Adding and Subtracting Fractions/Mixed Numbers
Multiplying and Dividing Fractions/Mixed Numbers
Solving Equations by Adding and Subtracting
Solving Equations by Multiplying and Dividing
Challengers
with Fractions
100
Jason and Kevin plan to ride their bicycles at least eight miles. They ride for \[5\frac{3}{8}\] miles and stop for a break. Then, they ride for another \[2\frac{5}{7}\] miles. Do they meet their goal? Explain your answer.
What is: Yes, Jason and Keven cycle for at least eight miles. In fact, they cycles for \[7\frac{{61}}{{56}}\] miles, which is equivalent to \[8\frac{5}{{56}}\] miles. Hence, Jason and Kevin reached their goal; in fact, they went over by \[\frac{5}{{56}}\] of a mile.
100
Simplify:

\[\frac{5}{6} \bullet \left( { - 1\frac{3}{{10}}} \right)\]
What is: \[ - 1\frac{1}{{12}}\]
100
Solve for the given variable:

\[5\frac{1}{3} + a = - 12\]
What is: \[a = - 16\frac{4}{3} = - 17\frac{1}{3}\]
100
Solve for the given variable: \[6 = - 1\frac{2}{7}m\]
What is: \[m = - 4\frac{2}{3}\]
100
Simplify:

\[ - \frac{3}{5} - 1\frac{2}{{15}} - \frac{7}{{10}}\]
What is: \[ - \frac{{73}}{{30}} = - 2\frac{{13}}{{30}}\]
200
Simplify:

\[2\frac{2}{3} - 6\frac{3}{5}\]
What is: \[ - 3\frac{{14}}{{15}}\]
200
Simplify:

\[\left( { - 7\frac{2}{3}} \right) \div \left( { - 1\frac{5}{6}} \right)\]
What is: \[4\frac{2}{{11}}\]
200
Solve for the given variable: \[x + 2\frac{1}{9} = 1\frac{1}{3}\]
What is: \[x = - \frac{7}{9}\]
200
Solve for the given variable:

\[4\frac{1}{6} = - 1\frac{2}{3}k\]
What is: \[k = - 2\frac{1}{2}\]
200
Simplify:

\[d + \frac{7}{{5d}}\]
What is: \[\frac{{5{d^2} + 7}}{{5d}}\]
300
Simplify:

\[ - 4\frac{7}{{10}} - 9\frac{7}{{15}}\]
What is: \[ - 13\frac{{35}}{{30}} = - 14\frac{5}{{30}} = - 14\frac{1}{6}\]
300
A teacher wants to tape sheets of paper together to make a math banner. She wants the banner to be \[127\frac{1}{2}\] inches long, and each sheet of paper is \[8\frac{1}{2}\] inches wide. How many sheets of paper will she need?
What is 15 sheets.
300
Solve for the given variable:

\[ - 2\frac{1}{3} = 4\frac{3}{8} - f\]
What is: \[ - f = - 6\frac{{17}}{{24}}\] \[f = 6\frac{{17}}{{24}}\]
300
Solve for the given variable:

\[2\frac{3}{4} = - 6\frac{3}{5}y\]
What is: \[y = - \frac{5}{{12}}\]
300
Solve for the given variable:

\[ - \frac{{2x}}{3} + 1\frac{1}{2}x = - 3\frac{1}{3}\]
What is: \[x = - 4\]
400
Simplify:

\[ - 2\frac{5}{{13}} - \left( { - 1\frac{1}{2}} \right)\]
What is: \[ - \frac{{23}}{{26}}\]
400
Simplify:

\[ - \frac{{15{a^2}{b^2}}}{{21a{c^3}}} \bullet \frac{{14{a^4}{c^2}}}{{6a{b^3}c}}\]
What is: \[ - \frac{{5{a^4}}}{{3b{c^2}}} = - \frac{5}{3}{a^4}{b^{ - 1}}{c^{ - 2}}\]
400
Solve for the given variable:

\[3\frac{1}{{12}} + h - 5\frac{2}{3} = - 4\frac{1}{5}\]
What is: \[h = - 1\frac{{37}}{{60}}\]
400
Solve for the given variable: \[\frac{7}{9}x - 1\frac{3}{4}x = 2\frac{1}{3}\]
What is: \[x = - \frac{{12}}{5} = - 2\frac{2}{5}\]
400
Simplify:

\[{\left( { - \frac{{xy}}{{2x{y^4}}}} \right)^5}\]
What is: \[ - \frac{1}{{32{y^{15}}}} = - \frac{1}{{32}}{y^{ - 15}}\]
500
Simplify:

\[ - 1\frac{5}{{12}} - \left( { - 4\frac{5}{{14}}} \right)\]
What is: \[2\frac{{79}}{{84}}\]
500
Simplify:

\[\frac{{4{t^3}{p^3}}}{{5{p^2}{t^2}}} \div \frac{{6t{p^2}}}{{15{p^3}}}\]
What is: \[2{p^2}\]
500
Simplify:

\[ - 3\frac{5}{{12}} + x - 2\frac{3}{8} = - 4\frac{5}{6}\]
What is: \[x = \frac{{23}}{{24}}\]
500
Solve for the given variable: \[\frac{{ - 5}}{{ - 8}}x + \left( { - \frac{3}{5}x} \right) = - \frac{7}{{10}}\]
What is: \[x = - 28\]
500
A sailfish can swim about \[11\frac{1}{3}miles\] in 10 minutes. How many miles can a sailfish swim per minute? Setup and solve an equation to solve for the unknown quantity.
What is: Let x = number of miles a sailfish can swim per min.

\[\begin{array}{l} 10x = 11\frac{1}{3}\\ x = 1\frac{2}{{15}}{\rm{miles per min}} \end{array}\]
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