Question

1. river needs to swim a total of 8 miles this week. so far, river has swum $5\frac{3}{8}$ miles. use the equation $5\frac{3}{8} + m = 8$ to find the number of miles river still needs to swim.

Explanation:

Step1: Subtract \( 5\frac{3}{8} \) from both sides

To solve for \( m \) in the equation \( 5\frac{3}{8}+m = 8 \), we subtract \( 5\frac{3}{8} \) from both sides:
\( m=8 - 5\frac{3}{8} \)

Step2: Convert 8 to a fraction with denominator 8

We know that \( 8=\frac{64}{8} \) (since \( 8\times8 = 64 \)) and \( 5\frac{3}{8}=\frac{43}{8} \) (because \( 5\times8+3 = 43 \)). Now substitute these into the equation:
\( m=\frac{64}{8}-\frac{43}{8} \)

Step3: Subtract the numerators

Subtract the numerators while keeping the denominator the same:
\( m=\frac{64 - 43}{8}=\frac{21}{8} \)

Step4: Convert to a mixed number

Convert \( \frac{21}{8} \) to a mixed number. Divide 21 by 8: \( 21\div8 = 2 \) with a remainder of 5. So \( \frac{21}{8}=2\frac{5}{8} \)

Answer:

\( 2\frac{5}{8} \) miles