$ can be used to represent this situation, where $b$ is the length of route b. how many miles will lucas walk if he takes route b?\
\bigcirc $1\frac{1}{2}$ miles\
\bigcirc $1\frac{3}{4}$ miles\
\bigcirc $2\frac{1}{4}$ miles\
\bigcirc $2\frac{1}{2}$ miles

Explanation:

Step1: Subtract \(\frac{3}{8}\) from both sides

To solve for \(b\) in the equation \(b+\frac{3}{8}=2\frac{1}{8}\), we subtract \(\frac{3}{8}\) from both sides. So we have \(b = 2\frac{1}{8}-\frac{3}{8}\).

Step2: Convert mixed number to improper fraction

First, convert \(2\frac{1}{8}\) to an improper fraction. \(2\frac{1}{8}=\frac{2\times8 + 1}{8}=\frac{17}{8}\).

Step3: Perform the subtraction

Now subtract \(\frac{3}{8}\) from \(\frac{17}{8}\): \(\frac{17}{8}-\frac{3}{8}=\frac{17 - 3}{8}=\frac{14}{8}\).

Step4: Simplify the fraction

Simplify \(\frac{14}{8}\) by dividing numerator and denominator by 2: \(\frac{14\div2}{8\div2}=\frac{7}{4}\), which is \(1\frac{3}{4}\) when converted back to a mixed number.

Answer:

\(1\frac{3}{4}\) miles (corresponding to the option " \(1\frac{3}{4}\) miles")