Questions: Use Appropriate Tools Find three different ways to decompose 1 5/6. Use number lines to justify your answer.

Solution Steps

Convert the mixed number \(1 \frac{5}{6}\) to an improper fraction. This gives us: \[ 1 \frac{5}{6} = \frac{6}{6} + \frac{5}{6} = \frac{11}{6} \]

Decompose \(\frac{11}{6}\) into two fractions. One possible decomposition is: \[ \frac{11}{6} = \frac{1}{2} + \frac{4}{3} \]

Decompose \(\frac{11}{6}\) into three fractions. One possible decomposition is: \[ \frac{11}{6} = \frac{1}{3} + \frac{1}{2} + \frac{1}{1} \]

Another way to express \(\frac{11}{6}\) is by separating the whole number and the fractional part: \[ \frac{11}{6} = 1 + \frac{5}{6} \]

Final Answer