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