1. Find the value of each sum. Explain or show your reasoning.

   1. \(\frac{5}{6} +\frac{2}{6}\)
   2. \(\frac{5}{6} + \frac{2}{3}\)
2. How are the calculations alike? How are they different?

1. Explain why the expressions \(\frac{2}{3} - \frac{7}{12}\) and \(\frac{8}{12} - \frac{7}{12}\) are equivalent.
2. How is the expression \(\frac{8}{12} - \frac{7}{12}\) helpful to find the value of \(\frac{2}{3} - \frac{7}{12}\)?

Find the value of each expression. Explain or show your reasoning.

1. \(\frac{1}{4} + \frac{1}{5}\)

2. \(\frac{10}{9} - \frac{3}{4}\)

1. Find the value of \(2\frac{3}{4} - \frac{1}{3}\). Explain or show your reasoning.

2. Find the value of \(3\frac{2}{7} - \frac{4}{5}\). Explain or show your reasoning.

Jada picks \(4 \frac{2}{3}\) cups of blackberries. Andre picks \(3\frac{5}{8}\) cups of blackberries. 

1. How many cups of blackberries do Jada and Andre pick together? Explain or show your reasoning.

2. How many more cups of blackberries does Jada pick than Andre? Explain or show your reasoning.

Find the value of each expression. Explain or show your reasoning.

1. \(\frac{7}{8} + \frac{4}{13}\)
2. \(\frac{7}{8} - \frac{3}{20}\)

Here are the lengths of some pieces of ribbon, measured in inches

1. Complete the line plot, with the ribbon lengths.

   

2. What is the sum of the ribbon lengths that measure greater than 4 inches each? Explain or show your reasoning.

Han is making a line plot of the seedlings his class grew.

Use this information to complete the line plot. Explain or show your reasoning.

• There are 15 seedlings altogether.
• The tallest seedling is \(2\frac{1}{8}\) inches taller than the shortest seedling.
• There are 3 seedlings of the shortest height.

Dot plot titled Growing Plants from 0 to 3 by 1’s. Hash marks by eighths. Horizontal axis, seedling heights, in inches. Beginning at 4 eighths, the number of X’s above each eighth increment is 2, 1, 0, 0, 2, 1, 0, 3, 1, 0, 2, 0, 0, 1.

1. Put the numbers 2, 3, 4, and 5 in the four boxes so that the expression is as close to 1 as possible.

   \(\frac{\boxed{\phantom{\frac{0}{000}}}}{\boxed{\phantom{\frac{0}{000}}}} + \frac{\boxed{\phantom{\frac{0}{000}}}}{\boxed{\phantom{\frac{0}{000}}}}\)

2. Put the numbers 2, 3, 4, and 5 in the four boxes so that the expression is as close to 1 as possible.

   \(\frac{\boxed{\phantom{\frac{0}{000}}}}{\boxed{\phantom{\frac{0}{000}}}} - \frac{\boxed{\phantom{\frac{0}{000}}}}{\boxed{\phantom{\frac{0}{000}}}}\)

Make a line plot of seedling heights so that each of these statements is true.

• There are 12 measurements.
• The tallest measurement is \(2 \frac{3}{8}\) inches taller than the shortest measurement.
• The sum of the measurements is \(18\frac{3}{8}\) inches.

Explain how you made the line plot.