`3/4xx8/9xx15/16xx...xx9999/10000`
`=(1xx3)/(2xx2)xx(2xx4)/(3xx3)xx(3xx5)/(4xx4)xx...xx(99xx101)/(100xx100)`
`= {1 xx 3 xx 2 xx 4 xx 3 xx 5 xx ... xx 99 xx 101}/{2 xx 2 xx 3 xx 3 xx 4 xx 4 xx ... xx 100 xx 100}`
\(=\dfrac{\left(1\text{ }\times2\text{ }\times\text{ }3\text{ }\times\text{ }4\text{ }\times\text{ }...\text{\text{ }\times}99\right)\text{ }\text{ }\times\left(3\text{ }\text{ }\times4\text{ }\text{ }\times5\text{ }\text{ }\times...\text{ }\text{ }\times101\right)}{\left(2\text{ }\text{ }\times3\text{ }\text{ }\times4\text{ }\text{ }\times...\text{ }\text{ }\times100\right)\text{ }\text{ }\times\left(2\text{ }\text{ }\times3\text{ }\text{ }\times4\text{ }\text{ }\times...\text{ }\text{ }\times100\right)}\)
\(=\dfrac{1\text{×}101}{100\text{×}2}\)
\(=\dfrac{101}{200}\)
