\displaystyle\frac{{2}}{{12}}\times\frac{{2}}{{5}}=\frac{{4}}{{60}} Explanation: When multiplying fractions, multiply the numerators together, and multiply the denominators together. \displaystyle\frac{{{2}\times{2}}}{{{12}\times{5}}}=\frac{{4}}{{60}}

\displaystyle\frac{{14}}{{24}} or \displaystyle\frac{{7}}{{12}} Explanation: To solve this following the rules for multiplying fractions you multiply the numerators and the denominators: \displaystyle\frac{{2}}{{3}}\times\frac{{7}}{{8}}\to\frac{{{2}\times{7}}}{{{3}\times{8}}}\to\frac{{14}}{{24}} ...

\displaystyle\frac{{1}}{{8}} Explanation: First, we can cancel common terms in the numerator and denominator: \displaystyle\frac{{1}}{{{2}}}\times\frac{{{2}}}{{8}}=\frac{{1}}{\cancel{{{\left({2}\right)}}}}\times\frac{\cancel{{{\left({2}\right)}}}}{{8}}=\frac{{1}}{{1}}\times\frac{{1}}{{8}} ...

\displaystyle\frac{{2}}{{5}} Explanation: \displaystyle\frac{{5}}{{12}}\times\frac{{24}}{{25}} \displaystyle\frac{{\cancel{{{5}}}{1}}}{{12}}\times\frac{{24}}{{\cancel{{{5}}}{5}}} \displaystyle\frac{{24}}{{{12}\cdot{5}}} ...

\displaystyle-{1} Explanation: When you are multiplying fractions, if you cancel like factors first, there will be no simplification to be done at the end. This means that the numbers stay ...

Suppose p=(\frac12, 1) is an interior point of \{\frac12\} \times (\frac12, 1]. As p is not an endpoint of [0,1]\times[0,1] in the lexicographic order, a local base for its neighbourhoods are ...