The shaded part of the diagram shows what Genie has left from a meter of string. She will use \(\frac{3}{5}\) meter of string to make bracelets. She wants to determine how much of the string she will have remaining after making the bracelets. For 7a–7c, select True or False for each statement.

a. To determine how much string will be left after making the bracelets, Rebecca must find \(\frac{9}{10}-\frac{3}{5}\) .

b. The fractions \(\frac{3}{5}\) and \(\frac{6}{10}\) are equivalent.

c. Rebecca will have \(\frac{1}{5}\) meter of string left.

For 8a–8c, tell whether the Commutative Property or the Associative Property can be used to show each equation is true without calculating. Choose the correct property of addition.

a. \(\begin{align}
\frac{1}{6}+\left(\frac{7}{8}+\frac{5}{6}\right)&=\frac{1}{6}+\left(\frac{5}{6}+\frac{7}{8}\right)\\
\end{align}\)

b. \(\begin{align}
\left(\frac{7}{10}+\frac{1}{3}\right)+\frac{1}{10}&=\left(\frac{1}{3}+\frac{7}{10}\right)+\frac{1}{10}\\
\end{align}\)

c. \(\begin{align}
\left(6\frac{2}{5}+\frac{4}{9}\right)+3\frac{2}{9}&=6\frac{2}{5}+\left(\frac{4}{9}+3\frac{2}{9}\right)\\
\end{align}\)

Joshua uses a rule to write the following sequence of numbers.

\(\begin{align}
\frac{1}{6},\frac{1}{2},\frac{5}{6},\text{ __________, }1\frac{1}{2}
\end{align}\)

What rule did Joshua use?

What is the missing number in the sequence?