Question

which expression has a value less than 1?\
$1\frac{6}{8}-\frac{3}{8}$ $1\frac{3}{8}-\frac{3}{8}$ $1\frac{3}{8}-\frac{5}{8}$ $1\frac{6}{8}-\frac{5}{8}$

Explanation:

Step1: Simplify \(1\frac{6}{8}-\frac{3}{8}\)

Convert the mixed number to improper fraction: \(1\frac{6}{8}=\frac{14}{8}\). Then \(\frac{14}{8}-\frac{3}{8}=\frac{11}{8}=1\frac{3}{8}>1\).

Step2: Simplify \(1\frac{3}{8}-\frac{3}{8}\)

\(1\frac{3}{8}=\frac{11}{8}\), so \(\frac{11}{8}-\frac{3}{8}=\frac{8}{8}=1\), not less than 1.

Step3: Simplify \(1\frac{3}{8}-\frac{5}{8}\)

\(1\frac{3}{8}=\frac{11}{8}\), then \(\frac{11}{8}-\frac{5}{8}=\frac{6}{8}=\frac{3}{4}<1\).

Step4: Simplify \(1\frac{6}{8}-\frac{5}{8}\)

\(1\frac{6}{8}=\frac{14}{8}\), so \(\frac{14}{8}-\frac{5}{8}=\frac{9}{8}=1\frac{1}{8}>1\).

Answer:

\(1\frac{3}{8}-\frac{5}{8}\)