1. Write \(\frac{4}{3}\) in as many ways as you can as a sum of fractions.
2. Write \(\frac{9}{8}\) in at least 3 different ways as a sum of fractions.

1. Draw jumps on the number lines to show two ways to use fourths to make a sum of \(\frac{7}{4}\).

   

   

2. Represent each combination of jumps as an equation.

1. Explain how the diagram represents \(\frac{13}{5} - \frac{4}{5}\).

   

   Number line. 16 evenly spaced tick marks. First tick mark, 0. Sixth, 1. Eleventh, 2. Sixteenth, 3. Arrow begins at the point on the fourteenth tick mark, points to the left, and ends at the point on the tenth tick mark.  

   Use the diagram to find the value of \(\frac{13}{5}- \frac{4}{5}\).

2. Use a number line to represent and find the difference \(\frac{9}{4} - \frac{3}{4}\).

   

Show two different ways to find the difference: \(2 - \frac{3}{4}\)

For each of the expressions, explain whether you think it would be helpful to decompose one or more numbers to find the value of the expression.

1. \(\frac{4}{3} + \frac{5}{3}\)
2. \(5\frac{1}{5} - 2\frac{2}{5}\)
3. \(9\frac{5}{6} - 6\frac{1}{6}\)

This shows the shoe lengths for a dad and his two daughters.

For each question, show your reasoning.

1. How much longer is the older daughter’s shoes than her sister’s shoes?

2. Which is longer, the dad’s shoes or the combined lengths of his daughters’ shoes?

A chocolate chip cookie recipe calls for \(2\frac{3}{4}\) cups of flour. You have only a \(\frac{1}{4}\)-cup measure and a \(\frac{3}{4}\)-cup measure that you can use.

1. What are different combinations of the cup measures that you can use to get a total of \(2\frac{3}{4}\) cups of flour?
2. Write each of the combinations as an addition equation.

The table shows some lengths of different shoe sizes in inches.