Use a model to explain why \( 1 / 2+3 / 8 \) do not equal \( 4 / 10 \).

We start by writing the two expressions properly: 1. Compute \[ \frac{1}{2} + \frac{3}{8} \] To add fractions, we need a common denominator. The common denominator between 2 and 8 is 8. Convert \(\frac{1}{2}\) into a fraction with denominator 8: \[ \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \] Now add the fractions: \[ \frac{4}{8} + \frac{3}{8} = \frac{4+3}{8} = \frac{7}{8} \] 2. Next, consider the expression \[ \frac{4}{10} \] This fraction can be simplified by dividing the numerator and the denominator by their greatest common divisor, 2: \[ \frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5} \] 3. To compare \(\frac{7}{8}\) and \(\frac{2}{5}\), we can find a common denominator or convert each to a decimal: - Find common denominator: The least common denominator (LCD) of 8 and 5 is 40. \[ \frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40} \] \[ \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} \] - Since \[ \frac{35}{40} \neq \frac{16}{40}, \] the two fractions are not equal. Alternatively, compare decimals: \[ \frac{7}{8} = 0.875 \quad \text{and} \quad \frac{2}{5} = 0.4. \] Since \(0.875 \neq 0.4\), we conclude that: \[ \frac{1}{2} + \frac{3}{8} = \frac{7}{8} \neq \frac{4}{10} \ (\text{or } \frac{2}{5}) \]